Thermodynamics and Heat Power [8 ed.] 9781482238563, 148223856X

Table of contents :
Front Cover
Contents
Preface
Author
Symbols
Chapter 1: Fundamental Concepts
Chapter 2: Work, Energy, and Heat
Chapter 3: First Law of Thermodynamics
Chapter 4: The Second Law of Thermodynamics
Chapter 5: Properties of Liquids and Gases
Chapter 6: The Ideal Gas
Chapter 7: Mixtures of Ideal Gases
Chapter 8: Vapor Power Cycles
Chapter 9: Gas Power Cycles
Chapter 10: Refrigeration
Chapter 11: Heat Transfer
Appendix 1: Answers to Even-Numbered Problems
Appendix 2: Supplemental Tables
References
Back Cover

Citation preview

Eighth Edition

Thermodynamics and Heat Power

Irving Granet and Maurice Bluestein

Eighth Edition

Thermodynamics and

Heat Power

Eighth Edition

Thermodynamics and

Heat Power Irving Granet, PE Professor of Engineering City University of New York

Maurice Bluestein Professor Emeritus Indiana University-Purdue University Indianapolis

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

This work was previously published by Pearson Education, Inc.

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20141020 International Standard Book Number-13: 978-1-4822-3856-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

This book is dedicated to the memory of Irving Granet

Contents Preface............................................................................................................................................ xiii Author..............................................................................................................................................xv Symbols........................................................................................................................................ xvii 1. Fundamental Concepts...........................................................................................................1 1.1 Introduction.................................................................................................................... 1 1.2 Thermodynamic Systems.............................................................................................2 1.2.1 Application of System Concept.......................................................................2 1.2.2 Properties of a System......................................................................................3 1.3 Temperature....................................................................................................................4 1.4 Force and Mass............................................................................................................. 15 1.4.1 English System................................................................................................ 15 1.4.2 SI System.......................................................................................................... 17 1.5 Elementary Kinetic Theory of Gases........................................................................ 25 1.6 Pressure......................................................................................................................... 28 1.6.1 Dead-Weight Piston Gauge............................................................................ 35 1.6.2 Manometer....................................................................................................... 36 1.6.3 Micromanometer............................................................................................ 40 1.6.4 Barometers.......................................................................................................42 1.6.5 McLeod Gauge................................................................................................43 1.7 Review........................................................................................................................... 50 Key Terms................................................................................................................................ 50 Equations Developed in This Chapter................................................................................. 51 Questions................................................................................................................................. 52 Problems................................................................................................................................... 52 2. Work, Energy, and Heat........................................................................................................ 59 2.1 Introduction.................................................................................................................. 59 2.2 Work............................................................................................................................... 60 2.3 Energy............................................................................................................................ 62 2.4 Internal Energy.............................................................................................................63 2.5 Potential Energy...........................................................................................................64 2.6 Kinetic Energy.............................................................................................................. 68 2.7 Heat................................................................................................................................ 72 2.8 Flow Work..................................................................................................................... 73 2.9 Nonflow Work.............................................................................................................. 75 2.10 Review........................................................................................................................... 81 Key Terms................................................................................................................................ 81 Equations Developed in This Chapter................................................................................. 82 Questions................................................................................................................................. 82 Problems................................................................................................................................... 82

vii

viii

Contents

3. First Law of Thermodynamics............................................................................................ 89 3.1 Introduction.................................................................................................................. 89 3.2 First Law of Thermodynamics................................................................................... 90 3.3 Nonflow System...........................................................................................................90 3.4 Steady-Flow System..................................................................................................... 97 3.4.1 Conservation of Mass—Continuity Equation............................................ 97 3.4.2 Steady-Flow Energy Equation..................................................................... 102 3.4.3 Bernoulli Equation........................................................................................ 106 3.4.4 Specific Heat.................................................................................................. 107 3.5 Applications of First Law of Thermodynamics..................................................... 109 3.5.1 Turbine............................................................................................................ 110 3.5.2 Pipe Flow........................................................................................................ 116 3.5.3 Boiler............................................................................................................... 118 3.5.4 Nozzle............................................................................................................. 120 3.5.5 Throttling Process........................................................................................ 123 3.5.6 Heat Exchanger............................................................................................. 124 3.5.7 Filling a Tank................................................................................................. 127 3.6 Review......................................................................................................................... 128 Key Terms.............................................................................................................................. 129 Equations Developed in This Chapter............................................................................... 129 Questions............................................................................................................................... 130 Problems................................................................................................................................. 131 4. The Second Law of Thermodynamics............................................................................. 141 4.1 Introduction................................................................................................................ 142 4.2 Reversibility—Second Law of Thermodynamics.................................................. 143 4.3 The Carnot Cycle........................................................................................................ 145 4.4 Entropy........................................................................................................................ 157 4.5 Review......................................................................................................................... 173 Key Terms.............................................................................................................................. 173 Equations Developed in This Chapter............................................................................... 174 Questions............................................................................................................................... 174 Problems................................................................................................................................. 175 5. Properties of Liquids and Gases...................................................................................... 183 5.1 Introduction................................................................................................................ 183 5.2 Liquids and Vapors.................................................................................................... 184 5.3 Thermodynamic Properties of Steam..................................................................... 188 5.4 Computerized Properties.......................................................................................... 212 5.5 Thermodynamic Diagrams...................................................................................... 216 5.6 Processes..................................................................................................................... 224 5.6.1 Throttling....................................................................................................... 224 5.6.2 Constant-Volume Process (Isometric Process).......................................... 226 5.6.3 Adiabatic Processes...................................................................................... 229 5.6.4 Constant-Pressure Process (Isobaric Process)........................................... 233 5.6.5 Constant-Temperature Process (Isothermal Process).............................. 233 5.7 Review......................................................................................................................... 235 Key Terms.............................................................................................................................. 236 Equations Developed in This Chapter............................................................................... 236

Contents

ix

Questions............................................................................................................................... 237 Problems................................................................................................................................. 237 6. The Ideal Gas........................................................................................................................ 243 6.1 Introduction................................................................................................................ 243 6.2 Basic Considerations.................................................................................................. 244 6.3 Specific Heat............................................................................................................... 252 6.4 Entropy Changes of Ideal Gas.................................................................................. 263 6.5 Nonflow Gas Processes............................................................................................. 269 6.5.1 Constant-Volume Process (Isometric Process).......................................... 269 6.5.2 Constant-Pressure Process (Isobaric Process)........................................... 272 6.5.3 Constant-Temperature Process (Isothermal Process).............................. 274 6.5.4 Constant-Entropy Process (Isentropic Process)........................................ 278 6.5.5 Polytropic Process......................................................................................... 283 6.6 The Gas Tables............................................................................................................ 290 6.7 Steady-Flow Gas Processes....................................................................................... 295 6.7.1 Constant-Specific Volume Process............................................................. 296 6.7.2 Constant-Pressure Process.......................................................................... 297 6.7.3 Constant-Temperature Process................................................................... 297 6.7.4 Isentropic Process......................................................................................... 297 6.7.5 Polytropic Process......................................................................................... 299 6.8 Real Gases...................................................................................................................300 6.9 Frictional Effects......................................................................................................... 302 6.10 Review......................................................................................................................... 303 Key Terms..............................................................................................................................304 Equations Developed in This Chapter...............................................................................305 Questions............................................................................................................................... 307 Problems................................................................................................................................. 307 7. Mixtures of Ideal Gases..................................................................................................... 317 7.1 Introduction................................................................................................................ 317 7.2 Pressure of a Mixture................................................................................................ 318 7.3 Volume of a Mixture.................................................................................................. 323 7.4 Mixture Composition................................................................................................ 327 7.5 Thermodynamic Properties of a Gas Mixture....................................................... 330 7.6 Air–Water Vapor Mixtures....................................................................................... 336 7.7 Thermodynamic Properties of Air–Water Vapor Mixtures.................................343 7.8 Psychrometric Chart..................................................................................................343 7.9 Air Conditioning........................................................................................................ 358 7.10 Review......................................................................................................................... 363 Key Terms..............................................................................................................................364 Equations Developed in This Chapter............................................................................... 365 Questions............................................................................................................................... 366 Problems................................................................................................................................. 367 8. Vapor Power Cycles............................................................................................................. 373 8.1 Introduction................................................................................................................ 374 8.2 Carnot Cycle............................................................................................................... 374 8.3 The Rankine Cycle..................................................................................................... 375

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Contents

8.3.1 Process 1–2..................................................................................................... 377 8.3.2 Process 2–3..................................................................................................... 377 8.3.3 Process 2–4..................................................................................................... 377 8.3.4 Process 4–5..................................................................................................... 378 8.3.5 Process 5–1..................................................................................................... 379 8.4 Rating of Power-Plant Cycles...................................................................................384 8.5 The Reheat Cycle........................................................................................................ 386 8.6 The Regenerative Cycle............................................................................................. 389 8.7 The Steam Generator.................................................................................................400 8.8 The Steam Turbine..................................................................................................... 401 8.9 Cogeneration............................................................................................................... 403 8.10 Direct Energy Conversion........................................................................................ 405 8.10.1 Thermoelectrical Converter........................................................................ 406 8.10.2 Fuel Cell.......................................................................................................... 407 8.10.3 Thermionic Converter..................................................................................408 8.10.4 Magnetohydrodynamic Generator............................................................. 409 8.10.5 Solar Energy.................................................................................................. 410 8.10.6 Wind Power................................................................................................... 412 8.10.7 Waste-to-Energy Resource Recovery......................................................... 415 8.10.8 Geothermal Energy...................................................................................... 415 8.10.9 Nuclear Power............................................................................................... 416 8.10.10 Motion-Generated Energy........................................................................... 416 8.11 Review......................................................................................................................... 416 Key Terms.............................................................................................................................. 417 Equations Developed in This Chapter............................................................................... 418 Questions............................................................................................................................... 418 Problems................................................................................................................................. 419 9. Gas Power Cycles.................................................................................................................425 9.1 Introduction................................................................................................................ 426 9.2 Air-Standard Analysis of the Otto Cycle................................................................ 431 9.3 Diesel Engine (Compression Ignition Engine).......................................................443 9.4 Air-Standard Analysis of the Diesel Cycle.............................................................446 9.5 Automotive Engine Analysis................................................................................... 451 9.6 Brayton Cycle..............................................................................................................454 9.7 Air-Standard Brayton Cycle Analysis..................................................................... 456 9.8 The Dual Combustion Cycle (The Dual Cycle)......................................................464 9.9 Stirling Cycle and Ericsson Cycle (Regeneration)................................................. 465 9.10 Review......................................................................................................................... 466 Key Terms.............................................................................................................................. 467 Equations Developed in This Chapter............................................................................... 468 Questions............................................................................................................................... 469 Problems................................................................................................................................. 469 10. Refrigeration......................................................................................................................... 475 10.1 Introduction................................................................................................................ 476 10.2 Reversed Carnot Cycle.............................................................................................. 476 10.3 Defined Ratings.......................................................................................................... 481 10.4 Refrigeration Cycles................................................................................................... 483

Contents

xi

10.4.1 Vapor-Compression Cycle...........................................................................483 10.4.2 Gas-Cycle Refrigeration............................................................................... 495 10.4.3 Absorption Refrigeration Cycle.................................................................. 501 10.4.4 Vacuum Refrigeration Cycle........................................................................ 501 10.4.5 Thermoelectric Refrigerator........................................................................504 10.5 Compressors...............................................................................................................505 10.5.1 Volumetric Efficiency...................................................................................508 10.6 The Heat Pump........................................................................................................... 510 10.7 Review......................................................................................................................... 514 Key Terms.............................................................................................................................. 515 Equations Developed in This Chapter............................................................................... 515 Questions............................................................................................................................... 517 Problems................................................................................................................................. 517 11. Heat Transfer........................................................................................................................ 523 11.1 Introduction................................................................................................................ 524 11.2 Conduction.................................................................................................................. 524 11.3 Convection..................................................................................................................543 11.3.1 Natural Convection......................................................................................545 11.3.2 Forced Convection........................................................................................ 551 11.4 Radiation..................................................................................................................... 556 11.5 Heat Exchangers......................................................................................................... 566 11.6 Combined Modes of Heat Transfer......................................................................... 579 11.7 Cooling Electronic Equipment................................................................................. 580 11.8 Analysis of Fins.......................................................................................................... 581 11.9 Heat Pipes.................................................................................................................... 583 11.10 Review......................................................................................................................... 584 Key Terms.............................................................................................................................. 585 Equations Developed in This Chapter............................................................................... 586 Questions............................................................................................................................... 587 Problems................................................................................................................................. 588 Appendix 1: Answers to Even-Numbered Problems........................................................... 599 Appendix 2: Supplemental Tables........................................................................................... 617 References.................................................................................................................................... 811

Preface It has been over ten years since this textbook was last revised. There have been many advancements in technology during this time, especially in the area of direct energy conversion. There has also been a need to expand on concepts in the areas of ideal gas flow, engine analysis, air conditioning, and heat transfer. This new edition marks a joining with the Taylor & Francis Group, including CRC Press, to continue what has been a 40-year process of providing students with an understanding of basic concepts in thermodynamics. Specifically, the following material has been added in this eighth edition: • • • • • • • • • • • • • •

An emphasis on a system approach to problems More discussion of the types of heat and of entropy Added explanations for understanding pound mass and the mole Analysis of steady-flow gas processes, replacing the compressible flow section The concept of paddle work to illustrate how frictional effects can be analyzed A clearer discussion of the psychrometric chart and its usage in analyzing air conditioning systems Updates of the status of direct energy conversion systems A description of how the cooling tower is utilized in high-rise buildings Practical automotive engine analysis Expanded Brayton cycle analysis including intercooling, reheat, and regeneration and their effect on gas turbine efficiency A description of fins and how they improve heat transfer rates Added illustrative problems and new homework problems Availability of a publisher’s website for fluid properties and other reference materials Properties of the latest in commercial refrigerants

To make room for these additions, out-of-date photographs have been removed as they were felt to lend little to the understanding of the basic concepts. Many of these changes have resulted from the input of reviewers. A special thanks to Professor Herbert Crosby of the University of Maine and Professor M. David Burghardt of Hofstra University for supplying new, challenging problems. I thank Professor Mohammad Hossain of York Technical College for his suggestions. My thanks to the staff at Taylor & Francis for their help with this new edition: Jonathan Plant, Arlene Kopeloff, Cynthia Klivecka, Florence Kizza, and especially Amber Donley. I thank my family, somewhat expanded since the last edition, for their support and encouragement: Maris, Karen, Richard, Jennifer, Michaelbarry, Chris, Jaxanna, and Bennett. Maurice Bluestein Pompano Beach, Florida

xiii

Author Maurice Bluestein is a professor emeritus of Mechanical Engineering Technology at Indiana University–Purdue University Indianapolis. He taught for 19 years at the undergraduate and graduate levels, following a 25-year career in the biomedical engineering industry. His industrial experience included developing artificial limbs for the Veterans Affairs Department, designing waste management systems for the Apollo space mission, managing the clinical usage of the intra-aortic balloon pump as a cardiac assist device, and using ultrasound imaging to detect carotid artery blockages and to aid in the diagnosis of breast cancer. He received a PhD degree in biomedical engineering from Northwestern University and MS and BS degrees in mechanical engineering from New York University and the City College of New York, respectively. He has authored numerous scientific papers and is the codeveloper of the Wind Chill Temperature Chart used by the weather services of the United States and Canada.

xv

Symbols Units Symbol a a, A A, B, C, D, E c c CD Cn Cp Cp cv Cv Cv COP d, D e F FA Fe g gc Gr H h h h hf hfg hg hr i J k K k k K.E. l, L m  m mep

Definition Acceleration Area Constants Clearance Specific heat Discharge coefficient Specific heat of any process Specific heat at constant pressure Total specific heat at constant pressure Specific heat at constant volume Total specific heat at constant volume Velocity coefficient Coefficient of performance Diameter Base of natural logarithms Force Geometric factor Emissivity factor Acceleration of gravity Gravitational constant Grashof number Enthalpy Heat-transfer coefficient Height Specific enthalpy Specific enthalpy—saturated liquid Specific enthalpy of vaporization (hg – hf) Specific enthalpy—saturated vapor Heat-transfer coefficient—radiation Current Mechanical equivalent of heat cp/cv Proportionality constant Spring constant Thermal conductivity Kinetic energy Length Mass Mass flow rate Mean effective pressure

British Engineering

SI

ft./s ft.2

m/s2 m2

2

dimensionless Btu/lbm·°R dimensionless Btu/lbm·°R Btu/lbm·°R Btu/°R Btu/lbm·°R Btu/°R dimensionless dimensionless ft. dimensionless lbf dimensionless Dimensionless ft./s2 32.174 ft.·lbm/lbf·s2 dimensionless Btu Btu/h·ft.2·°F ft. Btu/lbm Btu/lbm Btu/lbm Btu/lbm Btu/h·ft.2·°F amperes 778 ft.·lbf/Btu dimensionless lbf/in. Btu/h·ft.·°F ft.·lbf/lbm ft. lbm lbm/s lbf/in.2

kJ/kg·K kJ/kg·K kJ/kg·K kJ/K kJ/kg·K kJ/K

m N

m/s2

kJ kW/m2·K m kJ/kg kJ/kg kJ/kg kJ/kg kW/m2·K amperes

N/m kW/m·K kJ/kg m kg kg/s kPa

xvii

xviii

MW n n n n Nu p pm pm pr pr P.E. Pr Q Q q Q r R r R rc rc.o. re rp Rt Re s S sf sfg sg sg t T t Tr Tc (∆t)m U U u uf ufg ug v V V V

Symbols

Molecular weight Number of moles Number of moles Number of particles Polytropic exponent Nusselt number Pressure Mean effective pressure Mixture pressure Reduced pressure Relative pressure Potential energy Prandtl number Heat interchange Heat transfer rate Specific heat interchange Radiant heat transfer rate Electrical resistance Radius Universal gas constant Compression ratio Cutoff ratio Expansion ratio Pressure ratio Thermal resistance Reynolds number Specific entropy Total entropy Specific entropy of saturated liquid Specific entropy of vaporization (sg – sf) Specific entropy of saturated vapor Specific gravity Temperature Temperature, absolute Time Reduced temperature Critical temperature Logarithmic temperature difference Internal energy Overall heat transfer coefficient Specific internal energy Specific internal energy—saturated liquid Specific internal energy of vaporization (ug – uf) Specific internal energy—saturated liquid Specific volume Velocity Volume Volume flow rate

lbm/lbm·mol dimensionless mass/MW dimensionless dimensionless dimensionless lbf/in.2 lbf/in.2 lbf/in.2 dimensionless dimensionless ft. lbf/lbm dimensionless Btu Btu/h Btu/lbm Btu/h ohms ft. ft. lbf/lbm·°R dimensionless dimensionless dimensionless dimensionless °F·h/Btu dimensionless Btu/lbm·°R Btu/°R Btu/lbm·°R Btu/lbm·°R Btu/lbm·°R dimensionless °F °R s (seconds) dimensionless °R °F Btu Btu/h·ft.2·°F Btu/lbm Btu/lbm Btu/lbm

kg/kg·mol

Btu/lbm ft.3/lbm ft./s ft.3 3 ft. /min

kJ/kg m3/kg m/s m3 m3/s

mass/MW

kPa kPa kPa

kJ/g kJ kW kJ/kg kW ohms m kJ/kg·K

°C/W kJ/kg·K kJ/K kJ/kg·K kJ/kg·K kJ/kg·K °C K s K °C kJ kW/m2·K kJ/kg kJ/kg kJ/kg

xix

Symbols

vc vf vfg vg vr vr W  W W w W w x x x Z z α ∆ ε ϕ γ η ηv μ θ ρ ρ σ τ

Critical specific volume Specific volume of saturated liquid Specific volume of vaporization (vg – vf ) Specific volume of saturated vapor Reduced specific volume Relative specific volume Humidity ratio Power Weight Weight Work Work per unit mass Length Mole fraction Quality Compressibility factor Elevation above reference plane Absorptivity Small change of variable Emissivity Relative humidity Specific weight Efficiency Volumetric efficiency Viscosity A function of Density Reflectivity Stefan–Boltzmann constant Transmissivity

ft.3/lbm ft.3/lbm ft.3/lbm ft.3/lbm dimensionless dimensionless dimensionless Btu/min lbf lbf ft. lbf ft. lbf/lbm ft. dimensionless dimensionless dimensionless ft. dimensionless dimensionless dimensionless dimensionless lbf/ft.3 dimensionless dimensionless lbm/ft.2·h dimensionless lbm/ft.3 dimensionless Btu/h·ft.2·oR4 dimensionless

Note: In addition to the symbols listed above, the following notation is used: Subscript mixture property.

m3/kg m3/kg m3/kg m3/kg

kW kN N kJ kJ/kg m

m

kN/m3

N·s/m2 kg/m3 W/m2·K4

m

refers to the

1 Fundamental Concepts

L E A R N I NG G OA L S

After reading and studying the material in this chapter, you should be able to

1. Define thermodynamics as the study of energy and the conversion of energy from one form to another 2. Use the observable external characteristics that are known as properties to describe a system 3. Establish and convert from one system of temperature measurement to another and understand the four methods of measuring temperature 4. Use both the English and SI systems of units 5. Use the elementary kinetic theory of gases to establish the concepts of pressure, temperature, density, specific weight, specific volume, and Avogadro’s law 6. Use the concept of pressure in both English and SI units (Gauge and absolute pressure definitions are important ideas that are necessary in engineering applications.) 7. Use the concept that fluids exert pressures that can be expressed in terms of the height and specific weight of the column of fluid 8. Describe the various methods of measuring pressure and the methods used to calibrate pressure-measuring devices

1.1 Introduction Thermodynamics is the study of energy, heat, work, the properties of the media employed, and the processes involved. Thermodynamics is also the study of the conversion of one form of energy to another. Because energy can be derived from electrical, chemical, nuclear, or other means, thermodynamics plays an important role in all branches of engineering, physics, chemistry, and the biological sciences. In defining the word thermodynamics, we have used the terms energy, heat, and work. It is necessary to examine these terms in detail, and this will be done in subsequent chapters. In this chapter, certain fundamental concepts are defined, and basic ideas are developed for future use.

1

2

Thermodynamics and Heat Power

Even in our modern age, which has seen changes in our understanding of how the world works, the basics of thermodynamics remain valid. Even as Newton’s laws have been shown not to apply in all cases, the fundamental laws of thermodynamics are always applicable. They apply to biological, chemical, electromagnetic, and mechanical systems. They apply to microscopic as well as macroscopic systems. In this textbook, the emphasis is on practical mechanical systems, including engines and heat transfer devices.

1.2 Thermodynamic Systems In physics, when studying the motion of a rigid body (i.e., a body that is not deformed or only slightly deformed by the forces acting on it), extensive use is made of free-body diagrams. Briefly, a free-body diagram is an outline of a body (or a portion of a body) showing all the external forces acting on it. A free-body diagram is one example of the concept of a system. As a general concept applicable to all situations, we can define a system as a grouping of matter taken in any convenient or arbitrary manner. We can consider a fixed amount of mass and follow it as it changes shape, volume, or position. The mass will have a boundary that prevents any portion of mass from entering or leaving; this is called a closed system. It still permits energy (i.e., heat and/or work) to cross the boundary. On the other hand, we can choose as our system a region in space with a geographic boundary. Such a system permits mass to enter or leave the system across the boundary. It too allows for the movement of energy across the boundary. This is called an open system. In either case, a thermodynamic system will invariably have energy transferred from it or to it and can also have energy stored in it. From this definition, it will be noted that we are at liberty to choose the grouping, but once having made a choice, we must take into account all energies involved. An example of a closed system is the refrigerant fluid inside an air conditioner. An example of an open system is an automobile engine cylinder. 1.2.1 Application of System Concept Thermodynamic equipment is best analyzed by rigorously applying the concept of a system. It can be applied to a volume in space, to a single body or a body of components, and even to a series of processes. To see how effective such a system analysis can be, consider as an example a well-insulated closed room with only a refrigerator in it. There is an electrical outlet in the wall to power the refrigerator. The room is so well insulated that no work or heat can pass through the walls except for electrical energy through the outlet. The refrigerator is plugged in and its door left open. What will happen to the temperature of the air inside the room? Will it rise, fall, or remain constant? The room air represents a closed system. There is an inflow of energy to the system through the outlet and the refrigerator. No other energy or mass change occurs; thus, the air temperature must rise. This concept of the system should be remembered when considering alternative energy sources for transportation. In an attempt to find substitutes for our dependence on foreign oil, electric vehicles have been developed and ethanol has been added to gasoline. All too often, such measures ignore the system cost for developing those energy sources. In the case of electric vehicles, one must consider the source of the electricity: batteries and

3

Fundamental Concepts

coal-fired electric plants. As for ethanol, there is a significant energy cost in producing it, as for example planting and processing our most common source, corn. Another proposed energy source has been the fuel cell, using, for example, hydrogen and oxygen inputs with water and electricity as outputs. While the benefits to the atmosphere and the efficiency of such devices are often stressed, the means of production of the two gases and their inherent costs are often ignored. Treating all components of production is system analysis at its best. 1.2.2 Properties of a System Let us consider a given system and then ask ourselves how we can distinguish changes that occur in the system. It is necessary to have external characteristics that permit us to measure and evaluate system changes. If these external characteristics do not change, we should be able to state that the system has not changed. Some of these measurements that can be made on a system are temperature, pressure, volume, and position. These observable external characteristics are called properties. When all properties of a system are the same at two different times, we can say that we cannot distinguish any difference in the system at these times. The properties of a system enable us to uncover differences in the system after it has undergone a change. Therefore, the complete description of a system is given by its properties. The condition of the system, that is, its position, energy content, and so on, is called the state of the system. Thus, its properties determine its state. Those properties that depend on the size and total mass of a system are termed extensive properties; that is, they depend on the extent of the system. An intensive property is independent of the size of the system. Pressure and temperature are examples of intensive properties. In addition, there are properties that are known as specific properties because they are given per unit mass or per defined mass in the system. Specific properties are intensive properties. It has already been noted that a given state of a system is reproduced when all its properties are the same. Because a given set of properties determines the state of a system, the state is reproduced regardless of the history or path the system may undergo to achieve the state. For example, consider a weight that is lifted vertically from one position to another. This weight can be brought to the same position by first lifting it vertically part of the way, then moving it horizontally to the right, then lifting it another part of the way, then moving it horizontally to the left, and, finally, lifting it vertically to the desired point. In this example, the state of the system at the end of the two processes is the same, and the path the system took did not affect its state after the change had occurred. As we shall see in Chapter 2, a consequence of the foregoing is that the change in energy of a system between two given states is the same, regardless of the method of attaining the state. In mathematical terminology, energy is a state function, not a path function. The properties temperature and pressure are used throughout this book, and it is necessary to have a good understanding of them. The following sections deal in detail with these properties.

CALCULUS ENRICHMENT As we have stated, a property has a unique and singular value when the system in question is in a given state. This value does not depend on the intermediate states that the system has experienced. Thus, a property is not a function of the system’s path.

4

Thermodynamics and Heat Power

The change of a property is a function only of the initial and final states of the system. Mathematically, this can be written as φ2



∫ dφ = φ − φ (a) 2

1

φ1

where ϕ denotes the property. Notice that the value of the property change is a function only of the limits of the integral. The differential, dϕ, is known as an exact differential. There are quantities such as heat and work that are not exact differentials, and it becomes necessary to specify the path in order to evaluate them. These quantities are known as path functions.

1.3 Temperature The temperature of a system is a measure of the random motion of the molecules in the system. Temperature is therefore also a measure of the thermal energy in a system. It is different from heat, which is the transfer of thermal energy from one body or system to another. If there are different temperatures within the body (or bodies composing the system), the question arises as to how the temperature at a given location is measured and how this measurement is interpreted. Let us examine this question in detail, because similar questions will also have to be considered when other properties of a system are studied. In air at room pressure and temperature, there are approximately 2.7 × 1019 molecules per cubic centimeter. If we divide the cube whose dimensions are 1 cm on a side into smaller cubes, each of whose sides is one thousandth of a centimeter, there will be approximately 2.7 × 1010 molecules in each of the smaller cubes, still an extraordinarily large number. Although we speak of temperature at a point, we really mean the average temperature of the molecules in the neighborhood of the point. Let us now consider two volumes of inert gases separated from each other by a third volume of inert gas. By inert, we mean that the gases will not react chemically with each other. If the first volume is brought into contact with the second volume and left there until no observable change occurs in any physical property, the two volumes are said to be in thermal equilibrium. Should the third volume then be brought in contact with the second and no noticeable change in physical properties is observed, the second and third volumes can also be said to be in thermal equilibrium. For the assumed conditions of this experiment, it can be concluded that the three volumes are in thermal equilibrium. Based on this discussion, the three volumes can also be stated to be at the same temperature. This simple experiment can be repeated under the same conditions for solids, liquids, and gases, with the same result every time. The results of all these experiments are summarized and embodied in the zeroth law of thermodynamics, which states that two systems having equal temperatures with a third system also have equal temperatures with each other. As an alternative definition of the zeroth law, we can say that if two bodies are each in thermal equilibrium with a third body, they are in thermal equilibrium with each other. The importance of this apparently obvious statement was recognized after the first law was

5

Fundamental Concepts

TABLE 1.1 Defining Points for Temperature Scales Atmospheric boiling point Ice point Absolute zero

°F

°C

K

°R

212 32 –460

100 0 –273

373 273 0

672 492 0

given its name, and consequently, it was called the zeroth law to denote that it precedes the first law. It should be noted that a thermometer measures only its own temperature, and for it to be an accurate indication of the temperature of a second system, the thermometer and the second system must be in thermal equilibrium. As a consequence of the zeroth law, we can measure the temperatures of two bodies by a third body (a thermometer) without bringing the bodies in contact with each other. The common scales of temperature are called the Fahrenheit and Celsius (centigrade) temperatures and are defined by using the ice point and boiling point of water at atmospheric pressure. The Fahrenheit scale was developed by Gabriel Fahrenheit in 1724, who wanted a scale that had a normal body temperature of 100; he came close, as the normal body temperature is 98.6. The Fahrenheit scale is used in the United States and a few much smaller countries. It is used with English system units. The Celsius scale was developed by Anders Celsius in 1742. He wanted a scale that was much numerically simpler. It is used in the metric system. In the Celsius temperature scale, the interval between the ice point and the boiling point is divided into 100 equal parts. In addition, as shown in Table 1.1, the Celsius ice point is zero and the Fahrenheit ice point is 32. The conversion from one scale to the other is directly derived from Table 1.1 and results in the following relations:

°C =

5 (°F − 32) (1.1) 9

°F =

9 (°C) + 32 (1.2) 5

and

The ability to extrapolate to temperatures below the ice point and above the boiling point of water and to interpolate in these regions is provided by the International Scale of Temperature. This agreed-on standard utilizes the boiling and melting points of different elements and establishes suitable interpolation formulas in the various temperature ranges between these elements. The data for these elements are given in Table 1.2.

ILLUSTRATIVE PROBLEM 1.1 Determine the temperature at which the same value is indicated on both Fahrenheit and Celsius thermometers.

6

Thermodynamics and Heat Power

SOLUTION Using Equation 1.1 and letting °C = °F yield 5 °F = (°F − 32) 9 −160 4 °F = 9 9 °F = −40





Therefore, both the Fahrenheit and Celsius temperature scales indicate the same temperature at –40°.

By using the results of Illustrative Problem 1.1, it is possible to derive an alternative set of equations to convert from the Fahrenheit to the Celsius temperature scale. When this is done, we obtain

°F =

9 ( 40 + °C) − 40 (1.3) 5

°C =

5 ( 40 + °F) − 40 (1.4) 9

and

The symmetry of Equations 1.3 and 1.4 makes them relatively easy to remember and use. Let us consider the case of a gas that is confined in a cylinder (with a constant crosssectional area) by a piston that is free to move. If heat is now removed from the system, the piston will move down, but because of its weight, it will maintain a constant pressure on the gas. This procedure can be carried out for several gases, and if volume is plotted as a function of temperature, we obtain a family of straight lines that intersect at zero volume (Figure 1.1). This unique temperature is known as the absolute zero temperature, and the accepted values on the Fahrenheit and Celsius temperature scales are –459.67° and –273.15°, respectively, with the values –460° and –273°, respectively, used for most engineering calculations. TABLE 1.2 Temperature Data Temperature Element Oxygen Sulfur Antimony Silver Gold Water

Melting or Boiling Point at 1 atm Boiling Boiling Melting Melting Melting Melting Boiling

°C –182.97 444.60 630.50 960.8 1063.0 0 100

°F –297.35 832.28 1166.90 1761.4 1945.4 32 212

7

Fundamental Concepts

Cylinder of constant cross-sectional area

Volume

Piston (free to move) Gas Heat in or out Temperature

FIGURE 1.1 Gas thermometer.

It is also possible to define an absolute temperature scale that is independent of the properties of any substance, and we will consider this point later in this book. The absolute temperature scale begins at absolute zero temperature, is always positive, and more accurately represents the concept that temperature is a measure of the molecular motion of matter. Thus, molecular motion ceases at absolute zero temperature. In the English system of units, absolute temperature is given in degrees Rankine. In the SI system, the absolute temperature is given in degrees Kelvin. Thus, we define

degrees Rankine = °R = °F + 460 (1.5)

and

degrees Kelvin = K = °C + 273 (1.6)

The relation among degrees Rankine, degrees Fahrenheit, degrees Kelvin, and degrees Celsius is also shown in Table 1.1. As noted earlier, the state of a system is uniquely determined by its properties. Thus, the accurate measurement of these properties is of great importance from both a theoretical and practical standpoint. Temperatures are measured in many ways, but in general, all the methods of measuring temperature can be categorized into four classes depending on the basic physical phenomena used to make the measurement:

1. Methods utilizing the expansion of gases, liquids, or solids 2. Methods utilizing the change in electrical resistance of an element 3. Methods utilizing the change in electrical potential of an element 4. Methods utilizing the optical changes of a sensor

The most common device used to measure temperature is the familiar liquid-in-glass thermometer, which consists of a reservoir of liquid and a long glass stem with a fine-line capillary. The operation of this type of thermometer is based on the coefficient of expansion of the liquid (usually mercury) being greater than the coefficient of expansion of the glass. For accurate measurements, these thermometers are calibrated by partial, total, or complete immersion in a suitable bath, as shown in Figure 1.2. If the thermometer is calibrated by one method but is used in a different way, it is necessary to make corrections to the readings for the difference in usage. Advantages of the liquid-in-glass thermometers are low cost, simplicity, good reliability, and long life.

8

Total immersion

Liquid level

Bath

Complete immersion

Partial immersion line

Partial immersion

Thermodynamics and Heat Power

FIGURE 1.2 Methods of calibrating thermometers.

Another device that is used to measure temperature or temperature differences depends on the expansion of materials and is called the bimetallic element. This element usually consists of two thin, flat strips placed side by side and welded together. The composite strip can be used flat or coiled into a helix or spiral. Changes in temperature cause the strip to change its curvature, and the motion produced can be used to move a pointer. The flat bimetallic strip is commonly used in room thermostats, where the motion of one end is used to close or open an electrical contact. The action of a bimetallic strip is shown in Figure 1.3. Resistance thermometers (Figure 1.4) are commonly used in industry to measure process temperatures. The basic principle of this type of instrument is that the change in electrical resistance of a sensor due to a change in its temperature is easily measurable. The electrical resistivity of some metals increases very nearly in direct proportion to an increase of temperature. Thus, the measured change in resistance of a sensor can be converted to a temperature change. Metals used for the sensors include nickel, copper, and platinum. Because of their calibration stability, high temperature coefficient, and moderate cost, nickel resistance units are normally recommended for temperature ranges between –100 and +500°F. The resistance of the sensing element is usually measured by a Wheatstone bridge (shown schematically in Figure 1.5). When the indicator is nulled to read zero by using the variable resistance rb, Dissimilar metals

Unheated

FIGURE 1.3 Bimetallic strip.

Heated

9

Fundamental Concepts

FIGURE 1.4 Industrial resistance thermometer. (Courtesy of American Chain and Cable Corp., York, PA.)

re r1 = (1.7) rb r2



where the various resistances are as shown in Figure 1.5. Errors in using the Wheatstone bridge make the circuit shown in Figure 1.5 unsatisfactory for highly accurate work. These errors are due to the contact resistance of the variable resistor, resistance changes in lead wires due to temperature gradients along them, and self-heating of the sensor due to the supply current. Modifications of the basic Wheatstone bridge have been made to compensate for and correct these faults. These circuits will be found in the references by interested students. Thermistors are also included as resistance elements. The name thermistor is derived from thermally sensitive resistors, because their resistance varies rapidly with temperature. Thermistors are included in the class of solids known as semiconductors, which have electrical conductivities between those of conductors and insulators. The advantages of the thermistor over the resistance thermometer and the thermocouple (to be discussed later) are as follows:

1. A temperature coefficient of resistance approximately 10 times that of metals, with a correspondingly greater sensitivity to temperature change 2. A much higher resistivity than the metals so that small units may have high resistance, virtually eliminating the lead and contact resistance problem 3. No need for cold-end or lead material compensation, because the thermistor resistance is a function of its absolute temperature

For a limited temperature range, the thermistor combines all the best features of resistance thermometers and thermocouples and has greater sensitivity than either. B ib Power supply

A

re Sensor FIGURE 1.5 Wheatstone bridge.

r2 D

i1

ie C

r1

Indicator

i2

rb

10

Thermodynamics and Heat Power

When two wires of different materials are joined at their ends and their junctions are at different temperatures, a net thermal electromotive force (EMF) is generated that induces a net electric current. This is shown schematically in Figure 1.6a. The thermocouple is used as a thermometer by placing one junction in contact with the body whose temperature is to be measured and measuring the voltage produced at the other junction with a millivoltmeter, as shown schematically in Figure 1.6b. The practical reduction of the thermocouple to use as a temperature-measuring device in industry depends on three so-called laws:

1. If each section of wire in the circuit is homogeneous, that is, if there is no change in composition or physical properties along its length, the EMF in the circuit depends only on the nature of the metals and the temperatures of the junctions. 2. If both of the junctions involving a particular homogeneous metal are at the same temperature, this metal makes no net contribution to the EMF. Thus, if the complete circuit consists of iron, constantan (60% copper, 40% nickel alloy), and copper, but both of the junctions involving copper are at the same temperature, we can consider the circuit as if it consisted entirely of iron and constantan, with only two junctions. 3. If all junctions of the circuit except one are held at constant temperature, the EMF in the circuit will be a function of the temperature of the remaining junction and can be used to measure that temperature. It is customary to prepare tables giving this EMF as a function of temperature for the case where the reference junction (or junctions) is held at 0°C (32°F). Figure 1.6b shows a thermocouple with two continuous dissimilar wires from the measuring function to the reference junction. From the reference junction, copper wires and the potentiometer (or millivoltmeter) complete the circuit. For the case of more than one thermocouple to be monitored, a circuit of the type shown in Figure 1.7 can be used. It is important to note that each thermocouple consists of two continuous wires between the measuring junction and the reference junction. Rather than use a circuit with multiple junctions, it is possible to use the circuit shown in Figure 1.8, which has a single Reference junction

(a)

Material A Measuring junction

Material B

Material A

Copper

Material B

Copper

(b) Junction 1 T1

Junction 2

T2

emf

FIGURE 1.6 Elementary thermocouple circuit. (a) Basic thermocouple circuit. (b) Thermocouple measurement system. (b:  Benedict, R.P.: Fundamentals of Temperature, Pressure, and Flow Measurements. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

11

Fundamental Concepts

A M1

R1

B A

M2

R2

A Measuring junctions

Cu

Cu

Cu emf

Cu

B

Mn

Cu

Potentiometer

Cu Cu

Rn

B

Cu

Unbroken Copper thermocouple connecting wires Reference wires junctions

Copper selection switch

FIGURE 1.7 Ideal circuit when more than one thermocouple is involved.

Thermocouple wires Copper connecting wires A Cu 1

2

N Measuring junctions

B

Cu

A

Cu

B

Cu

A

Cu

B

Cu

B

Cu

A

Cu

Uniform temperature zone

Ice bath (reference junction) FIGURE 1.8 Single reference junction thermocouple circuit.

Cu

Selector switch (copper) 2-pole N-throw

Potentiometer

Copper connecting wires

12

Thermodynamics and Heat Power

reference junction. A typical industrial circuit using a potentiometer that is constructed to compensate automatically for the reference junction temperature is shown in Figure 1.9. All bodies radiate energy at a rate proportional to the fourth power of their absolute temperature. This is the well-known Stefan–Boltzmann law (discussed in some detail in Chapter 11). For the moment, we concern ourselves with the optical pyrometer, which provides us with a method of converting this radiation to a temperature measurement. The optical pyrometer, shown schematically in Figure 1.10, consists of a telescope within which there is mounted a red glass filter and a small light bulb. In practice, the telescope is aimed at the body whose temperature is to be measured. The filament of the bulb appears black against the bright background being measured. The current through the bulb is varied by adjusting the rheostat until the brightness of the filament matches the brightness of the body being measured. By prior calibration, the reading of the ammeter is directly convertible to temperature. The advantage of this device is that no part of it is in contact with the body, and the optical pyrometer can be used to measure temperature above the melting points of either resistance thermometers or thermocouples. A summary of commercially available measuring devices is given in Table 1.3, showing their temperature ranges and characteristics.

M1

M2

Mn Measuring junctions

A

A´

B

B´

A

A´

B

B´

A

A´

B

B´

T/C wires

T/C extension wires

T/C switch

A´ B´ Switch wires emf Autocompensated potentiometer

FIGURE 1.9 Typical industrial thermocouple circuit.

Hot body

Lens

Bulb

Rheostat

Lens

Ammeter Battery

FIGURE 1.10 Schematic of the optical pyrometer.

Red filter

Eye

Low price, reasonable accuracy, easily broken, short scale length

Remarks

Bimetal

1000°F (538°C)

–100°F (–73°C) 600°F (316°C)

–127°F (–20 K)

Vapor Pressure

Easier to read Normally than liquid-​ has in-glass, nonlinear sometimes scale, has damaged by “cross overheating ambient” effect, No auxiliary equipment required cheapest of the filled systems

1100°F (593°C)

High temp limit

–32°F (–196°C) (pentane)

–38°F (–39°C)

Other Liquids

Low temp limit

Kind of Instrument Mercury

Glass Stem (Liquid-in-Glass)

Can be compensated accurately for ambient temperature variations

1200°F (649°C)

–125°F (–87°C)

LiquidFilled

Filled Systems

Suitable for wide ranges, linear scale, requires large bulb

1000°F (538°C)

–452°F (4 K)

GasFilled Iron/Constantan About –300°F (–184°C)

–424°F (20 K)

Copper/ Constantan

38 at 1100°C

41 at 25°C

12 at 1200°C (alloy 10% Rh) 14 at 1200°C (alloy 13% Rh) Expensive

2600°F to 2800°F (1427°C to 1538°C) 3216°F (1769°C) spot readings (not to be used in reducing atm)

Commonly 32°F (0°C)

Platinum/ Platinum– Rhodium

(continued)

The couple most Chromel is 90 Constantan widely used in Ni, 10 Cr is 57 Cu, industry, poor (chromel P); 43 Ni reproducibility alumel is 94 Ni, above 1600°F (871°C) 3 Mn, 2Al, 1 Si Can give very rapid response, matched only by the radiation and optical pyrometers

64 at 760°C

2100°F to 2300°F 660°F (1149°C to (349°C) 1260°C), 2400°F 930°F (1316°C) spot (499°C) readings (not to spot be used in readings reducing atm) Thermoelectric power, microvolts per degree C

1400°F (760°C) in oxidizing atm, 1800°F (982°C) in reducing atm, 2000°F (1093°C) spot readings

About –320°F (–196°C)

Chromel/ Alumel

Thermocouples

Summary of Information Regarding Commercially Available Temperature-Measuring Instruments or Systems

TABLE 1.3

Fundamental Concepts 13

(R100°C – R0°C)/100 R0°C 0.0066

600°F (316°C)

–300°F (–184°C)

Nickel

–0.0098 (one type)

–76°F (–60°C) (most types) 750°F (399°C) (glass coated)

Thermistors

High sensitivity, only fair stability Give greater accuracy than thermocouples, for the same investment. High sensitivity makes them suitable for narrow range instruments.

May drift at the higher temperatures

0.0043

250°F (121°C)

1400°F to 1800°F (760°C to 982°C)

0.0039

–220°F (–140°C)

Copper

–300°F (–184°C)

Platinum

Resistance Thermometers

Indication somewhat affected by heating rate

Cannot operate a recorder or automatic controls

2500°F (1371°C)

113°F (45°C)

Melting Pellets

A single cone or pellet can indicate only its rated temperature and is normally used only once.

1085°F (585°C) 3659°F (2015°C)

Pyrometric Cones

1400°F (760°C) (normally) As high as desired

Optical Pyrometer

Absorbers of radiation, such as windows or dirt, can affect accuracy. Emissivity of source important. Very rapid response.

Can operate a recorder and automatic controls

About room temperature As high as desired

Radiation Pyrometer

Source: Wolfe, H.C. (ed.), Temperature, Its Measurement and Control in Science and Industry, Reinhold Publishing, New York, 1955. With permission.

Remarks

Low temp limit High temp limit

Kind of Instrument

Summary of Information Regarding Commercially Available Temperature-Measuring Instruments or Systems

TABLE 1.3 (Continued)

14 Thermodynamics and Heat Power

15

Fundamental Concepts

1.4 Force and Mass 1.4.1 English System Force is very often defined in elementary physics texts as the push or pull exerted on a body. Although this definition serves to satisfy our daily experience, it is not satisfactory when dealing with the motion of bodies that are subjected to resultant forces that are not zero. The following paragraphs deal with the concept of force in a consistent manner, and we attempt to clarify the confusion concerning the units of force and mass. The basis of much of the physical sciences rests on the work of Newton. For the present, two physical laws that are attributed to him will be used:

1. Law of universal gravitation 2. Second law of motion

The first of these, the law of universal gravitation, states simply that the force of attraction experienced by two bodies is proportional to the product of their masses and inversely proportional to the square of the distance (d) separating them. At this point, we define the mass of a body as the quantity of matter contained in the body. Thus, if the Earth is assumed to be spherical and its mass center is taken to be at its geometrical center, a body on the surface will experience a constant force due to the Earth’s attraction. This force is given the name weight. Because the Earth is an oblate spheroid, a body at different locations at the surface will have different weights. Also, the surface of the Earth is not smooth, so weight is a function of elevation. While a body’s weight can change with altitude, its mass is constant. So far, it would appear that the foregoing concepts are both clear and relatively simple. In its simplest form, it can be stated that the weight of a body, in a given location, is proportional to its mass. By choosing the constant of proportionality to be unity, the mass of an object in pounds at the Earth’s surface may, for most practical purposes, be assumed to be numerically equal to the weight of the body. The weight of a body can also be defined by Newton’s second law of motion in terms of the fundamental units of length, time, and mass. This relation can be stated as follows:

F ∝ ma (1.8)

where a is the acceleration of a body due to gravity, m its mass, and F is its weight. In the English system, the basic unit of mass is the slug; of distance, the foot; and of time, the second. The unit for acceleration is therefore ft./s2. The derived unit of force, called the pound, is that amount of force which will accelerate one slug at 1 ft./s2. On the surface of the Earth, the acceleration of gravity is considered to be 32.174 ft./s2, so a mass of one slug, per Equation 1.8, will weigh 32.174 pounds. The slug is an inconvenient term; it would be easier to express mass in pounds so that mass and weight could be expressed the same numerically using a familiar word. This is accomplished by the introduction of a proportionality constant in the Equation 1.9, where gc is numerically equal to 32.174.

F=

ma (1.9) gc

16

Thermodynamics and Heat Power

TABLE 1.4 Common Combinations of Units Length Foot Foot Foot Foot Centimeter Meter Meter Meter

Time

Mass

Force

gc

Second Hour Second Second Second Second Second Second

Pound Pound Pound Slug Gram Kilogram Kilogram Gram

Pound Pound Poundal Pound Dyne Newton Kilogram Gram

32.174 ft./s2 × pound mass/pound force 4.17 × 108 ft./h2 × pound mass/pound force 1.0 ft./s2 × pound mass/poundal 1.0 ft./s2 × slug/pound force 1.0 cm/s2 × gram/dyne 1.0 m/s2 × kilogram/newton 9.81 m/s2 × kilogram mass/kilogram force 981 cm/s2 × gram mass/gram force

It is in this constant of proportionality, gc, that the confusion occurs, as well as in the ambiguous use of the word pound. To differentiate between the pound force and the pound mass, we will use the notation lbf and lbm. Also, note that gc = 32.174 lbm·ft./lbf·s2. Use of gc provides a benefit in that at sea level, the number of pound mass is the same as the number of pound force. Thus, thermodynamic parameters can be stated as per pound regardless of whether it is a pound mass or a pound force. Table 1.4 lists some of the most common combinations of units that can be used. To avoid the obvious confusion that this multitude of units can cause, the definition of pound mass and pound weight, as given in this section, is applied in conjunction with Equation 1.9 throughout this book. Note that gc is always 32.174 in the ft./s2 system even if the acceleration of gravity changes, and remember that in the English system, which uses lbm, any equation with mass must be divided by gc. As a consequence of these considerations, weight and mass, at a location in which the local gravitational attraction is expressed as g, can be interrelated in the following manner:

w=

mg (1.10) gc

We also note that mass can be operationally defined as the inertia a body has in resisting acceleration. ILLUSTRATIVE PROBLEM 1.2 A mass of 1 lb. weighs 1 lb. on the Earth. How much will it weigh on the moon? Assume that the diameter of the moon is 0.273 when the earth’s diameter is taken to be unity and that the mass of the moon is 0.0123 in relation to the Earth’s mass. SOLUTION The force exerted on the mass by the moon will determine its “weight” on the moon. In general, the law of universal gravitation can be written as

F=K

m1m2 d2

17

Fundamental Concepts

where K is a proportionality constant. Using the subscripts e for Earth and m for moon, we have Fe =



Kme m (re )2



because re, the radius of Earth, is the distance separating the mass center of the body m on Earth and the mass center of Earth. Similarly, Fm =

Kmmm (rm )2

Fe m r = e m Fm mm re

2

=

1 (0.273)2 = 6.06 0.0123



Thus, a body on Earth feels a force (weight) approximately six times the force it would feel on the moon. The solution to the problem is that a mass of 1 lb. will weigh approximately 1/6 lb. on the moon.

1.4.2 SI System For the engineer, the greater confusion has been the units for mass and weight. As we have noted, the literature abounds with units such as slugs, pounds, mass, pound force, poundal, kilogram force, kilogram mass, dyne, and so on. In the SI system, the base unit for mass (not weight or force) is the kilogram (kg), which is equal to the mass of the international standard kilogram located at the International Bureau of Weights and Measures. It is used to specify the quantity of matter in a body. The mass of a body never varies, and it is independent of gravitational force. The SI derived unit for force is the newton (N). The unit of force is defined from Newton’s law of motion: force is equal to mass times acceleration (F = ma). By this definition, 1 N applied to a mass of 1 kg gives the mass an acceleration of 1 m/s2 (N = kg·m/s2). The newton is used in all combinations of units that include force, for example, pressure or stress  . By this procedure, the unit of force is not (N/m2), energy (N·m), and power (N⋅m/s = W) related to gravity, as was the older kilogram force. Table 1.5 gives the seven base units of the SI system. Several observations concerning this table should be noted. The unit of length is the meter and the kilogram is a unit of mass, not weight. Also, symbols are never pluralized and never written with a period, and uppercase and lowercase symbols must be used as shown without exception. Table 1.6 gives the derived units with and without symbols often used in engineering. These derived units are formed by the algebraic combination of base and supplementary units. Note that where the name is derived from a person, the first letter of the symbol appears as a capital; for example, newton is N. Otherwise, the convention is to make the symbol lowercase.

18

Thermodynamics and Heat Power

TABLE 1.5 Base SI Units Quantity Length Mass Time Electric current Thermodynamic temperature Amount of substance Luminous intensity

Base SI Unit

Symbol

Meter Kilogram Second Ampere Kelvin Mole Candela

m kg s A K mol cd

TABLE 1.6 Derived SI Units Quantity Acceleration Area Density Energy or work Force Moment Moment of inertia of area Plane angle Power Pressure or stress Rotational frequency Temperature Torque (see “moment”) Velocity (speed) Volume

Name

Symbol

Formula

Expressed in Terms of Base Units

Acceleration Square meter Kilogram per cubic meter Joule Newton Newton-meter – Radian Watt Pascal Revolutions per second Degree Celsius Newton-meter Meter per second Cubic meter

m/s2 m2 kg/m3 J N N·m m4 rad  W

m/s2 m2 kg/m3 N·m m·kg·s–2 N·m m4 rad J/s N/m2 s–1 °C N·m m/s m3

m/s2 m2 kg·m–3 m2·kg·s–2 m·kg·s–2 m2·kg·s–2 m4 rad m2·kg·s–3 N·m–2 s–1 °C m2·kg·s–2 M·s–1 m3

Pa rev/s °C N·m m/s m3

Weight has been defined as a measure of gravitational force acting on a material object at a specified location. Thus, weight is a force that has both a mass component and an acceleration component (gravity). Gravitational forces vary by approximately 0.5% over the Earth’s surface. For nonprecision measurements, these variations normally can be ignored. Thus, a constant mass has an approximate constant weight on the surface of the Earth. The agreed standard value (standard acceleration) of gravity is 9.806 650 m/s2. Figure 1.11 illustrates the difference between mass (kilogram) and force (newton). The term mass or unit mass should be used to indicate only the quantity of matter in an object, and the old practice of using weight in such cases should be avoided in engineering and scientific practice. However, because the determination of an object’s mass will be accomplished by the use of a weighing process, the common usage of the term weight instead of mass is expected to continue but should be avoided. Based on the foregoing, Equation 1.10 can be written in SI units as

w  = mg (1.10a)

19

Fundamental Concepts

1.64 N (moon, tranquility base)

9.81 N (Earth, sea level)

1 kg FIGURE 1.11 Mass and force.

ILLUSTRATIVE PROBLEM 1.3 A body has a mass of 5 kg. How much will it weigh on Earth? SOLUTION The weight of the body will be its mass multiplied by the local acceleration of gravity, that is,

w = mg

Thus,

w = 5 kg × 9.81

kg⋅m m = 49.05 2 s2 s

and because 1 N = 1 kg·m/s2,

w = 49.05 N

ILLUSTRATIVE PROBLEM 1.4 A body has a mass of 10 kg. If the local gravitational acceleration is 9.5 m/s2, determine (a) its weight and (b) its horizontal acceleration if it is acted on by a 10 N horizontal force.

20

Thermodynamics and Heat Power

SOLUTION

a. From Equation 1.10a, w = (10 kg) 9.5

kg⋅m m = 95.0 2 = 95.0 N 2 s s

b. Because F = ma, a = F/m. Therefore, kg⋅m s2 = 1 m a= 10 kg s2 10



For the SI system to be universally understood, it is most important that the symbols for the SI units and the conventions governing their use be adhered to strictly. Care should be taken to use the correct case for symbols, units, and their multiples (e.g., K for Kelvin, k for kilo, m for milli, M for mega). As noted earlier, unit names are never capitalized except at the beginning of a sentence. SI unit symbols derived from proper names are written with the first letter in uppercase; all other symbols are written in lowercase, for example, m (meter), s (second), K (Kelvin), Wb (weber). Also, unit names form their plurals in the usual manner. Unit symbols are always written in singular form, for example, 350 megapascals or 350 MPa, 50 milligrams or 50 mg. Because the unit symbols are standardized, the symbols should always be used in preference to the unit names. Unit symbols are not followed by a period unless they occur at the end of a sentence, and the numerical value associated with a symbol should be separated from that symbol by a space, for example, 1.81 mm, not 1.81mm. The period is used only as a decimal marker. Because the comma is used by some countries as a decimal marker, the SI system does not use the comma. A space is used to separate large numbers in groups of three. Thus, 3 807 747 and 0.030 704 254 indicate this type of grouping. Note that for numerical values less than 1, the decimal point is preceded by a zero. For a number of four digits, the space can be omitted. In addition, certain style rules should be adhered to:

1. When a product is to be indicated, use a space between unit names (e.g., newton meter). 2. When a quotient is indicated, use the word per (e.g., meter per second). 3. When a product is indicated, use the square, cubic, and so on (e.g., square meter). 4. In designating the product of units, use a centered dot (e.g., N·s, kg·m). 5. For quotients, use a solidus (/) or a negative exponent (e.g., m/s or m·s–1). The solidus (/) should not be repeated in the same expression unless ambiguity is avoided by the use of parentheses. Thus, one should use m/s2 or m·s–2 but not m/s/s; also, use m·kg/(s3·A) or m·kg·s–3·A–1 but not m·kg/s3/A.

One of the most useful features of the older metric system and the current SI system is that multiples and submultiples of units are in terms of factors of 10. Thus, the prefixes

21

Fundamental Concepts

TABLE 1.7 Factors of 10 for SI Units Prefix

Symbol

Factor

Tera Giga Mega Kilo Hector Deka Deci Centi Milli Micro Nano Pico Femto Atto

T G M k h da d C m μ n p f a

1012 109 106 103 102 101 10–1 10–2 10–3 10–6 10–9 10–12 10–15 10–18

1 000 000 000 000 1 000 000 000 1 000 000 1 000 100 10 0.1 0.01 0.001 0.000 001 0.000 000 001 0.000 000 000 001 0.000 000 000 000 001 0.000 000 000 000 000 001

given in Table 1.7 are used in conjunction with SI units to form names and symbols of multiples of SI units. Certain general rules apply to the use of these prefixes:

1. The prefix becomes part of the name or symbol without separation (e.g., kilometer, megagram). 2. Compound prefixes should not be used; use GPa, not kMPa. 3. In calculations, use powers of 10 in place of prefixes. 4. Try to select a prefix so that the numerical value will fall between 0.1 and 1000. This rule may be disregarded when it is better to use the same multiple for all items. It is also recommended that prefixes representing 10 raised to a power that is a multiple of 3 be used (e.g., 100 mg, not 10 cg). 5. The prefix is combined with the unit to form a new unit, which can be provided with a positive or negative exponent. Therefore, mm3 is (10 –3 m)3 or 10 –9 m3. 6. Where possible, avoid the use of prefixes in the denominator of compound units. The exception to this rule is the prefix k in the base unit kg (kilogram). There are certain units outside the SI system that may be used together with the SI units and their multiples. These are recognized by the International Committee for Weights and Measures as having to be retained because of their practical importance. It is almost universally agreed that when a new language is to be learned, the student should be completely immersed and made to “think” in the new language. This technique has been proved most effective by the Berlitz language schools and the Ulpan method of language teaching. A classic joke about this is the American traveling in Europe who was amazed that 2-year-old children were able to speak “foreign” languages. In dealing with the SI system, students should not think in terms of customary units and then perform a mental conversion; it is better to learn to think in terms of the SI system, which will then become a second language. However, there will be times when it may be necessary to convert from customary US units to SI units. To facilitate such conversions, Table 1.8 gives some commonly used conversion factors.

22

Thermodynamics and Heat Power

TABLE 1.8 Conversions from Conventional to SI Units Multiply Atmospheres (760 torr) Atmospheres Atmospheres Bars Bars British thermal units (Btu) British thermal units (Btu) British thermal units (Btu) British thermal units (Btu) Btu/hour-square foot Btu/hour-square foot-°F Btu/minute Btu/minute Calories Cubic feet Cubic feet Cubic feet/minute Cubic meters Cubic meters Cubic meters Cubic meters/second Cubic meters/second Degrees Celsius Degrees Fahrenheit Feet Feet of H2O (39.2°F) Feet of H2O (39.2°F) Feet/second Foot-pound (force) Foot-pounds (force)/minute Gallons Gallons/minute Horsepower Horsepower Horsepower-hours Horsepower-hours Inches of H2O (39.2°F) Inches mercury (32°F) Inches mercury (32°F) Inches mercury (32°F) Inches mercury (32°F) Joules Joules

By

To Obtain

2.992 × 101 1.033 × 104 1.013 × 102 9.869 × 10–1 1.000 × 102 3.927 × 10–4 1.056 2.928 × 10–4 1.221 × 10–1 3.153 × 10–4 5.676 × 10–4 2.356 × 10–2 1.757 × 101 4.1868 2.832 × 10–2 2.832 × 101 4.720 × 10–4 8.107 × 10–4 3.531 × 101 2.642 × 102 2.119 × 103 1.585 × 104 (9/5)C + 32 5/9(F – 32) 3.048 × 10–1 3.048 × 102 4.335 × 10–1 3.048 × 10–1 1.356 2.260 × 10–2 3.785 × 10–3 6.309 × 10–5 4.244 × 101 7.457 × 10–1 2.545 × 103 7.457 × 10–1 2.491 × 10–1 3.342 × 10–2 3.453 × 102 3.386 4.912 × 10–1 7.376 × 10–1 1.000

Inches mercury (32°F) Kilograms/square metera Kilopascals Atmospheres Kilopascals Horsepower-hours Kilojoules Kilowatt-hours Megawatt-days Watts/square centimeter Watts/square centimeter-°C Horsepower Watts Joules Cubic meters Liters Cubic meters/second Acre-feet Cubic feet Gallons (U.S.) Cubic feet/minute Gallons/minute Degrees Fahrenheit Degrees Celsius Meters Kilograms/square meter Pounds force/square inch Meters/second Joules Watts Cubic meters Cubic meters/second British thermal units/minute Kilowatts British thermal units Kilowatt-hours Kilopascals Atmospheres Kilograms/square meter Kilopascals Pounds force/square inch Foot-pounds (force) Watt-seconds (continued)

23

Fundamental Concepts

TABLE 1.8 (Continued) Conversions from Conventional to SI Units Multiply Joules Kilograms Kilograms Kilograms/cubic meter Kilograms/square meter Kilograms/square meter Kilograms/square meter Kilograms/square meter Kilojoules Kilopascals Kilopascals Kilopascals Kilopascals Kilopascals Kilowatts Kilowatt-hours Kilowatt-hours Kilowatt-hours Liters Megawatt-days Megawatt-days Meters Newtons Pounds Pounds (force) Pounds mass/cubic feet Pounds force/square inch Pounds force/square inch Pounds force/square inch Pounds force/square inch Square feet Square meters Square meters Tonnes (metric tons) Tons (short) Watts Watts Watt-seconds Watts-square centimeter Watts/square centimeter-°C a

Force units with gc = 9.81.

By

To Obtain

2.387 × 10–1 2.205 1.102 × 10–3 6.243 × 10–2 9.678 × 10–5 3.281 × 10–3 2.896 × 10–3 1.422 × 10–3 9.471 × 10–1 4.015 1.450 × 10–1 2.953 × 10–1 1.000 × 10–2 9.869 × 10–3 1.341 3.413 × 103 1.341 4.167 × 10–5 3.531 × 10–2 8.189 × 107 2.400 × 104 3.281 2.248 × 10–1 4.536 × 10–1 4.448 1.602 × 101 2.307 2.036 7.031 × 102 6.895 9.290 × 10–2 2.471 × 10–4 1.076 × 101 2.205 × 103 9.072 × 102 5.688 × 10–2 4.427 × 101 1.000 3.171 × 103 1.762 × 103

Calories Pounds force Tons (short) Pounds force/cubic foot Atmospheresa Feet of H2O (at 39.2°F)a Inches mercury (32°F)a Pounds force/square incha British thermal units Inches H2O (at 39.2°F) Pounds force/square inch Inches mercury (32°F) Bars Atmospheres (760 torr) Horsepower British thermal units Horsepower-hours Megawatt-days Cubic feet British thermal units Kilowatt-hours Feet Pounds force Kilograms Newtons Kilograms/cubic meter Feet of H2O (at 39.2°F) Inches mercury (32°F) Kilograms/square metera Kilopascals Square meters Acres Square feet Pounds force Kilograms Btu/minute Foot-pounds force/minute Joules Btu/hour-square foot Btu/hour-square foot-°F

24

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 1.5 Table 1.8 lists the conversation factor for obtaining square meters from square feet as 9.290 × 10 –2. Starting with the definition that 1 in. equals 2.54 cm (0.0254 m), derive this conversion factor. SOLUTION In solving this type of conversion problem, it must be kept in mind that units need to be consistent and that we can use the familiar rules of algebra to manipulate units. Proceeding as noted, we have

1 in. = 0.0254 m

or

1 = 0.0254

m (a) in.

Because 1 ft. = 12 in.,

1 = 12

in. (b) ft.

If we now multiply Equation a by Equation b, we obtain

1 = 0.0254

m in. × 12 in. ft.

Because inches cancel, we have

1 = 0.0254 × 12

m ft.

We can now square both sides to obtain

(1)2 = (0.0254 × 12)2

m2 m2 = 9.290 × 10−2 2 2 ft. ft.

or the desired result,

1 ft.2 = 9.290 × 10 –2 m2

which states that ft.2 × 9.290 × 10 –2 = m2. The foregoing can also be obtained in a single chain-type calculation as

0.0254

m 12 in. × in. ft.

2

= 9.290 × 10−2

m2 ft.2

25

Fundamental Concepts

1.5 Elementary Kinetic Theory of Gases The following derivation, based on elementary kinetic gas theory, is very useful and will serve later to introduce the theory of ideal or perfect gases. Imagine a cube, as shown in Figure 1.12, with sides l. In this cube, it will be assumed that there are n identical molecules (particles), each having a mass m. These particles are further assumed to be perfectly elastic spheres each traveling with the same velocity. By perfectly elastic, it is implied that the collision of a molecule with another molecule or the walls of the container causes the molecule to rebound without loss of energy or momentum. The size of the molecule will be taken to be negligibly small compared to dimensions of the system. If the velocity in the x direction is essentially constant over the length l and is denoted by Vx, the molecule shown in Figure 1.12 will travel a distance equal numerically to Vx in a unit time. In this same time, the molecule will collide elastically with the walls (parallel to the y–z plane) a number of times equal to Vx divided by l. This last statement has considered only the x-directed velocity of the molecule. It is also assumed that the molecules do not collide with each other. At this point, it will be necessary to involve the concepts of impulse and momentum for a rigid particle that has only translatory motion. On the basis of Newton’s laws of motion for such a particle, it is possible to write Equation 1.9 as follows:

F=



ma m∆V = ; gc g c ∆t

F∆t =

m∆V gc

(1.11)



(Equation 1.11 is written in English units.) The symbol Δt is used to indicate a small interval of time, and ΔV is the change in velocity during this time interval. The term FΔt is known as the impulse imparted to the particle by the force F acting for the time Δt, and the term (mΔV/gc) is called the momentum change that the particle undergoes during this same time interval. Let us consider the collision of a particle with a wall. As shown in Figure 1.13, the particle travels in the x direction with a velocity Vx prior to striking the wall. Because the particle has been assumed to be perfectly elastic, it will collide with the wall and

z z

I

Vz V I

x

Vx

I Vy

y FIGURE 1.12 Kinetic theory derivation.

V

y

x

26

Thermodynamics and Heat Power

Vx F Vx

FIGURE 1.13 Particle collision with wall.

rebound with a speed equal to Vx, but it will be traveling in a direction opposite to its initial direction. Thus, its velocity will be –Vx. The wall is stationary, and as a result of the impact, a reactive force F is set up. Because the molecule has a momentum equal to mVx/gc just before colliding with the wall and a momentum of –mVx/gc after the collision, the change in momentum per molecule will be 2mVx/gc. As stated earlier, the number of collisions with the walls in a unit time will be Vx/l, and we must consider that the n identical particles each undergo the same collision with the walls. The total number of collisions will therefore be nVx/l. Multiplying the total number of impacts per unit of time by the momentum change per impact yields the total change of momentum per unit of time for the system:



2mVx nVx gc l

(1.12)

Equation 1.12 also expresses the force exerted on the wall. Pressure is the normal force exerted per unit surface area. For present purposes, it will be reasonable to assume that the force expressed by Equation 1.12 is distributed uniformly over the y–z planes. Because these consist of two faces, each l2 in area, the pressure exerted on the y–z plane is



2 mVx nVx gc l 2l 2

=

mnVx2 (1.13) gcl 3

However, it was previously assumed that the molecule had the same velocity in each of the three component directions. Therefore, in the unit time interval under consideration, there is an equal probability that the particle will hit one of the three sets of parallel faces composing the cube. If this were not so, there would be unequal pressures on the various faces of the tube. Because the volume of the cube (V) equals l3, Equation 1.14 follows from Equations 1.11 and 1.13 combined:



pV =

1 mnVx2 (1.14) 3 gc

27

Fundamental Concepts

or

pV =

1 (mnVx2 ) (SI) (1.14a) 3

Equation 1.14 is used repeatedly later (in slightly different form) and has special significance. However, for the present, only certain limited conclusions will be deduced from it. It should be remembered that this equation was derived on the basis of certain simplifying and therefore restrictive assumptions. In addition to the assumptions stated, it is important to note that the rotations and vibrations of the molecule have been neglected. Also, molecule collisions with other molecules have been ignored. This corresponds to assuming that the dimensions of the unit cube are small compared with the mean free path of the gas particles, that is, the distance molecules travel between molecule–molecule collisions. Although these assumptions and others inherent to this derivation lead to varying degrees of deviation of real gases from Equation 1.14, it is amazing that this equation can be used with a reasonable degree of accuracy for engineering purposes to describe the behavior of many gases over a wide range of conditions. On the basis of experimental and theoretical investigations by Joule and others, it can be shown that for ideal gases, the pressure of these gases increases equally for equal temperature increments. This is equivalent to stating that the product mVx2 is a constant for all gases at a given temperature. As a consequence of this conclusion, Equation 1.14 yields Avogadro’s law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules (particles). It is also possible to deduce another concept from Equation 1.14, specifically, density. The product mn found in the numerator of Equation 1.14 is the total mass of the molecules in the volume under consideration. The total mass divided by the total volume yields the property of density (ρ). The reciprocal of density is called specific volume. It is the total volume that a unit mass occupies under a given set of conditions. It is denoted by v. We summarize some of the conclusions of the foregoing analysis (the first three conclusions are limited to gases and the last three are general definitions): 1. Pressure (which is defined as the normal force per unit area) results from the collisions of the molecules with the walls of the container and is a function of the number of impacts per unit time, the mass of the particle, and the velocity of the particle. 2. Avogadro’s law states that equal volumes of gases at the same pressure and temperature contain the same number of particles. 3. Temperature can be taken to be a measure of the translational energy of the particles. In a more general sense, it can be said to be a measure of the molecular activity (and internal energy) of the gases. 4. Density is defined as the mass per unit volume (ρ). 5. The reciprocal of density is the volume per unit mass and is called specific volume (v). 6. Specific weight (γ) is defined as the weight per unit volume. Note that this term, which equals pg/gc, does not exist in SI as a basic unit. 7. Specific gravity (sg) is defined as the ratio of the density of a substance to the density of water at 4°C. It can also be defined as the ratio of the specific weight of a substance to the specific weight of water at 4°C. The density of water at 4°C is 1000 kg/ m3. In the older cgs (centimeter-gram-second) system, the density of water at 4°C is 1 g/ cm3, making specific gravity numerically equal to density in this system.

28

Thermodynamics and Heat Power

1.6 Pressure We have seen that when a gas is confined in a container, molecules of the gas strike the sides of the container, and these collisions with the walls of the container cause the molecules of the gas to exert a force on the walls. When the component of the force that is perpendicular (normal) to the wall is divided by the area of the wall, the resulting normal force per unit area is called the pressure. To define the pressure at a point, it is necessary to consider the area in question to be shrinking steadily. Pressure at a point is defined to be the normal force per unit area in the limit as the area goes to zero. Mathematically,

p=

∆F ∆A

(1.15) lim( ∆ A

0)

In common engineering units, pressure is expressed as pounds force per square inch or pounds force per square foot, which are usually abbreviated as psi and psf. In SI units, pressure is expressed in N/m2, which is known as the pascal (Pa). The bar is 105 Pa. These units are the ones used most frequently in the literature, but certain others are also used because of the manner in which the pressure measurements are made. Most mechanical pressure gauges, such as the Bourdon gauge (see Figure 1.28), measure the pressure above local atmospheric pressure. This pressure is called gauge pressure and is measured in units of pounds force per square foot or pounds force per square inch, that is, psfg or psig. The relation of gauge pressure to absolute pressure is shown in Figure 1.14 and is

absolute pressure = atmospheric pressure + gaugee pressure (1.16)

Absolute pressure is indicated as psia or psfa. It is usual to take the pressure of the atmosphere as being equal to 14.7 psia. However, in Europe, 1 “ata” has been defined and is used as 1 kg/cm2 for convenience, but this unit is not 14.7 psia. It is more nearly 14.2 psia. Care should be exercised when using the unit of pressure that is expressed as ata. In SI, the equivalent of 14.696 (14.7) psia is 101.325 kPa. The terms gauge and vacuum are not used in SI, because all pressures are absolute in this system.

Defined standard atmosphere 101.325 kPa o 14.7 psia or 760 mm Hg at 0 C (fixed)

Vacuum (negative gauge pressure) Absolute pressure

FIGURE 1.14 The relation of gauge to absolute pressure.

Gauge pressure Local atmospheric pressure (variable) Absolute pressure Absolute zero (fixed)

29

Fundamental Concepts

Referring again to Figure 1.14, it will be noted that pressure below atmospheric pressure is called vacuum. By reference to this figure, we obtain the relation between absolute pressure and vacuum as

absolute pressure = atmospheric pressure – vacuum

(1.17)

ILLUSTRATIVE PROBLEM 1.6 Assume that a fluid whose specific weight is constant and equal to γ lbf/ft.3 is placed in a uniform tube until its height in the tube is h feet above the base of the column. Determine the pressure at the base of the column. SOLUTION From our definition of pressure as force divided by area, we must find the force being exerted on the base by the column of fluid. This force will equal the weight of the fluid, which in turn will equal the volume of fluid multiplied by the specific weight of the fluid. Denoting the weight to be w, the cross-sectional area to be A, and the liquid height to be h, as shown in Figure 1.15, we have w = γV, where V is the volume of fluid. The volume of fluid is equal to A × h, giving us w = γAh (1.18)



which is the force on the base. Dividing w by A yields the pressure

p=

γAh = γ h (1.19) A

Because it is usual to measure distance up from the base, our result is

p = −γ h (1.19a)

Pressure at top ( p) taken to be zero (zero gauge pressure)

Specific weight lbf / ft.3

FIGURE 1.15 Illustrative Problem 1.6.

Cross-sectional area of tube = A

h

30

Thermodynamics and Heat Power

In English units,

p=

−ρg (1.20) h gc

In SI units,

p = −ρgh (1.20a)

CALCULUS ENRICHMENT The relation between the pressure and height of a fluid can be derived considering this figure. Force = (p + dp)A

Weight = Adh

+

dh

Force = pA

h h=0

Summing the forces in the vertical direction and noting that up is positive yields

dp = –γdh (a)

where γ is also ρg. Thus,

dp = –ρgdh (b)

In order to solve Equation a or b, it is necessary to know p as a function of h. In general, we can integrate these equations: h



∫

p( h) − p(0) = − ρgdh (c) 0

For the special case of a liquid having a constant density, Equation c can be integrated, starting at the surface, where p = 0, and noting that h is measured positive upward. This gives us the result that

p = –ρgh (d)

or

p = –γh (e)

31

Fundamental Concepts

Equations d and e are the same as Equations 1.19a and 1.20a. Let us consider the case of a fluid whose density is a linear function of pressure. We can write this in terms of the height as ρ = ρ 0(1 – αh) (f)



where ρ 0 corresponds to h0 and α is the rate at which density decreases with elevation. Placing (f) into (c) gives us h

∫

p( h) − p(0) = − ρ0 (1 − αh) dh (g)



0

αρ h2 p( h) − p(0) = − ρ0 h − 0 2

Integrating

p( h) − p(0) = −ρ0 h 1 −

Simplifying

h

(h) 0

αh (i) 2

In meteorology, the decrease of temperature with height is called the lapse rate. The lapse rate is obviously related to Equations c and i.

The most common fluid used to measure pressure differences, atmospheric pressure, and vacuum pressure is mercury. At approximately room temperature, the specific gravity of mercury is very nearly 13.6. It will usually be assumed that the specific gravity of mercury is 13.6 unless otherwise stated. The effect of temperature on the specific gravity of mercury is given in Figure 1.16.

Specific gravity

14.0

13.5

13.0

12.5

FIGURE 1.16 Specific gravity of mercury.

0

100

200 Temperature (ºF)

300

32

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 1.7 A tube of glass open at the top has a 1-in. level of mercury in it. Take the specific gravity of mercury (Hg) to be 13.6, and determine the pressure on the base of the column. SOLUTION To solve this problem, let us first convert the unit of weight of grams per cubic centimeter to pounds per cubic foot. In 1 lbf, there is approximately 454 g. Also, there is 2.54 cm in 1 in. Thus, 1 g is 1/454 lbf, and 1 ft. has 12 × 2.54 cm. To convert 1 g per cubic centimeter to pounds per cubic foot, we apply the following dimensional reasoning: g lb. cm 3 lb. × × 3 = 3 =γ 3 g cm ft. ft.

Continuing yields

3 1g 1 lbf 62.4 lbf 3 cm × × ( 2 . 54 × 12 ) = =γ 3 3 454 g cm ft. ft.3

Thus, the conversion factor from grams per cubic centimeter to pounds per cubic foot is 62.4. Students are strongly urged to check all computations for dimensional consistency when doing problems. Applying Equation 1.19 gives us

p=

lb 1 lb ft. (13.6 × 62.4) 3f = 70.72 2f 12 ft. ft.

In pounds force per square inch, p



1 lbf ft.2 × 2× = psi 2 144 ft. in.

Therefore,



p=

1 1 ft.2 × 13.6 × 62.4 × = 0.491 psi 12 144 in.2

This is a gauge pressure. If the local atmospheric pressure is 14.7 psia,

p = 0.491 + 14.7 = 15.19 psia

The value of 0.491 psi/in. Hg is a useful conversion factor.

33

Fundamental Concepts

ILLUSTRATIVE PROBLEM 1.8 The density of mercury is 13.595 kg/m3. Determine the pressure at the base of a column of mercury that in 25.4 mm high. SOLUTION Using Equation 1.20a, we obtain

p = −ρgh = −13.595

kg m × 9.806 2 × − 0.0254 m = 3386.1 Pa 3 m s

Note: 1 psi ≃ 6895 Pa. Therefore, 3386.1/6895 = 0.491 psi, which checks with Illustrative Problem 1.7.

In vacuum work, it is common to express the absolute pressure in a vacuum chamber in terms of millimeters of mercury. Thus, a vacuum may be expressed as 10 –5 mm Hg. If this is expressed in pounds force per square inch, it would be equivalent to 0.000000193 psi, with the assumption that the density of mercury (for vacuum work) is 13.6 g/cm3. Another term, torr, is also found in the technical literature. A torr is defined as 1 mm Hg. Thus, 10 –5 torr is the same as 10 –5 mm Hg. Another unit of pressure used in vacuum work is the micron, μ. A micron is defined as one thousandth of 1 mm Hg, so 10 –3 mm Hg is equal to 1 μ.

ILLUSTRATIVE PROBLEM 1.9 A mercury manometer (vacuum gauge) reads 26.5 in. of vacuum when the local barometer roads 30.0 in. Hg at standard temperature. Determine the absolute pressure in psia. SOLUTION

p = (30.0 – 26.5) in. Hg absolute

and from Illustrative Problem 1.7, 1 in. Hg exerts a pressure of 0.491 psi. Thus,

p = (30 – 26.5)(0.491) = 1.72 psia

If the solution is desired in psfa, it is necessary to convert from square inches to square feet. Because there are 12 in. in 1 ft., there will be 144 in.2 in 1 ft.2. Thus, the conversion to psfa requires that psia be multiplied by 144. This conversion is often necessary to keep the dimensions of equations consistent.

34

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 1.10 A column of fluid is 10 m high. If its density is 2000 kg/m3, determine the pressure at the base of the column if it is located in a local gravity of 9.6 m/s2. SOLUTION Applying Equation 1.20a gives us p = −ρgh = −2000



kg m × 9.6 2 × −10 m = 192 kPa m3 s

The height is negative, because it is measured up from the base.

ILLUSTRATIVE PROBLEM 1.11 Using the data of Illustrative Problem 1.9, determine the absolute pressure in kPa. SOLUTION As before, p = (30 – 26.5) = 3.5 in. Hg absolute. Using “standard” temperature yields 3.5 in. × 12

ft. lb × (13.6 × 62.4) 3f 12 in. ft. in. ft.

2

× 0.0254

m in.

2

×

kg N × 9.806 = 11.875 kPa 2.2 lbf kg

Note: 11.875 × 1000/6895 = 1.72 psia, which checks with Illustrative Problem 1.9.

In performing any measurement, it is necessary to have a standard of comparison in order to calibrate the measuring instrument. In the following paragraphs, five pressure standards currently used as the basis for all pressure measurement work will be discussed. Table 1.9 summarizes these standards, the pressure range in which they are used, and their accuracy. Figure 1.17 shows the basic pressure-measurement concepts on which all pressure standards are based. TABLE 1.9 Characteristics of Pressure Standards Type Dead-weight piston gauge Manometer Micro manometer Barometer McLeod gauge

Range

Accuracy

0.01 to 10,000 psig 0.01 to 100 psig 0.0002 to 20 in. H2O 27 to 31 in. Hg 0.01 μm to 1 mm Hg

0.01 to 0.05% of reading 0.02 to 0.2% of reading 1% of reading to 0.001 in. H2O 0.001 to 0.03% of reading 0.5 to 3% of reading

35

Fundamental Concepts

Datum 1

F

1

Fluid

1

F

1

F 1

h

1

Static fluid

Static fluid (lb./in.2,

Pressure is the normal force F lb./ft.2, dynes/cm2) exerted on a unit area of a surface bounding a fluid.

F2 h2

h1

Weight of element

F1

Variation of fluid pressure with elevation is found by balancing the forces 2 on a static-fluid element (F1 is equal to 1 F2 plus the weight of the element). For a constant-density fluid, the pressure difference p2 _ p1 is equal to the specific weight times (h2 _ h1).

F1

Fluid pressure varies with depth, but is the same in all directions at a given depth.

Level 2

h

Pressure is independent of the shape and size of the vessel. The pressure difference between level 1 and level 2 is always p _ 1

p2 = h, where is the specific weight of the constant-density fluid in the vessel.

F2 A1

Fluid

Level 1

Fluid

Gauge A2

Piston

Known W weight

A

Fluid Supply pressure

Constant pressure transmission in a confined fluid can be used to multiply force by the relative p = F1/A1 = F2/A2.

When the known weight is balanced, the gauge pressure is p = W/A; this is the basic principle of dead-weight testing.

FIGURE 1.17 Basic pressure-measurement concepts.

1.6.1 Dead-Weight Piston Gauge The dead-weight free-piston gauge consists of an accurately machined piston inserted into a close-fitting cylinder. Masses of known weight are loaded on one end of the free piston, and pressure is applied to the other end until enough force is developed to lift the piston– weight combination. When the piston is floating freely between the cylinder limit stops,

36

Thermodynamics and Heat Power

Deadweight gauge

Test gauge

System pressure

Inlet valve

Variable portion of system volume

Vent valve

Atmosphere Movable piston

FIGURE 1.18 Pressure volume regulator to compensate for fluid leakage in a dead weight gauge.

the gauge is in equilibrium with the unknown system pressure. The dead-weight pressure can then be defined as

pdw =

Fe (1.21) Ae

where Fe is the equivalent force of the piston–weight combination, dependent on such factors as local gravity and air buoyancy, and Ae is the equivalent area of the piston–cylinder combination, dependent on such factors as piston–cylinder clearance, pressure level, and temperature. A fluid film provides the necessary lubrication between the piston and cylinder. In addition, the piston, or less frequently the cylinder, may be rotated or oscillated to reduce friction even further. Because of fluid leakage, system pressure must be continuously trimmed upward to keep the piston–weight combination floating. This is often achieved by decreasing the system volume using a pressure–volume apparatus (as shown in Figure 1.18). As long as the piston is freely balanced, system pressure is  defined  by Equation 1.21. Corrections must be applied to the indication of the dead-weight piston gauge pi to obtain the accurate system pressure pdw. The two most important corrections concern air buoyancy and local gravity. The effective area of the dead-weight piston gauge is usually taken as the mean of the cylinder and piston areas, but temperature affects this dimension. The effective area increases between 13 and 18 ppm (parts per million)/°F for commonly used materials, and a suitable correction for this effect may also be applied. 1.6.2 Manometer We have already shown that the pressure at the base of a column of liquid is simply a function of the height of the column and the specific weight of the liquid. Therefore, the height of a column of liquid of known specific weight can be and is used to measure pressure and pressure differences. Instruments that utilize this principle are known as manometers, and the study of these pressure-measuring devices is known as manometry. By properly arranging a manometer and selecting the fluid judiciously, it is possible

37

Fundamental Concepts

pu

pa

h A

A

FIGURE 1.19 U-tube manometer.

to measure extremely small pressures, very large pressures, and pressure differences. A simple manometer is shown in Figure 1.19, where the right arm is exposed to the atmosphere while the left arm is connected to the unknown pressure. As shown, the fluid is depressed in the left arm and raised in the right arm until no unbalanced pressure forces remain. It has already been demonstrated that the pressure at a given level in either arm must be the same so that we can select any level as reference and write a relation for the pressure. Actually, it is much easier and more convenient to select the interface between the manometer fluid and the unknown fluid as a common reference level. In Figure 1.19, the pressure at elevation AA is the same in both arms of the manometer. Starting with the open manometer arm (right), we have atmospheric pressure pa acting on the fluid. As one proceeds down the arm, the pressure increases until we arrive at level AA, where the pressure is pa + γh. This pressure must equal the unknown pressure on the connected arm pu. Therefore,

pu = pa + γh (1.22)

or

pu – pa = γh (1.23)

Temperature and capillary effects must be considered for accurate pressure measurements. To minimize the effect of a variable meniscus, which can be caused by dirt, the method of approaching equilibrium, tube bore, and so on, the tubes are always tapped before reading, and the measured liquid height is always based on readings taken at the center of the meniscus in each leg of the manometer. To reduce the capillary effect itself, the use of large-bore tubes (more than 3/8 in. diameter) is most effective. To achieve greater accuracy and sensitivity in manometers, several different arrangements have been used. Perhaps the simplest of these is the inclined manometer. Consider a relatively large reservoir of liquid connected to a small-bore tube that makes an angle θ with the horizontal. The pressure or pressure differential to be measured is connected to the large reservoir; the inclined tube is open ended. Schematically, this is shown in Figure 1.20. The unknown pressure pu is given by

pu = pa + γh (1.24)

38

Thermodynamics and Heat Power

Specific weight =

pu

pa

h´ h

FIGURE 1.20 Inclined manometer.

or

pu – pa = γh (1.25)



pu – pa = γh′ sin θ (1.26)

Because θ is fixed, a scale placed along the tube can be calibrated to read directly in units of h of a fluid. Usually, this is done by directly reading inches of water for pu – pa. Another method of achieving greater sensitivity and accuracy is to use a manometer with more than one fluid. The manometer shown in Figure 1.21 can be used for this purpose by properly selecting the manometer fluid. Starting at level A, we have

PA – hγ1 – yγ3 + hγ2 = pB (1.27)

or PA – PB = (–hBγ2 + hAγ1) + yγ3 (1.28)



In the usual case, the manometer is connected to different positions on the same pipe. Thus, A and B would be at the same level, and γ1 can be taken to be equal to γ2. Also, hB – hA = y. Thus, PA – PB ≃ y(γ3 – γ1) or y(γ3 – γ2) (1.29)



1 3

hA

2

A B FIGURE 1.21 Three-fluid manometer.

hB

39

Fundamental Concepts

Note that when you go down in a fluid column, you add hγ, and when you go up a fluid column, you subtract hγ. One can start at either end of the system and work around to the other end. Also, note that most manometer problems refer to the fluid’s specific gravity rather than its specific weight. Thus γ = sg × 62.4 lb./ft.3 in the English system and γ = sg × 9.81 kN/m3 in SI units. For small differences in pA – pB, it is apparent that the manometer fluid (γ3) should have a specific weight very nearly equal to the specific weight of the fluid in the pipes. For large pressure differences, one can use a heavy fluid such as mercury to increase y3 – y2 and reduce the manometer reading.

ILLUSTRATIVE PROBLEM 1.12 For the manometer shown in Figure 1.22, find the absolute pressure at point A and the nominal pressure in the water pipe. SOLUTION Starting at the top of the manometer open to the atmosphere, p = 100 kPa. Going down the column of 1.2 m of 0.8 sg oil adds (γh)oil = 0.8 × 9.81 × 1.2 = 9.418 kPa, so the pressure at A is 109.418 kPa. Continuing around the manometer until the water pipe is reached, we add 0.3 m of mercury, subtract 1.6 m of oil, and add 1.5 m of water. The net result is 109.418 + 13.6 × 9.81 × 0.3 – 0.8 × 9.81 × 1.6 + 1 × 9.81 × 1.5 = 151.6 kPa.

Oil SG = 0.8

atm (100 kPa) Oil SG = 0.8

Water 1.5 m

1.2 m 1.6 m

Water pipe

A 0.3 m

Mercury SG = 13.6 FIGURE 1.22 Illustrative Problem 1.12.

40

Thermodynamics and Heat Power

A word on the reference pressures employed in manometry is pertinent at this point in the discussion. If atmospheric pressure is used as a reference, the manometer yields gauge pressures. Because of the variability of air pressure, gauge pressures vary with time, altitude, latitude, and temperature. If, however, a vacuum is used as reference, the manometer yields absolute pressures directly, and it may serve as a barometer. In any case, the absolute pressure is always equal to the sum of the gauge and ambient pressures; by ambient pressure, we mean the pressure surrounding the gauge, which is usually atmospheric pressure. 1.6.3 Micromanometer While the manometer is a useful and convenient tool for pressure measurements, it is unfortunately limited when making low-pressure measurements. To extend its usefulness in the low-pressure range, micromanometers have been developed that have extended the useful range of low-pressure manometer measurements to pressures as low as 0.0002 in. H2O. One type is the Prandtl-type micromanometer, in which capillary and meniscus errors are minimized by returning the meniscus of the manometer liquid to a null position before measuring the applied pressure difference. As shown in Figure 1.23, a reservoir, which forms one side of the manometer, is moved vertically to locate the null position. This position is reached when the meniscus falls within two closely scribed marks on the nearhorizontal portion of the micromanometer tube. Either the reservoir or the inclined tube is then moved by a precision lead-screw arrangement to determine the micromanometer liquid displacement (Δh), which corresponds to the applied pressure difference. The Prandtltype micromanometer is generally accepted as a pressure standard within a calibration uncertainty of 0.001 in. H2O. Another method for minimizing capillary and meniscus effects in manometry is to measure liquid displacements with micrometer heads fitted with adjustable, sharp index points. Figure 1.24 shows a manometer of this type; the micrometers are located in two connected, transparent containers. In some commercial micromanometers, contact with the surface of the manometric liquid may be sensed visually by dimpling the surface with p2

p1

p2

p1

p2

p1

Meniscus Scribed marks

h

Inclined tube

Reservoir

h

Flexible connector tube Reference position

Movable reservoir

FIGURE 1.23 Two variations of the Prandtl-type micromanometer.

Movable inclined tube

41

Fundamental Concepts

p1

p2

Micrometer heads Large-bore tubes

Movable pointed index

h

FIGURE 1.24 Micrometer-type manometer.

the index point, or even by electrical contact. Micrometer-type micromanometers also serve as pressure standards within a calibration uncertainty of 0.001 in. H2O. An extremely sensitive, high-response micromanometer uses air as the working fluid and thus avoids all the capillary and meniscus effects usually encountered in liquid manometry. In this device, as shown in Figure 1.25, the reference pressure is mechanically amplified by centrifugal action in a rotating disk. The disk speed is adjusted until the amplified reference pressure just balances the unknown pressure. This null position is recognized by observing the lack of movement of minute oil droplets sprayed into a glass indicator tube. At balance, the air micromanometer yields the applied pressure difference as Δpmicro = Kpn2

(1.30)

where p is the reference air density, n is the rotational speed of the disk, and K is a constant that depends on disk radius and annular clearance between the disk and the housing. Measurements of pressure differences as small as 0.0002 in. H2O can be made with this type of micromanometer within an uncertainty of 1%. Atomized oil droplets

Rotating disk Mercury seal

Unknown pressure

Balance indicator tube

FIGURE 1.25 Air-type centrifugal micromanometer.

Amplified reference pressure Mercury seal

Stationary housing Reference pressure

42

Thermodynamics and Heat Power

1.6.4 Barometers The reservoir or cistern barometer consists of a vacuum-reference mercury column immersed in a large-diameter, ambient-vented mercury column that serves as a reservoir. The most common cistern barometer in general use is the Fortin type, in which the height of the mercury surface in the cistern can be adjusted. The operation of this instrument can best be explained with reference to Figure 1.26. The datum-adjusting screw is turned until the mercury in the cistern makes contact with the ivory index, at which point the mercury surface is aligned with zero on the instrument scale. Next, the indicated height of the mercury column in the glass tube is determined. The lower edge of a sighting ring is lined up with the top of the meniscus in the tube. A scale reading and a vernier reading are taken and combined to yield the indicated height at the barometer temperature. Because atmospheric pressure on the mercury in the cistern is exactly balanced by the weight per unit area of the mercury column in the glass tube, pbaro = γHghto (1.31)



The referenced specific weight of mercury, γHg, depends on such factors as temperature and local gravity; the referenced height of mercury, hto, depends on such factors as thermal expansion of the scale and the mercury.

Closed end, vacuum-referred Reading level

Glass tube

Glass-cylinder ambient-vented cistern

Ivory index point

Leather sac

Datum adjusting screw FIGURE 1.26 Fortin barometer.

43

Fundamental Concepts

Other factors may also contribute to the uncertainty of hto. Proper illumination is essential to define the location of the crown of the meniscus. Precision meniscus sighting under optimum viewing conditions can approach ±0.001 in. With proper lighting, contact between the ivory index and the mercury surface in the cistern can be detected to much better than ±0.001 in. To keep the uncertainty in hto within 0.01% (≃0.003 in. Hg), the mercury temperature must be taken within ±1°F. Scale temperature need not be known to better than ±10°F for comparable accuracy. Uncertainties caused by nonequilibrium temperature conditions can be avoided by installing the barometer in a uniform temperature room. The barometer tube must be vertically aligned for accurate pressure determination. This is accomplished by a separately supported ring encircling the cistern; adjustment screws control the horizontal position. Depression of the mercury column in commercial barometers is accounted for in the initial calibration setting at the factory. The quality of the barometer is largely determined by the bore of the glass tube. Barometers with a bore of 1/4 in. are suitable for readings of about 0.01 in. Hg, whereas barometers with a bore of 1/2 in. are suitable for readings down to 0.002 in. Hg. 1.6.5 McLeod Gauge The McLeod gauge is used in making low-pressure measurements. This instrument (shown in Figure 1.27) consists of glass tubing arranged so that a sample of gas at unknown pressure can be trapped and then isothermally compressed by a rising mercury column. This amplifies the unknown pressure and allows measurement by conventional manometric Unknown pressure p1 Trapped gas sample at pressure p2 Tubes of area a

hc

Zero level

h

B C V

Capillary depression A

Cutoff

Mercury reservoir FIGURE 1.27 McLeod gauge.

44

Thermodynamics and Heat Power

means. All the mercury is initially contained in the area below the cutoff level. The gauge is first exposed to the unknown gas pressure, p1; the mercury is then raised in tube A beyond the cutoff, trapping a gas sample of initial volume V1 = V + ahc. The mercury is continuously forced upward until it reaches the zero level in the reference capillary B. At this time, the mercury in the measuring capillary C reaches a level h, where the gas sample is at its final volume, V2 = ah, and at the amplified pressure, p2 = p1 + h. Then,

p1V1 = p2V2 (1.32)



p1 =

ah2 (1.33) V1 − ah

If ah  V1, as is usually the case,

p1 =

ah2 (1.34) V1

The larger the volume ratio (V1/V2 ), the greater the amplified pressure p2 and manometer reading h. Therefore, it is desirable that measuring tube C have a small bore. Unfortunately, for tube bores less than 1 mm, the compression gain is offset by reading uncertainty caused by capillary effects. Reference tube B is introduced to provide a meaningful zero for the measuring tube. If the zero is fixed, Equation 1.34 indicates that manometer indication h varies nonlinearly with initial pressure p1. A McLeod gauge with an expanded scale at the lower pressures exhibits a higher sensitivity in this region. The McLeod pressure scale, once established, serves equally well for all the permanent gases (those whose critical pressure is appreciably less than room temperature). There are no corrections to be applied to the McLeod gauge reading, but certain precautions should be taken. Moisture traps must be provided to avoid taking any condensable vapors into the gauge. Such vapors occupy a larger volume at the initial low pressures than they occupy in the liquid phase at the high reading pressures. Thus, the presence of condensable vapors always causes pressure readings to be too low. Capillary effects, while partially counterbalanced by using a reference capillary, can still introduce significant uncertainties, because the angle of contact between mercury and glass can vary by ±30°. Finally, because the McLeod gauge does not give continuous readings, steady-state conditions must prevail for the measurements to be useful. In the earlier portions of this section, we discussed five pressure standards that can be used for either calibration or measurement of pressure in static systems. In the following, we discuss some common devices that are used for making measurements using an elastic element to convert fluid energy to mechanical energy. Such a device is known as a pressure transducer Examples of mechanical pressure transducers having elastic elements only are dead-weight free-piston gauges, manometers, Bourdon gauges, bellows, and diaphragm gauges. Electrical transducers have an element that converts their displacement to an electrical signal. Active electrical transducers generate their own voltage or current output as a function of displacement. Passive transducers require an external signal. The piezoelectric pickup is an example of an active electrical transducer. Electric elements employed in

45

Fundamental Concepts

passive electrical pressure transducers include strain gauges, slide-wire potentiometers, capacitance pickups, linear differential transformers, and variable-reluctance units. In the Bourdon gauge, the elastic element is a small-volume tube that is fixed at one end but free at the other end to allow displacement under the deforming action of the pressure difference across the tube walls. In the most common model, shown in Figure 1.28, a tube with an oval cross-section is bent in a circular arc. Under pressure, the tube tends to become circular, with a subsequent increase in the radius of the arc. By an almost frictionless linkage, the free end of the tube rotates a pointer over a calibrated scale to give a mechanical indication of pressure. The reference pressure in the case containing the Bourdon tube is usually atmospheric, so that the pointer indicates gauge pressures. Absolute pressures can be measured directly without evacuating the complete gauge casing by biasing a sensing Bourdon tube against a reference Bourdon tube, which is evacuated and sealed as shown in Figure 1.29. Bourdon gases are available for a wide range of absolute gauge and differential pressure measurements within a calibration uncertainty of 0.1% of the reading. Another common elastic element used in pressure transducers is the bellows, shown as a gauge element in Figure 1.30. In one arrangement, pressure is applied to one side of a bellows, and the resulting deflection is partially counterbalanced by a spring. In a differential arrangement, one pressure is applied to the inside of one sealed bellows, and the pressure difference is indicated by a pointer.

Spring Oval cross-section

Hairspring

Free closed end

Pinion

Sector

30

Adjustable link

20

10 0

Movement plate

Dial Fixed open end

Stem

Applied pressure FIGURE 1.28 Bourdon gauge.

46

Thermodynamics and Heat Power

Reference Bourdon tube sealed at zero absolute pressure Case open to atmospheric pressure Pointer movement

Sensing Bourdon tube

Pinion and sector gauge movement

Applied pressure FIGURE 1.29 Bourdon gauge for absolute pressure measurement.

Scale

Pointer Pinion and sector gauge movement Connecting link Spring

Bellows Case

Applied pressure FIGURE 1.30 Bellows gauge.

47

Fundamental Concepts

Diaphragms in form of capsule

Pointer movement

Pinion and sector gauge movement

Case pressure

Dished

Applied pressure

Flat

Corrugated

FIGURE 1.31 Diaphragm-based pressure transducer.

A final elastic element to be mentioned because of its widespread use in pressure transducers is the diaphragm. One such arrangement is shown in Figure 1.31. Such elements may be flat, corrugated, or dished plates; the choice depends on the strength and amount of deflection desired. In high-precision instruments, a pair of diaphragms is used back to back to form an elastic capsule. One pressure is applied to the inside of the capsule; the other pressure is external. The calibration of this differential transducer is relatively independent of pressure magnitude. Thus far, we have discussed a few mechanical pressure transducers. In many applications, it is more convenient to use transducer elements that depend on the change in the electrical parameters of the element as a function of the applied pressure. The only active electrical pressure transducer in common use is the piezoelectric transducer. Sound-pressure instrumentation makes extensive use of piezoelectric pickups in such forms as hollow cylinders and disks. Piezoelectric pressure transducers are also used in measuring rapidly fluctuating or transient pressures. In a recently introduced technique called electrocalibration, the transducer is calibrated by electric field excitation rather than by physical pressure. The most common passive electrical pressure transducers are the ­variable-resistance types. The strain gauge is probably the most widely used pressure transducer element. Strain gauges operate on the principle that the electrical resistance of a wire varies with its length under load. In unbounded strain gauges, four wires run between electrically insulated pins located on a fixed frame and other pins located on a movable armature, as shown in Figure 1.32. The wires are installed under tension and form the legs of a bridge circuit.

48

Thermodynamics and Heat Power

Strain-sensitive wires

Movable armature

Applied pressure Clamped elastic element

Electrically insulated pins

Fixed frame

FIGURE 1.32 Typical unbonded strain gauge.

Under pressure, the elastic element (usually a diaphragm) displaces the armature, causing two of the wires to elongate while reducing the tension in the remaining two wires. The resistance change causes a bridge imbalance proportional to the applied pressure. The bonded strain gauge takes the form of a fine wire filament set in cloth, paper, or plastic and fastened by a suitable cement to a flexible plate, which takes the load of the elastic element. This is shown in Figure 1.33. Two similar strain gauge elements are often connected in a bridge circuit to balance unavoidable temperature effects. The nominal bridge output impedance of most strain gauge pressure transducers is 350 ohms (Ω), nominal Elastic element

Applied pressure Lead wires fastened to plate

Plunger

Filament wires to bridge

To bridge

Flexible plate

FIGURE 1.33 Typical bonded strain gauge.

Gauge, cemented to plate

49

Fundamental Concepts

excitation voltage is 10 V (alternating current [ac] or direct current [dc]), and natural frequency can be as high as 50 Hz. Transducer resolution is infinite, and the usual calibration uncertainty of such gauges is within 1% of full scale. Many other forms of electrical pressure transducers are in use in industry, and a few of these will be discussed briefly. These elements fall under the categories of potentiometer, variable capacitance, linear variable differential transformer (LVDT), and variable-­ reluctance transducers. The potentiometer operates as a variable-resistance pressure transducer. In one arrangement, the elastic element is a helical Bourdon tube, while a precision, wire-wound potentiometer serves as the electric element. As pressure is applied to the open end of the Bourdon tube, it unwinds, causing the wiper (connected directly to the closed end of the tube) to move over the potentiometer. In the variable-capacitance pressure transducer, the elastic element is usually a metal diaphragm that serves as one plate of a capacitor. Under an applied pressure, the diaphragm moves with respect to a fixed plate. By means of a suitable bridge circuit, the variation in capacitance can be measured and related to pressure by calibration. The electric element in an LVDT is made up of three coils mounted in a common frame to form the device shown in Figure 1.34. A magnetic core centered in the coils is free to be displaced by a bellows, Bourdon, or diaphragm elastic element. The center coil, the primary winding of the transformer, has an ac excitation voltage impressed across it. The two outside coils form the secondaries of the transformer. When the core is centered, the induced voltages in the two outer coils are equal and 180° out of phase; this represents the zero-pressure position. However, when the core is displaced by the action of an applied pressure, the voltage induced in one secondary increases while that in the other decreases. The output voltage difference varies essentially linearly with pressure for the small core displacements allowed in these transducers. The voltage difference is measured and related to the applied pressure by calibration. The last elastic element to be discussed is the variable-reluctance pressure transducer. The basic element of the variable-reluctance pressure transducer is a movable magnetic vane in a magnetic field. In one type, the elastic element is a flat magnetic diaphragm located between two magnetic output coils. Displacement of the diaphragm changes the inductance ratio between the output coils and results in an output voltage proportional to pressure. Output voltage Displacement

Primary coil

Magnetic core Common frame Secondary coil 1

Secondary coil 2

AC input voltage FIGURE 1.34 Linear variable differential transformer.

Elastic element

50

Thermodynamics and Heat Power

1.7 Review After defining thermodynamics as the study of the conversion of one form of energy to another, we started our study by setting forth certain concepts concerning systems and properties. A system is any grouping of matter taken in a convenient or arbitrary manner, whereas a property is an observable characteristic that is determined by the state of a system and, in turn, aids in determining the state of a system. The condition of a system, described by its position, energy, and so on, is called the state of the system. We studied in detail the properties of temperature and pressure and the methods used to measure them. Because both the English and SI systems of units are used, we are required to have facility in each. This caused us to spend some time in establishing and defining the basic rules and styles of these systems. Using elementary kinetic theory, we were able to quantify the concepts of pressure, temperature, density, specific weight, specific volume, and Avogadro’s number. Some of the material covered in this chapter may have been covered in other courses and may appear to be elementary. It cannot be emphasized strongly enough that this material must be fully mastered before proceeding further. You are urged to be sure of all the units used in any equation and to be equally sure of the meaning of all terms. Problems at the end of the chapters are included to develop a better level of understanding through the application of the text material. Reading and studying alone are not sufficient. The ability to apply the material studied indicates that you have really mastered it and are not just repeating material from memory.

Key Terms Terms used for the first time in this chapter are as follows: Avogadro’s law: Equal volumes of gases at the same temperature and pressure contain the same number of particles. density: Mass per unit of volume. micron (μ): 10 –3 mm of mercury A unit of pressure used in vacuum systems. pressure: Normal force per unit of area. property: An observable characteristic of state that is determined by the state and, in turn, aids in determining the state of the system. It is not dependent on the path or the means of attaining the state. specific gravity: The ratio of the density of a substance to the density of water at 4°C. It can also be defined as the ratio of the specific weight of a substance to the specific weight of water at 4°C. In the older cgs system, the density of water at 4°C is 1 g/cm3, making specific gravity numerically equal to density in this system. specific volume: The reciprocal of density, that is, the volume per unit mass. specific weight: Weight per unit of volume. state: The condition of a system that fixes the position and the energy stored in the system and is identified by the properties of the system. system: A grouping of matter taken in any convenient or arbitrary manner. temperature: The temperature of a system is a measure of the random motion of the molecules of the system. The Celsius, Fahrenheit, Kelvin, and Rankine temperature

51

Fundamental Concepts

scales represent the conventional and absolute temperature scales, respectively. Celsius and Kelvin are SI units, and Fahrenheit and Rankine are English units. thermodynamics: The study of energy, heat, work, the properties of the media employed, and the processes used; also the study of the conversion of one form of energy to another. torr: A unit of pressure equal to 1 mm of Hg. weight: The force of attraction between a body and the Earth or another planet or moon. zeroth law of thermodynamics: When two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with one another.

Equations Developed in This Chapter Temperature conversion

°C =

5 (°F − 32) 9

(1.1)

Temperature conversion

°F =

9 (°C) + 32 5

(1.2)

Temperature conversion

°F =

9 ( 40 + °C) − 40 5

(1.3)

Temperature conversion

°C =

5 (40 + °F) − 40 9

(1.4)

Absolute temperature Absolute temperature

Degrees Rankine = °R = °F + 460 Degrees Kelvin = K = °C + 273

(1.5) (1.6)

Force–mass relation

F=

ma gc

(1.9)

Weight–mass relation

w=

mg gc

(1.10)

Weight–mass relation (SI)

w = mg

Ideal gas relation

Ideal gas relation (SI) Absolute pressure Absolute pressure Pressure–height relation

pV =

(1.10a) 2 x

1 mnV 3 gc

pV =

1 mnVx2 3

Absolute pressure = atmospheric pressure + gauge pressure Absolute pressure = atmospheric pressure – vacuum p = –γh

(1.14)

(1.14a) (1.16) (1.17) (1.19a)

Pressure–height relation

p=

−ρg h gc

(1.20)

Pressure–height relation

p = –ρgh

(1.20a)

52

Thermodynamics and Heat Power

QUESTIONS 1.1 Indicate which of the following are or are not properties: (a) location, (b) velocity, (c) time, (d) weight, or (e) size. 1.2 Would you expect that your weight would be (a) greater, (b) less, or (c) equal to your Earth weight on the planet Jupiter? Why? 1.3 State on which factor or factors the pressure at the bottom of a column of liquid depends: (a) its height, (b) the specific weight of the fluid, (c) the local acceleration of gravity, or (d) the cross-sectional area of the column. 1.4 What temperature does a thermometer measure? 1.5 What condition or conditions must exist if a thermometer is to measure a person’s temperature accurately? 1.6 If a thermometer measures a temperature difference of 10°C, what is the temperature difference in K? 1.7 If a thermocouple measures a temperature difference of 5°F, what is the temperature difference in °R? 1.8 Comment on the fact that commodities such as bread and meat are sold by the kilo (kilogram) in many countries of the world. 1.9 The unit of 100 is not a recommended unit in the SI system. Comment on whether it would or would not have been desirable to define the pascal as N/cm2. 1.10 If an equation is not dimensionally consistent, is it necessarily incorrect? Why? 1.11 If the average velocity of the molecules in a box is doubled, would you expect that its pressure would (a) double, (b) stay the same, (c) be four times greater, or (d) be indeterminate? 1.12 What is temperature a measure of? 1.13 How are density and specific volume related? 1.14 A student states that the use of a digital readout will increase the accuracy of an instrument. Comment on this statement. 1.15 What must be done to establish the accuracy of any instrument? PROBLEMS More difficult problems are preceded by an asterisk (*) in this chapter and in all following chapters. Unless indicated otherwise, use g = 32.17 ft./s2 or 9.806 m/s2, and use patm = 14.696 psia or 101.325 Pa. Also, use gc = 32.174 lbm·ft./lbf·s2. Problems Involving Conversion of Units 1.1 Convert a length of 15 ft. to meters. 1.2 Convert 3.85 in. to centimeters. 1.3 Convert 90.68 cm to inches. 1.4 Convert 5787 lb. to tons. 1.5 Convert 6.3 tn. to pounds. 1.6 Convert 35.4 in. to feet. 1.7 Convert 3.87 ft. to inches.

Fundamental Concepts

1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40

Convert 8.6 lb. to grams. Convert 462 g to pounds. Convert 2 td. 2 ft. 5 in. to centimeters. Convert 550 mi./h to m/s. Convert a flow rate of 2000 ft.3/min to L/s. Convert 200 gal./h (gph) to m3/s.4 Convert 200 gph to L/s. Convert 200 gph to L/min. Convert 200 L/min to m3/s. Convert 200 gpm to L/min. Convert 50.7 cm3/s to m3/s. Convert 861 gpm to L/min. Convert 1.71 m3/s to L/min. Convert 100 m3/s to gpm. Convert 3.52 ft.3/s to gpm. Convert 3.52 ft.3/s to m3/s. Convert 150 gpm to m3/s. Convert 6.52 m3/s to gpm. Convert 3.65 m3/s to L/s. Convert 1.2 ft.3/s to gpm. Convert 4.8 ft.3/s to L/s. Convert 101 kPa (kN/m2) to lbf/in.2. A rectangle has the dimensions of 12 in. × 10 in. Calculate its area in square meters. A rectangle has the dimensions of 2 m × 3.5 m. Determine the area of the rectangle in square inches. A box has the dimensions 12 in. × 12 in. × 6 in. How many cubic meters are there in the box? A cylinder has a diameter of 10 cm and a height of 25 cm. Determine its volume in cubic meters. A cylinder has a diameter of 5 in. and a height of 10 in. Determine its volume in cubic meters. A cube is made 8 in. on a side. Calculate its volume in cubic meters. An automobile engine has a displacement of 240 in.3. Determine its displacement in liters. A car is claimed to obtain a fuel usage in Europe of 12 km/L. Determine its equivalent fuel usage in mi./gal. A driveway requires 38 yd.3 of concrete. How many m3 of concrete does this correspond to? A man weighs 175 lb. and stands 6 ft. 0 in. tall. What is his weight in newtons and his height in meters? A barrel of oil contains 55 gal. If a gallon is a volume of 231 in.3, determine the volume of 15 bbl. in cubic meters.

53

54

Thermodynamics and Heat Power

*1.41 A gallon is a measure of volume that equals 231 in.3, so determine the number of liters in a gallon. Note that the liter is sometimes called the metric quart. Does your answer support this name? 1.42 A 1500-m race is often called the “metric mile.” What part of a mile (5280 ft.) is the metric mile? 1.43 A car is operated at 50 mi./h. How many feet per second does this correspond to? 1.44 A car travels at 64 km/h. What is the speed of the car in mi./h? 1.45 A car weighs 2650 lb. and is 18 ft. long. What are its weight in kilonewtons and its length in meters? 1.46 A block of metal weighing 1200 lb. is hung from the end of a vertical rod, and it causes the rod to lengthen 0.001 in. Express these data in terms of newtons and meters. 1.47 Is one gigapascal (GPa) equal to (a) 106 Pa, (b) 108 Pa, (c) 103 Pa, (d) 109 Pa, or (e) none of these? Problems Involving Temperature 1.48 Convert 20°C, 40°C, and 60°C to equivalent degrees Fahrenheit. 1.49 Change 0°F, 10°F, and 50°F to equivalent degrees Celsius. 1.50 Convert 500°R, 500 K, and 650°R to degrees Celsius. 1.51 Derive a relation between degrees Rankine and degrees Kelvin, and based on the results, show that (°C + 273)1.8 = °F + 460. *1.52 If a Fahrenheit temperature is twice a Celsius temperature, determine both temperatures. *1.53 If a Celsius temperature is 2/3 of a Fahrenheit temperature, determine both temperatures. *1.54 Fahrenheit and Celsius thermometers are used to measure the temperature of a fluid. If the Fahrenheit reading is 1.5 times the Celsius reading, what are both readings? *1.55 An arbitrary temperature scale is proposed in which 20° is assigned to the ice point and 75° is assigned to the boiling point. Derive an equation relating this scale to the Celsius scale. *1.56 For the temperature scale proposed in Problem 1.55, what temperature corresponds to absolute zero? *1.57 A new thermometer scale on which the freezing point of water at atmospheric pressure would correspond to a marking of 200 and the boiling point of water at atmospheric pressure would correspond to a marking of minus 400 is proposed. What would the reading of this new thermometer be if a Fahrenheit thermometer placed in the same environment read 80°? Problems Involving Mass and Weight 1.58 A mass of 5 kg is placed on a planet whose gravitational force is 10 times that of Earth. What does it weigh on this planet? 1.59 A mass of 10 kg weighs 90 N. Is the acceleration of gravity at this location equal to (a) 1/9 m/s2, (b) 9.0 m/s2, (c) 90 m/s2, (d) 10 m/s2, or (e) none of these? 1.60 At a location on Earth where g = 32.2 ft./s2, a body weighs 161 lb. At another location where g = 32.0, how much will the same body weigh: (a) 161 lb., (b) 162 lb., (c) 160 lb., (d) 163 lb., or (e) none of these?

Fundamental Concepts

1.61 A body at mean sea level weighs 100 lb. (g = gc). Estimate the weight of this body at an elevation of 7500 ft.. Assume that the mean diameter of the Earth is 12,742 km. *1.62 A mass of 100 kg weighs 980.6 N at sea level. Estimate the weight of this body at the top of a mountain 5 km high. Assume that the mean diameter of the Earth is 12,742 km. *1.63 A balance-type scale is used to weigh a sample on the moon. If the value of g is 1/6 of Earth’s gravity and the “standard” weights (Earth weights) add up to 20 lb., what is the mass of the body? *1.64 A balance-type scale is used to weigh a sample on the moon. If the value of g is 1/6 of Earth’s gravity and the “standard” weights (Earth weights) add up to 100 N, what is the mass of the body? *1.65 Solve Problem 1.64 if a spring balance is used that was calibrated on Earth and reads 20 lb. *1.66 Solve Problem 1.64 if a spring balance is used that was calibrated on Earth and reads 100 N. *1.67 A mass of 100 kg is hung from a spring in a local gravitational field where g = 9.806 m/s2, and the spring is found to deflect 25 mm. If the same mass is taken to a planet where g = 5.412 m/s2, how much will the spring deflect if its deflection is directly proportional to the applied force? *1.68 The mass of the planet Mars is 0.1069 relative to Earth, and its diameter is 0.523 relative to Earth. What is the weight of a pound of mass on Mars? *1.69 A body having an unknown mass “weighs” 1 lb. on the planet Jupiter. Jupiter has a mass 318.35 times that of Earth, and its diameter is 10.97 times larger: (a) What will the body weight on Earth be? (b) What is the mass of the body? *1.70 Solve Problem 1.68 for a mass of 10 kg. *1.71 Solve Problem 1.69 for a weight of 10 Newtons on Jupiter. Problems Involving Newton’s Second Law, F = ma 1.72 A force of 100 N acts horizontally on a 10-kg body. What is its horizontal acceleration? 1.73 An unbalanced force in pounds equal numerically to the weight of a body in pounds causes the body to accelerate. What is its acceleration? 1.74 If a body is accelerating at the rate of 5 m/s2 when acted on by a net force of 10 N, determine its mass. 1.75 A body has a mass of 321.7 lb. and is accelerated at the rate of 5 ft./s2. Determine the magnitude of the unbalanced force acting on it. 1.76 A mass of 2 kg has an acceleration of 1.2 m/s2. Calculate the magnitude of the unbalanced force acting on it. 1.77 What is the acceleration of a body if a net force of 25 lb. acts on it if its mass is 160.8 lb.? Problems Involving Specific Weight, Specific Volume, and Specific Gravity 1.78 Determine the density and specific volume of the contents of a 10-ft.3 tank if the contents weigh 250 lb.

55

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Thermodynamics and Heat Power

1.79 A tank contains 500 kg of a fluid. If the volume of the tank is 0.5 m3, what is the density of the fluid, and what is the specific volume? 1.80 Calculate the specific weight of a fluid if a gallon of it weighs 20 lb. Also, calculate its density. 1.81 The specific gravity of a fluid is 1.2. Calculate its density and its specific weight in SI units. 1.82 A fluid has a density of 0.90 g/cm3. What is its specific weight in both the English and SI systems? 1.83 It is proposed by gasoline dealers to sell gasoline by the liter. If gasoline has a specific gravity of 0.85, what is the weight of 60 L of gasoline? 1.84 A household oil tank can hold 275 gal. of oil. If oil has a specific weight of 8800 N/ m3, how many pounds of oil will there be in a full tank? 1.85 A car has a fuel tank that holds 14 gal. of gasoline. If the gasoline has a specific gravity of 0.70, calculate the weight of gasoline in units of pounds. 1.86 An oil has a specific gravity of 0.8. Determine its specific weight, density, and specific volume in SI units. 1.87 An oil has a specific weight of 0.025 lbf/in.3. Calculate its specific gravity. 1.88 A can weighs 12 N when empty, 212 N when filled with water at 4°C, and 264 N when filled with an oil. Calculate the specific gravity of the oil. 1.89 The density of a liquid is 48.6 lbm/ft.3. Calculate the specific weight and the specific gravity of the liquid. 1.90 A shipping company requires that packages have a base perimeter plus the height not to exceed 108 in. By calculation, a student determines that the optimum package size should be an 18-in. square base and a 36-in. height. If the company further specifies that the weight must not exceed 70 lbf, determine the maximum specific weight of the contents of the package. 1.91 A body has a specific gravity of 1.48 and a volume of 7.24 × 10 –4 m3. What is the weight of the body? 1.92 Oil has a specific gravity of 0.83. What is the weight of a liter of this oil in SI units? 1.93 What is the weight in pounds of a gallon of oil that has a specific gravity of 0.86? 1.94 A cylinder 6 in. in diameter and 10 in. in height contains oil that has a density of 850 kg/m3. Determine the weight of the oil in English units. 1.95 A liquid has a density of 1100 kg/m3. Determine its specific gravity and its specific weight. 1.96 The fuel tank of a car holds 60 L of gasoline. Assuming that the gasoline has a specific gravity of 0.74, determine the weight of the gasoline in the tank. 1.97 If the density of a liquid is 780 kg/m3, calculate its specific gravity and its specific weight. 1.98 A liquid has a specific weight of 200 lbf/ft.3. Calculate the volume needed to have a weight of 390 lb. *1.99 In the older cgs system, the density in g/cm3 is numerically equal to the specific gravity of the fluid. Show that this is indeed true.

57

Fundamental Concepts

Problems Involving Pressure 1.100 A skin diver descends to a depth of 60 ft. in fresh water. What is the pressure on the diver’s body? The specific weight of fresh water can be taken as 62.4 lbf/ft.3. 1.101 A skin diver descends to a depth of 25 m in a salt lake where the density is 1026 kg/m3. What is the pressure on the diver’s body at this depth? 1.102 If a Bourdon gauge reads 25 psi when the atmosphere is 14.7 psia, what is the absolute pressure in pascals? 1.103 A column of fluid is 1 m high. The fluid has a density of 2500 kg/m3. What is the pressure at the base of the column? 1.104 A column of fluid is 25 in. high. If the specific weight of the fluid is 60.0 lbf/ft.3, what is the pressure in psi at the base of the column? 1.105 Determine the density and specific volume of the contents of a 20-ft.3 tank if the contents weigh 250 lb. 1.106 A tank contains 500 kg of a fluid. If the volume of the tank is 2.0 m3, what is the density of the fluid, and what is the specific gravity? *1.107 Convert 14.696 psia to 101.325 kPa. 1.108 A pressure gauge indicates 25 psi when the barometer is at a pressure equivalent to 14.5 psia. Compute the absolute pressure in psi and feet of mercury when the specific gravity of mercury is 13.0. 1.109 Same as Problem 1.108, but the barometer stands at 750 mm Hg and its specific gravity is 13.6. 1.110 A vacuum gauge reads 8 in. Hg when the atmospheric pressure is 29.0 in. Hg. If the specific gravity of mercury is 13.6, compute the absolute pressure in psi. 1.111 A vacuum gauge reads 10 in. Hg when the atmospheric pressure is 30 in. Hg. Assuming the density of mercury to be 13.595 kg/m3, determine the pressure in pascals. 1.112 A U-tube mercury manometer, open on one end, is connected to a pressure source. If the difference in the mercury levels in the tube is 6.5 in., determine the unknown pressure in psfa. *1.113 Two sources of pressure M and N are connected by a water–mercury differential gauge as shown in Figure P1.113. What is the difference in pressure between M and N in psi? M N

6 ft.

Water (γ = 62.4 lbf/ft.3)

2 ft. 2 ft.

Mercury (γ = 850 lbf/ft.3) FIGURE P1.113

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Thermodynamics and Heat Power

*1.114 Determine the difference in pressure between A and B in Figure P1.114 if the specific weight of water is 62.4 lbf/ft.3. Oil (γ = 50 lbf/ft.3)

10 in.

Water

5 in. A

B

FIGURE P1.114

*1.115 If the liquid in pipe B in Problem 1.114 is carbon tetrachloride, whose specific weight is 99 lbf/ft.3, determine the pressure difference between A and B. *1.116 In a U-tube manometer, one end is closed, trapping atmospheric air in the column. The other end is connected to a pressure supply of 5 psig. If the level of mercury in the closed end is 2 in. higher than that in the open end, what is the pressure of the trapped air? *1.117 For the arrangement shown in Figure P1.117, determine pA – pB. γ = 50 lbf/ft.3 γ = 40 lbf/ft.3

8 in.

15 in.

20 in.

B A

γ = 60 lbf/ft.3

FIGURE P1.117

*1.118 A bathyscape dives 8000 m below the surface in the Pacific. Atmospheric pressure is 101 kPa, and seawater density is 1.03 g/cm3. Working in SI units, determine the following: (a) absolute pressure (kPa) and (b) force on a 250-mm-diameter window. *1.119 A fuel tank on the moon (g = 5.32 ft./s2) holds 2 m3 of jet fuel (specific gravity = 0.70). Water density is 1 g/cm3. Determine the fuel weight, in newtons.

2 Work, Energy, and Heat

L E A R N I NG G OA L S

After reading and studying the material in this chapter, you should be able to



1. State the definitions of work, energy, and heat 2. Use the fact that both work and heat are forms of energy in transition 3. Apply the convention that heat into a system is to be taken as a positive quantity and that work out of a system is also to be taken as a positive quantity (This convention is taken from the customary power-producing cycle in which heat into a system is used to generate useful work.) 4. Show that internal energy is a form of energy in which a body is said to possess internal energy by virtue of the motion of the molecules of the body 5. Differentiate between a nonflow or closed system and a flow or open system 6. Understand the origin of the term flow work and apply it to a flow system 7. Use the fact that the work of a quasi-static, nonflow system is the area under the pressure–volume curve 8. Understand the difference between sensible heat and latent heat

2.1 Introduction In Chapter 1, certain concepts were arrived at by considering the motion of gas particles in an enclosure. Briefly, pressure was found to involve the principle of momentum interchange with the container walls, temperature was associated with the motion of the particles, and density was taken to be a measure of the number of particles per unit volume. This simple analysis followed the history of a single particle, and it was subsequently generalized to all the particles in the enclosure. This type of analysis is representative of a microscopic description of the processes occurring within the boundaries of the defined system, because the history of a single particle was followed in detail. Rather than pursue further the microscopic concept of matter, we shall be concerned with the macroscopic, or average, behavior of the particles composing a system. The macroscopic viewpoint essentially assumes that it is possible to describe the average behavior of these particles at a given time and at some subsequent time after changes have occurred to the system. The 59

60

Thermodynamics and Heat Power

system changes of concern to us in this study are temperature, pressure, density, work, energy, velocity, and position. The power of the macroscopic approach lies in its ability to describe the changes that have occurred to the system without having to detail all the events of the processes involved.

2.2 Work The work done by a force is the product of the displacement of the body multiplied by the component of the force in the direction of the displacement. Thus, in Figure 2.1, the displacement of the body on the horizontal plane is x, and the component of the force in the direction of the displacement is (F cos θ). The work done is (F cos θ)x. The constant force (F cos θ) is plotted as a function of x in Figure 2.1b, and it should be noted that the resulting figure is a rectangle. The area of this rectangle (shaded) is equal to the work done, because it is (F cos θ)(x). If the force varies so that it is a function of the displacement, it is necessary to consider the variation of force with displacement in order to find the work done. Figure 2.1c shows a general plot of force as a function of displacement. If the displacement is subdivided into many small parts, Δx, and for each of these small parts F is assumed to be very nearly constant, it is apparent that the sum of the small areas (F) (Δx) will represent the total work done when the body is displaced from x1 to x2. Thus, the area under the curve of F as a function of x represents the total work done if F is the force component in the direction of the displacement x.

θ

F

F

Work

F cos θ

F cos θ x

x (a)

(b)

F

F

x x1

(c)

x2

x

FIGURE 2.1 Work. (a) Force component in x direction. (b) Plot of force vs. displacement. (c) Force a function of displacement.

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Work, Energy, and Heat

ILLUSTRATIVE PROBLEM 2.1 A spring is slowly compressed by a varying force F until it reaches an equilibrium position. Assuming that the force on the spring is proportional to the spring displacement, determine the work done on the spring. Assume that the constant of proportionality k is constant and expressed in pounds force per foot of spring deflection or newtons per meter of spring deflection. SOLUTION As shown in Figure 2.2a, the system consists of a spring and a force F directed along the axis of the spring. A plot of F as a function of x is shown in Figure 2.2b. It will be noted that the force–displacement relation is a linear one, in which the force equals kx at all times. Thus, the work done is represented by the shaded triangular area of Figure 2.2b. 1 1 Because the base of the triangle is l and the height is kl, the work done is (l) (kl) or (k) (l2). 2 2 F

x

F

F = kx

l L

Spring modulus =k

Slope, k = spring constant

kl

l (a)

x

(b)

FIGURE 2.2 Illustrative Problems 2.1 and 2.2. (a) Spring-force system. (b) Spring-force work.

CALCULUS ENRICHMENT The work done on a spring by a force can be found by integration of the expression for work, namely,

W=

∫ F ⋅ dx (a)

where the force and displacement are related by the spring constant k as

F = kx (b) Using the spring equation in conjunction with Equation a between the limits l1 and l2, l2



W=

∫ kx dx l1

(c)

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Thermodynamics and Heat Power

Integrating,

(

)

W = k l22 − l12 /2





(d)

If the initial length is zero, we obtain the same result as before, namely, (l/2)kl2.

ILLUSTRATIVE PROBLEM 2.2 A spring has a spring constant k of 100 lbf/in. deflection. How much work is done when the spring is compressed 2 in.? SOLUTION Referring to Figure 2.2 and the results of Illustrative Problem 2.1, we have work =



1 2 kl 2

For this problem,



work =

1 ((100)lbf/in.)(2)2 in.2 = 200 in. ⋅ lbf 2

ILLUSTRATIVE PROBLEM 2.3 If the spring constant in Illustrative Problem 2.2 is 20 kN/m, how much work is done when the spring is compressed 75 mm? SOLUTION As before, work =

1 2 1 kl = (20 × 103 ) N/m × (0.075)2 (m)2 2 2

= 56.25 N ⋅ m = 56.25 J

2.3 Energy At this point, let us define energy in terms of work. Energy can be described as the capacity to do work. At first, it may appear that this definition is too restrictive when applied to electrical and magnetic systems. Yet in all instances, the observed effects on a system can (in principle and ideally) be converted to mechanical work. Because work has been defined as the product of a force multiplied by a displacement, it is not stored in a system.

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Work, Energy, and Heat

It represents a form of energy that must be crossing the boundaries (real or imaginary) of the system and can properly be placed in the category of energy in transition. To distinguish between the transfer of energy as work to or from a system, we shall adopt the convention that the work done by a system on its surroundings is positive, and the work done by the surroundings on the system is negative. For students, it is best to think of this convention regarding the useful work out of a system as a conventional, desirable quantity and, therefore, positive. Thus, in Illustrative Problem 2.1, the spring has work done on it by a force. If we consider the spring as our system, the work is negative; if we consider the system as the external variable force that is compressing the spring, the work is positive. Students will note that the decision whether the work term is positive or negative requires that the system be carefully defined. The work that a system can perform on its surroundings is not an intrinsic property of the system. The manner in which the process is carried out will determine the effect on the surroundings. As stated earlier, work is a transitory effect and is neither a property of a system nor stored in a system. There is one process, however, that does permit the evaluation of the work done, because the path is uniquely defined. This process is frictionless and quasi-static, and we shall find it useful in subsequent discussions. To describe this process, we first define equilibrium state in the manner given by Hatsopoulos and Keenan (1961): A state is an equilibrium state if no finite rate of change can occur without a finite change, temporary or permanent, in the state of the environment. The term permanent change of state refers to one that is not canceled out before completion of the process. Therefore, the frictionless quasi-static process can be identified as a succession of equilibrium states. Involved in this definition is the concept of a process carried out infinitely slowly, so that it is in equilibrium at all times. The utility of the frictionless, quasi-static process lies in our ability to evaluate the work terms involved in it, because its path is uniquely defined. Energy or work done per unit time is called power or the rate of energy change. Energy, work, and power units as well as their conversions are detailed in Table 1.8.

2.4 Internal Energy To this point, we have considered the energy in a system that arises from the work done on the system. However, it was noted in Chapter 1 and earlier in this chapter that a body possesses energy by virtue of the motion of the molecules of the body. In addition, it possesses energy due to the internal attractive and repulsive forces between particles. These forces become the mechanism for energy storage whenever particles become separated, such as when a liquid evaporates or the body is subjected to a deformation by an external energy source. Also, energy may be stored in the rotation and vibration of the molecules. Additional amounts of energy are involved with the electron configuration within the atoms and with the nuclear particles. The energy from all such sources is called the internal energy of the body and is designated by the symbol U. Per unit mass (m), the specific internal energy is denoted by the symbol u, where mu = U. Thus,

mu = U (2.1)

or

u=

U m

(2.2)

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Thermodynamics and Heat Power

From a practical standpoint, the measurement of the absolute internal energy of a system in a given state presents an insurmountable problem and is not essential to our study of thermodynamics. We are concerned with changes in internal energy, and the arbitrary datum for the zero of internal energy will not enter into these problems. Just as it is possible to distinguish the various forms of energy, such as work and heat, in a mechanical system, it is equally possible to distinguish the various forms of energy associated with electrical, chemical, and other systems. For the purpose of this book, these forms of energy, work, and heat are not considered. Students are cautioned that if a system includes any forms of energy other than mechanical, these items must be included. For example, the energy that is dissipated in a resistor as heat when a current flows through it must be taken into account when all the energies of an electrical system are being considered.

2.5 Potential Energy Let us consider the following problem, illustrated in Figure 2.3, where a body of mass m is in a locality in which the local gravitational field is constant and equal to g. A force is applied to the body, and the body is raised a distance Z from its initial position. The force is assumed to be only infinitesimally greater than the mass, so the process is carried out on a frictionless, quasi-static basis. In the absence of electrical, magnetic, and other extraneous effects, determine the work done on the body. The solution to this problem is obtained by noting that the equilibrium of the body requires that a force be applied to it equal to its weight. The weight of the body is given from Chapter 1 as mg/gc in English units. In moving through a distance Z, the work done by this force will then equal work =

mg Z gc

(2.3)

The work done on the body can be returned to the external environment by simply reversing this frictionless, quasi-static process, a feature that is discussed in detail in Chapter 3. Returning to Equation 2.3, we conclude that this system has had work done on it equal to (mg/gc) (Z) and that, in turn, the system has stored in it an amount of energy in Mass m

W

Z Datum

FIGURE 2.3 Potential energy.

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Work, Energy, and Heat

excess of the amount it had in its initial position. The energy added to the system in this case is called potential energy. Thus,



potential energy (P.E.) =

mg Z ft. ⋅ lbf (2.4) gc

In terms of SI units, Equations 2.3 and 2.4 become

work = mgZ (2.5)

and

potential energy (P.E.) = mgZ joules (2.6)

A feature of importance of potential energy is that a system can be said to possess it only with respect to an arbitrary initial or datum plane. An interesting application of the concept of potential energy storage is the pumped storage hydroelectric power plant. The principle of operation can be illustrated using Figure 2.4. In this system, reversible turbine–generator units are used as follows: At those times when excess generating capacity is available from other generating stations, the water can be pumped from the lower to the upper reservoir. When additional generating capacity is required, the water is allowed to run downhill, passing through the generating station where it operates the reversible turbine–generator as a turbine to rotate the generator and

(a)

PM

AM (b) FIGURE 2.4 Pumped storage concept. (a) Generating mode. (b) Pumping mode.

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Thermodynamics and Heat Power

produce electricity. Thus, the pumped storage station helps to smooth out fluctuations in the load demand, resulting in steady, more efficient operation of other stations. In this application, the potential energy of the water stored in the upper reservoir provides the energy to the system as needed. Dams also use the potential energy of water to generate electrical power.

ILLUSTRATIVE PROBLEM 2.4 A pumped storage plant uses water pumped to an elevation of 600 ft. above the turbogenerators. How much work is done lifting the water to this elevation? Assume that local gravity is g, which is numerically equal to gc. SOLUTION Because local gravity is g, which is equal to gc, for each pound mass of water,



P.E. =

mg 32.174 ft./s 2 (Z) = 1 lbm × × 600 ft. = 600 ft. ⋅ lbf gc 32.174 lbm ⋅ ft./lbf ⋅ s 2

Note that the use of the term g/gc is equivalent to a conversion factor lbf/lbm.

ILLUSTRATIVE PROBLEM 2.5 A pump delivers water from a well that is 50 m deep. Determine the change in potential energy per kg of water. Use g = 9.81 m/s2. SOLUTION The change in potential energy is mgZ, where Z is 50 m, using the bottom of the well as the datum. Therefore, P.E. = mgZ m × 50 m s2 kg·m 2 = 490.5 s2 = 1 kg × 9.81

= 490.5 N ⋅ m because N = = 490.5 J

kg·m s2

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Work, Energy, and Heat

ILLUSTRATIVE PROBLEM 2.6 If the pumped-storage plant of Illustrative Problem 2.4 has a flow of 10 000 gal./min, determine the power generated. Assume that the local gravity is g = gc and that the density of water is 62.4 lbm/ft.3. SOLUTION In Illustrative Problem 2.4, we determined the work done to be 600 ft.·lbf/lbm. The power generated is the energy stored per pound mass (also equal to the potential energy) multiplied by the pounds mass per minute that flows. One gallon is a volumetric measure equal to 231 in.3. Thus,

10 000 gal./min ×

231 in.3 = 1337 ft.3/min 1728 in.3/ft.3

(because the flow is given as 10 000 gal./min). The mass flow is m = ρAV = 62.4 lbm/ft3 × 1337 ft.3/min = 83 429 lbm/min. The power generated = 83 429 lbm/min × 600 ft.·lbf/lbm = 50 057 000 ft.·lbf/min. Finally, 50 057 000/33 000 = 1517 hp, since 1 hp = 33 000 ft.·lbf/min.

ILLUSTRATIVE PROBLEM 2.7 Determine the horsepower required by the pump in Illustrative Problem 2.5 if the water has a density of 1000 kg/m3 and the pump delivers 1000 kg/min from the well. SOLUTION From Illustrative Problem 2.5, we found the potential energy to be 490.5 N·m above the bottom of the well. Therefore,  power = (P.E.)m

= 490.5 = 81175

N⋅m 1 × 1000 kg/min × kg 60 s/min

J N⋅m = 8175 = 8175 W s s

Because 1 hp = 746 W,

8175 W = 10.96 hp 746 W/hp

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Thermodynamics and Heat Power

2.6 Kinetic Energy Let us consider another situation in which a body of mass m is at rest on a frictionless plane (Figure 2.5). If the force F is applied to the mass, it will be accelerated in the direction of the force. After moving through a distance x, the velocity of the body will have increased from 0 to V2. The only effect of the work done on the body will be to increase its velocity. Because velocity is the time rate of change of displacement,

V=

x (2.7) ∆t

Also, acceleration is the time rate of change of velocity,

a=

∆V (2.8) ∆t

Combining Equation 2.7 with Equation 2.8 by eliminating the Δt terms yields V Δ V = ax (2.9)



If we now multiply both sides of Equation 2.9 by the mass, m, we obtain mV Δ V = max (2.10)



The left side of Equation 2.10 can be evaluated by referring to Figure 2.6, where V is plotted against V. It will be noted that V Δ V is the area of the shaded rectangle. Summing these small rectangles up to V2 represents the area of the triangle whose base is V2 and 1 whose altitude is V2. This area is V22 making the left side of Equation 2.10 mV22/2. 2 The right side of Equation 2.10 is interpreted by noting that ma = F (in SI units). Therefore, max is the work done by the force F to move the body a distance x. Thus, we can write mV22 = Fx (2.11) 2



The term mV 2/2 is called the kinetic energy of the body. At the beginning of a process, it is mV12/2, and at the end, it is mV12/2. Equation 2.11 therefore permits us to evaluate

Initial velocity =0

Final velocity V2 F

FIGURE 2.5 Kinetic energy.

F

69

Work, Energy, and Heat

V V2

V

V

O

V2

V

FIGURE 2.6 Evaluation of V Δ V.

the energy possessed by a body of mass m having a velocity V relative to a stationary reference. It is usual to use the Earth as the reference. In English units, Equation 2.11 becomes

kinetic energy (K.E.) =

mV22 mV 2 (2.12) or , in general , 2 gc 2 gc

In terms of SI units,

kinetic energy (K.E.) =

mV 2 (2.12a) 2

ILLUSTRATIVE PROBLEM 2.8 A mass of 10 lb. is slowed from a velocity of 88 ft./s to 10 ft./s. What is the change in the kinetic energy of the system if the body is considered to be the system? SOLUTION The kinetic energy of the body before it is slowed down is 2

ft. mV 2 s K.E. = = 2 gc ft. ⋅ lbm 2 × 32.174 2 s ⋅ lbf 10 1bm × 88



= 1203.5 ft. ⋅ lbf

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Thermodynamics and Heat Power

After slowing down, 2

ft. mV 2 s K.E. = = 2 gc ft. ⋅ lbm 2 × 32.174 2 s ⋅ lbf 10 lbm × 10



= 15.5 ft. ⋅ lbf

The change in kinetic energy Δ(K.E.) therefore is ΔK.E. = 1203.5 – 15.5 = 1188 ft.·lbf



ILLUSTRATIVE PROBLEM 2.9 A car having a mass of 1500 kg is slowed from 50 km/h to 30 km/h (Figure 2.7). What is the change in its kinetic energy if g = 9.81 m/s2? SOLUTION The car’s initial kinetic energy is mV 2/2. Therefore, K.E. =



1500 kg 50 × 1000 m/h × 2 3600 s/h

2



= 144 676 J = 144.68 kJ After slowing down, we have K.E. =



30 × 1000 m/h mV 2 1500 kg = × 2 2 3600 s/h

2

= 52 0833 J = 52.08 kJ The change in kinetic energy therefore is ΔK.E. = 144.68 – 52.08 = 92.6 kJ



Note that g did not enter the problem in this system of units.

50 km/h FIGURE 2.7 Illustrative Problem 2.9.

30 km/h



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Work, Energy, and Heat

ILLUSTRATIVE PROBLEM 2.10 A body has a mass of 10 kg and falls freely from rest (Figure 2.8). After falling 10 m, what will its kinetic energy be? Also, what will its velocity be just before impact? Neglect air friction. SOLUTION Because there are no losses in the system, we conclude that the initial potential energy plus the initial kinetic energy must equal the sum of the final potential energy plus the final kinetic energy. Therefore, P.E.1 + K.E.1 = P.E.2 + K.E.2 (a) By selecting our reference plane as shown in Figure 2.8, K.E.1 = 0 and P.E.2 = 0. Equation a reduces to P.E.1 = K.E.2 (b) Substituting the data of the problem into Equation b gives



10 kg × 10 m × 9.81 m/s 2 =

10 kg × V 2 (m/s)2 2

10 kg V1 = 0

Z1 = 10 m

Z2 = 0

FIGURE 2.8 Illustrative Problem 2.10.

Reference plane

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Thermodynamics and Heat Power

Solving yields

V2 = 2 × 9.81 × 10

and

V = 14.0 m/s

Note that this result is independent of the mass of the body. The kinetic energy is readily found from Equation b to be equal to 10 kg × 10 m × 9.81 m/s2 = 981 N·m.

2.7 Heat When a heat interaction occurs in a system, two distinct events are observed. The first is an interchange of energy, and the second is that this interchange would not have taken place if there were no temperature difference between the system and its surroundings. Therefore, we may define heat as the energy in transition across the boundaries of a system due to a temperature difference between the system and its surroundings. In this definition of heat, the transfer of mass across the boundaries of the system is excluded. It should be noted that this indicates a similarity between heat and work. Both are energies in transition, and neither is a property of the system in question. Just as in work, heat can transfer quasi-statically to or from a system. The difference in temperature between the system and its surroundings for quasi-static heat transfer can be only an infinitesimal amount at any time. Once again, it is necessary to adopt a convention for the energy interchanged by a system with its surroundings. We shall use the convention that heat to a system from its surroundings is positive and that heat out of a system is negative. To learn these conventions, it is convenient to consider the typical situation in which heat is transferred to a system to obtain useful work from the system. This sets the convention that heat into a system is positive and work out of the system is also positive. Positive in this sense means either desirable or conventional from the viewpoint of conventional power cycles. For refrigeration cycles, the opposite of this convention will be more useful. It is important to recognize the difference between heat and temperature. Temperature is a measure of the energy contained in the molecules of a system due to their motion. When the temperature of a system is greater than that of its surroundings, some of that molecular energy is transferred to the surroundings in what we call heat. Thus, temperature is a property of a system in a given state, whereas heat is associated with a change in the state of a system. Because work and heat are both forms of energy in transition, it follows that the units of work should be capable of being expressed as heat units, and vice versa. In the English system of units the conversion factor between work and heat, sometimes called mechanical equivalent of heat, is 778.169 ft.·lbf/Btu and is conventionally given the symbol J. We shall use this symbol to designate 778 ft.·lbf/Btu, because this is sufficiently accurate for engineering applications of thermodynamics. In the SI system, this conversion factor is not necessary, because the joule (N·m) is the basic energy unit. There are two forms of heat transfer: sensible heat and latent heat. Sensible heat transfer occurs when there is a temperature difference between bodies or systems and the amount

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of heat transferred is related to the magnitude of that difference. This is the most common form. Latent heat transfer occurs when a body is changing state, such as evaporating from liquid to gas or condensing from gas to liquid. The change of phase occurs at constant temperature. This form of heat transfer is utilized in refrigeration and air conditioning systems (see Chapters 7 and 10).

2.8 Flow Work At this time, let us look at two systems, namely, the nonflow or closed system and the steady-flow or open system. The nonflow system has boundaries that both heat and work can penetrate, but no mass can cross these boundaries. In the steady-flow system, both mass and energy can cross the system boundaries. The term steady denotes a process or system that is not time dependent. When a fluid is caused to flow in a system, it is necessary that somewhere in the system work must have been supplied. At this time, let us evaluate the net amount of work required to push the fluid into and out of the system. Consider the system shown in Figure 2.9, where a fluid is flowing steadily across the system boundaries as shown. At the inlet sec and the fluid density is ρ1 (or tion ①, the pressure is p1, the area is A1, the mass flow rate is m, its reciprocal specific volume, 1/v1); at the outlet section ②, the pressure is p2, the area is A2, the  and the fluid density is ρ2 (or its reciprocal specific volume, 1/v2). Let mass flow rate is still m, us now consider a plug of fluid of length l1 entering the system such that the amount of fluid  The force acting on the inlet cross-sectional area A1 is contained in the plug is numerically m. p1A1. To push the plug into the system, it is necessary for this force to move the plug a distance equal to l1. In so doing, the work done will be p1A1l1. However, A1l1 is the volume of the plug containing a mass m. Using this, we find the work, W, to be

W = p1 A1l1 = m(p1v1) ft.·lbf or N·m

(2.13)

The work per unit mass is W/m = w

w = p1v1 ft.·lbf/lbm or N·m/kg

(2.14)

If we now consider the outlet section using the same reasoning, we have

W = m(p2v2) ft.·lbf or N·m 1

(2.15)

2

p1, A1, m, ρ1

p2, A2, m, ρ2 System

l1 FIGURE 2.9 Steady-flow system: flow work.

l2

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Thermodynamics and Heat Power

or

w = p2v2 ft.·lbf/lbm or N·m/kg

(2.16)

Each of the pv terms is known as the flow work. The net flow work becomes

net flow work = p2v2 − p1v1 ft.·lbf/lbm or N·m/kg

(2.17)

or in thermal units,

net flow work =

p2 v2 p1 v1 − J J

Btu/lbm (2.18)

or

net flow work = p2 v2 − p1v1

N·m/kg

(2.19)

Equations 2.18 and 2.19 are interpreted to mean that the difference in the pv terms represents the amount of work that is done on a system to introduce a unit mass into it minus the work done on its environment as it leaves the system. However, a word of caution is necessary at this time. Any fluid in any system has both properties, pressure and specific volume, and therefore the product pv can always be evaluated. The product pv represents flow work only in the steady-flow system. Thus, even though the term pv/J appears in the nonflow process, it cannot and does not represent flow work, because the system is by definition stationary. Flow work exists only to cause fluid to cross the boundaries of a flow system. In the foregoing derivations, certain assumptions were made, and these are repeated here for emphasis. When applied to a flow situation, the term steady means that the condition at any section of the system is independent of time. Even though the velocity, specific volume, and temperature of the fluid can vary in any arbitrary manner across the stream, they are not permitted to vary with time. The mass entering the system per unit time must equal the mass leaving the system in the same period of time; otherwise, the system would either store or be depleted of fluid. ILLUSTRATIVE PROBLEM 2.11 At the entrance to a steady-flow device, it is found that the pressure is 100 psia and that the density of the fluid is 62.4 lbm/ft.3. At the exit, the pressure is 50 psia and the corresponding density 30 lb./ft.3. Determine the flow work term at the entrance and exit of the device. SOLUTION Refer to Figure 2.9. At the entrance,



pv = J

100

lbf in.2 1 × 144 2 2 in. ft. 62.4 lbm/ft.3 ft. ⋅ lbf 778 Btu

= 0.297 Btu/lbm

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Work, Energy, and Heat

At the exit,

pv = J



50

lbf in.2 1 × 144 in.2 ft.2 30 lbm /ft.3 ft. ⋅ lbf 778 Btu

= 0.308 Btu/lbm

ILLUSTRATIVE PROBLEM 2.12 Determine the flow work at the entrance and exit of a steady-flow device in which the entrance pressure is 200 kPa and the density of the fluid is 1000 kg/m3. At the exit, the pressure is 100 kPa and the density 250 kg/m3. SOLUTION At the entrance,

pv = 200 kPa × 1000

Pa N 1 N⋅ m × = 200 2 3 g kPa m kg 1000 kg/m

pv = 100 kPa × 1000

Pa N 1 N⋅ m × = 400 2 3 kPa m kg 250 kg/m

At the exit,

Because 1 N·m/kg is 1 J/kg, the answers are in J/kg.

2.9 Nonflow Work Let us now consider the case of the piston and cylinder arrangement shown in Figure 2.10. We assume that the piston is in equilibrium with the contents and, initially, a distance l above the end of the cylinder. The piston will now be permitted to compress the contents of the cylinder frictionlessly and quasi-statically. After the piston has moved a distance Δl, a very small change in distance, the pressure in the cylinder will have increased from its initial value of p to a value of p + Δp, where Δp indicates a very small change in pressure. Because this process was specified to be quasi-static, it is possible to evaluate the work as 1 the product of the average force multiplied by the displacement. The average forces is 2 [pA + (p + Δp)A], and the displacement is Δl. Thus,



w( per unit mass) =

p + ( p + ∆p) ( A∆l) (2.20) 2

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Thermodynamics and Heat Power

p

F l p p+ p Contents = unit mass

l v

p

v

System (a)

(b)

FIGURE 2.10 Quasi-static nonflow compression process. (a) Piston-cylinder system. (b) Differential work.

However, the product of AΔl is the small change in volume that the piston has swept out. Replacing AΔl by Δv and saying that the product of two very small numbers (Δv Δp) is indeed so small as to be negligible, we have

w = p∆v per unit mass of working fluid (2.21)

Equation 2.21 can be interpreted by referring to Figure 2.10b. It will be noted that the term pΔv represents a small element of area, and that the total work can be evaluated by summing all the pΔv terms. Therefore, we can conclude that the work done in a quasistatic, frictionless, non-flow process is the area under the pv curve.

ILLUSTRATIVE PROBLEM 2.13 A process is carried out in a nonflow, quasi-static manner so that the pressure volume relationship of the fluid is given by

pv = constant

where p is the pressure and v is the specific volume of the fluid. Determine the work done on the fluid if it undergoes a process in which its specific volume goes from v1 to v2. SOLUTION To solve this problem, it is necessary to sum all values of pΔv over the entire range of the problem. As shown in Figure 2.11b, this corresponds to obtaining the area under the p–v curve between the limits of v2 and v1. Therefore, per unit mass,

w = ∑ pΔv

where the symbol ∑ means the sum of all such values. To carry out this summation, we must first express p as a function of v. From the given p,v relation, p = constant/v,

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Work, Energy, and Heat

pv = constant

p1

(a)

p

pv = constant p

v

p2 v1

(b)

v

v2

FIGURE 2.11 Illustrative Problem 2.13. (a) Piston-cylinder system. (b) Summation of work.

where the constant is pv = p1v1 = p2v2. When this is substituted in the pΔv expression, we obtain

w = constant

∑ ∆vv

where the total work is the sum of these terms. The summation referred to can best be illustrated by plotting 1/v as a function of v. The shaded area of Figure 2.12 is simply Δv/v. Thus, the total work per pound of fluid is the area under this curve between v1 and v2 multiplied by a constant. Using the methods of calculus, we find 1 v

1 v

FIGURE 2.12 Evaluation of ∑(Δv/v).

∆v

v

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Thermodynamics and Heat Power

the summation to be numerically equal to ln(v2/v1). Note that ln x = logex = 2.3026 log10x. Because the constant was either p1v1 or p2v2,



w = p1v1 ln

v2 ft ⋅ lbf N⋅ m or v1 lbm kg

w = p2 v2 ln

v2 ft ⋅ lbf N⋅ m or v1 lbm kg



or

We shall have occasion to perform this type of summation in connection with other situations, and the procedure should be understood at this time for ease of application in the future.

CALCULUS ENRICHMENT The work of the nonflow, quasi-static process, where the equation of path is known, is v2



w=

∫ p dv (a)

v1



a. If the given relationship between p and v is pv = constant, then p = constant/v. Using this with Equation a gives us v2



∫

w = constant dv/v (b) v1



The integral of dv/v between the limits of v2 and vx is ln(v2/v1), or w = (constant) ln(v2/v1) but the constant equals pv. Therefore, w = (pv) ln(v2/v1) (d) b. If the given relationship between p and v is pvn = constant, then p = constant/ vn. Again, using this with Equation a, v2

w=

∫

v2

p dv =

v1



(c)

Integrating , w = constant

∫ (constant/v ) dv n

(e)

v1

v21− n − v11− n 1− n



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Work, Energy, and Heat

The constant can be determined from either p1v1n or p2 v2n. Using both of these, the work is found to be

w=

p2 v2 − p1v1 (f) 1− n

Note that Equation f is valid for every value of n except 1.0. For n = 1.0, the results of part (a) must be used. The previous analyses, both (a) and (b), apply in the same way to problems using total volume V instead of specific volume. Thus for pVn = constant,

w=

p2V2 − p1V1 1− n

Note that pressure must be in lb./ft2 and volume in ft.3 to obtain work in foot-pounds.

ILLUSTRATIVE PROBLEM 2.14 For the process described in Illustrative Problem 2.13, the initial pressure is found to be 100 psia and the initial specific volume 2 ft.3/lb. If the final specific volume is 1 ft.3/lb., how much work was done on the fluid per pound of fluid? SOLUTION From Illustrative Problem 2.13, w = p1v1 ln(v2/v1). For the proper units, it is necessary that pressure be expressed as psfa when the volume is in cubic feet. Thus, 100 psia = (100) (144) psfa, and v1 = 2 ft.3/lb. w = (100 × 144 × 2) ln



1 2

1 This is evaluated by noting that ln = ln 1 – ln 2. The ln 2 is 0.693, and the ln 1 is 2 zero. Therefore,

w = –100 × 144 × 2 × 0.693 = –19 958 ft.·lbf/lbm

This computation is also readily done using the In function of any scientific calculator. In thermal units,

w=

−19 958ft. ⋅ lbf /lb. mass = −25.7 Btu/lbm 778 ft. ⋅ lbf /Btu

The minus sign in the answer indicates work into the system. As an exercise, it is left to students to solve this problem by graphically evaluating the area under the pressure–volume curve.

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Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 2.15 For the process pv = constant, a gas compression is carried out from an initial pressure of 200 kPa to a final pressure of 800 kPa. If the initial specific volume is 0.1 m3/kg, determine the work done per kilogram of gas. SOLUTION Because p1v1 = p2v2,

v2 =

p1v1 200 = × 0.1 m 3/kg = 0.025 m 3/kg p2 800

and w = p1v1 ln

v2 v1

= 200 kPa × 0.1 m 3/kg × ln

0.025 0.100

= −27.7 kJ/kg (into the system)



ILLUSTRATIVE PROBLEM 2.16 A gas with an initial volume of 0.3 m3 is compressed slowly from 500 kPa to 1000 kPa according to pV 1.25 = constant. Find the work done. SOLUTION Here W = (p2V2 – p1V1)/(1 – n), so we must first find V2. Using the pV relationship, (V2)n = p1(V1)n/P2. Therefore, (V2 )1.25 =



500(0.3)1.25 = 0.111 1000

Taking the 1.25 root of 0.111, we obtain V2 = 0.1723 m3 Thus,

W=

(1000 × 0.1723) − (500 × 0.30) = −89.2 kJ (1 − 1.25)

The minus sign indicates work into the system as expected for compression of a gas.

Work, Energy, and Heat

81

2.10 Review This chapter has been devoted to developing qualitatively and quantitatively the concepts of work, energy, and heat. A careful study of the contents of this chapter will be invaluable later on in our study. In addition to defining work, energy, and heat, we also showed that the work of a nonflow, quasi-static process can be taken to be the area under the p–v curve. The term steady implies a system that does not vary with time. In the steady-flow system, both mass and energy are permitted to cross the boundaries of the system, but such a system is not time dependent. We also noted that when a fluid is caused to flow in a system, somewhere in the system, work must have been supplied to sustain this flow. Using this concept, we demonstrated that the difference in the pv terms equals the amount of work that is done on a system to introduce a unit mass into it minus the work done on its environment as it leaves the system. Even though all systems have pressure and specific volume, the pv term represents flow work only in a flow system. For a nonflow, quasi-static, frictionless process, the work done is in the area under the pv curve.

Key Terms Terms used for the first time in this chapter are as follows: closed system: See nonflow system. energy: The capacity to do work. equilibrium state: A state in which no finite rate of change can occur without a finite change, temporary or permanent, in the state of the environment. flow work: The product of the pressure and specific volume of a fluid in a given state in a flow process. heat: A form of energy in transition to or from a system due to the fact that temperature differences exist. internal energy: The energy possessed by a body by virtue of the motion of the molecules of the body and the internal attractive and repulsive forces between molecules. kinetic energy: The energy possessed by a body due to its motion. mechanical equivalent of heat: In the English system of units, 1 Btu = 778 ft.·lbf. This is termed the mechanical equivalent of heat. nonflow system: A system in which there is no mass crossing the boundaries. potential energy: The energy possessed by a body due to its location with respect to an arbitrary reference plane. quasi-static process: A frictionless process carried out infinitely slowly so that it is in equilibrium at all times. work: The product of force and distance in which the distance is measured in the direction of the force; a form of energy in transition that is not stored in a system.

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Equations Developed in This Chapter Internal energy Internal energy Potential energy Potential energy (SI) Kinetic energy Kinetic energy (SI) Net flow work Net flow work Work of a nonflow, quasi-static process

mu = U U u= m mg P.E. = Z ft ⋅ lbf gc

(2.1)

P.E. = mgZ joules

(2.6)

K.E. =

2

mV 2 gc

ft ⋅ lbf/lbm

mV 2 joules 2 pv pv Net flow work = 2 2 − 1 1 Btu/lbm J J K.E. =

Net flow work = p2v2 – p1v1 N·m/kg w = pΔv

(2.2) (2.4)

(2.12) (2.12a) (2.18) (2.19) (2.21)

QUESTIONS 2.1 A person picks up a package, walks with it for a distance, and then places it on a table. Discuss our concept of work for each of these actions. 2.2 A weight is held stationary at arm’s length by a student. Is energy being expended, and is work being done? 2.3 A spring is compressed and placed into an acid solution, where it dissolves. What has happened to the work done on the spring? 2.4 Both heat and work represent forms of energy. Discuss the differences between them. 2.5 What is the value of the mechanical equivalent of heat in the SI system? 2.6 What distinguishes a nonflow system from a flow system? 2.7 Can you describe any quasi-static processes? 2.8 Of what utility is the quasi-static process concept? 2.9 The term pΔv is the area under the p–v curve. How do you interpret this area? 2.10 In discussing potential energy, what is a necessary requirement? 2.11 Why do we say that a body that is moving possesses energy? 2.12 All substances are subjected to pressure and have a specific volume. Because they all have the product pv, do they all have flow work? 2.13 State the convention that we have adopted for net heat and net work. PROBLEMS Unless indicated otherwise, use gc = 32.174 ft. lbm/lbf s2, and 32.174 ft./s2 or 9.81 m/s2 for g.

Work, Energy, and Heat

Problems Involving Potential Energy, Kinetic Energy, and Work 2.1 A 2-kg mass is elevated to a distance of 6 m above a reference plane. Determine its potential energy with respect to the plane. 2.2 A mass of 10 lb. is placed at an elevation of 30 ft. above a reference plane. Another mass of 15 lb. is placed at an elevation of 40 ft. above a second reference plane that is 8 ft. below the first plane. a. Compare the potential energy of each mass with respect to its own reference plane. b. Compare the potential energy of each mass with respect to the second reference plane. 2.3 A body of mass 10 lb. is placed 10 ft. above an arbitrary plane. If the local gravitational field is equivalent to an acceleration of 16.1 ft./s2, how much work (ft.·lb.) was done lifting the body above the plane? 2.4 A body of mass of 10 kg is placed 3 m above a plane. How much work was done to lift the body above the plane? 2.5 A body having a mass of 3 lb. is moving with a velocity of 30 ft./s relative to the Earth. a. Calculate its kinetic energy. b. If the body is resisted by a constant force of 8 lb., how far will it move before coming to rest? 2.6 A body has a mass of 5 kg. If its velocity is 10 m/s, what is its kinetic energy? 2.7 From what height would the body in Problem 2.6 have to fall to attain its velocity? 2.8 A body weighs 25 lb. If it is moving at 10 ft./s, evaluate its kinetic energy. 2.9 From what height would the body in Problem 2.8 have to fall to achieve its velocity? 2.10 A 500-kg mass is lifted 2 m above a datum plane. a. Determine its potential energy. b. If it is dropped, what will its velocity be at the instant just before it strikes the Earth? 2.11 A jet of air is discharged from a nozzle. If the jet has a velocity of 100 m/s, determine its kinetic energy in joules if 1 kg leaves the nozzle. 2.12 A body weighing 10 lb. is lifted 100 ft. What is its change in potential energy? What velocity will it possess after falling 100 ft? 2.13 A body weighing 10 lb. (g = gc) is moving with a velocity of 50 ft./s. From what height would it have to fall to achieve this velocity? What is its kinetic energy? 2.14 A body weighing 100 N is lifted 3 m. What will its velocity be after a free fall of 3 m? 2.15 Water flows over the top of a dam and falls freely until it reaches the bottom some 600 ft. below. What is the velocity of the water just before it hits the bottom? What is its kinetic energy per pound mass at this point? 2.16 An object is dragged from rest a distance of 40 ft. up an inclined plane that is smooth. During this time, it is elevated 10 ft. and acquires a velocity of 10 ft./s. Given that its mass is 25 lb., perform the following:

83

84

2.17 2.18 2.19 2.20 2.21 2.22

2.23 *2.24

2.25

2.26

2.27

2.28

Thermodynamics and Heat Power

a. Determine the work done in the process. b. Determine the change in potential energy. c. Determine the increase in kinetic energy. A truck having a weight of 50 kN is moving with a velocity of 25 m/s. Determine its kinetic energy. If an object has a kinetic energy of 1 kJ when moving at a velocity of 2 m/s, determine its kinetic energy when its velocity is (a) 4 m/s and when it is (b) 6 m/s. A force of 100 lb. deflects a spring 5 in. Calculate the spring constant and work done. A spring is deflected 250 mm from its free length by a force of 500 N. Calculate the spring constant and the work done. A spring is used in a shock absorber. It is found to absorb 2000 J of energy after deflecting 0.35 m. Determine the spring constant. A spring is compressed 5 in. from its equilibrium position. If the spring modulus k is 10 lbf/in. of deflection, how much work was done in foot-pounds to deflect the spring? A spring is deflected by a weight a distance of 100 mm. If the modulus of the spring is 100 N/m, what is the mass that was placed on the spring? A 100-N weight causes a spring to stretch an unknown distance, h. The addition of a weight of 250 N causes the spring to deflect an additional distance 100 mm. Determine the spring constant. A spring is initially compressed 75 mm by a 400-N force. If it is compressed an additional distance of 50 mm, determine the work required for this additional compression. A 5-lb. mass (g = gc) falls 25 ft. until it strikes a spring. If the spring modulus k is 25 lbf/ft of deflection, how far will the spring be deflected? Assume that all the energy of the falling body just goes to compress the spring. A 10-kg mass falls 3 m until it strikes a spring. If the spring modulus k is 1000 N/m, how far will the spring be deflected if all the energy of the falling body goes into compressing the spring? In Figure P2.28, a force of 1000 N moves the block 5 m along the plane. How much work was done by the force on the block? 1000 N 30O

5m FIGURE P2.28

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Work, Energy, and Heat

2.29 What is the least amount of work required to move the block 3 m up in the plane shown in Figure P2.29? Assume the plane to be frictionless.

3m

45

kg

30o

FIGURE P2.29

2.30 How much work must be done on a car to decrease its velocity from 90 km/h to 45 km/h? The car has a mass of 1000 kg. 2.31 An automobile has a weight of 3000 lb. and a velocity of 30 mi./h. What constant braking force is required to bring it to a stop in 190 ft.? *2.32 Show that the kinetic energy of a fluid flowing in a pipe varies inversely as the fourth power of the pipe diameter. *2.33 If 50 × 106 lbm/h of water flows over the dam of Problem 2.15, what ideal power can be generated by a power plant located at the base of the fall? Express your answer in kilowatts and horsepower. *2.34 If 25 × 106 kg/h flows over a waterfall that is 200 m high, what ideal power in kilowatts can be generated by a power plant located at the base of the fall? 2.35 A bicycle and rider with a combined weight of 800 N travels 40 km/h on a level carriage road. Determine (a) the kinetic energy and (b) the stopping distance if a 200-N braking force is applied to the bicycle (tires do not skid). Problems Involving the p–v Concept 2.36 A pressure of 500 kPa is presented to the piston of a pump and causes it to travel 100 mm. The cross-sectional area of the piston is 1000 mm2. How much work is done by the steam on the piston if the steam pressure is constant? 2.37 A gas expands according to the equation pv = 100, where p is the pressure in pounds per square foot absolute and v is the specific volume in cubic feet per pound. If the pressure of the gas drops from 100 to 50 psfa, how much work was done by the gas? 2.38 A gas expands according to the equation pv = 1000, where p is the pressure in kPa and v is the specific volume in m3/kg. If the gas pressure drops from 1000 to 500 kPa, how much work was done by the gas?

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*2.39 A gas undergoes a process that starts at a pressure of 25 psia and an initial volume of 4 ft.3. Work is done on the gas in the amount of 12 Btu. If the p–v curve is given by pV = constant, determine the final pressure of the gas. *2.40 A gas that is contained in a cylinder undergoes two processes that are in series. The first process, from 1 to 2, consists of a constant-pressure compression at 50  psia, and the volume goes from 0.5 to 0.25 ft.3. The second process consists of a constant-volume heating in which the pressure doubles to 100 psia. Sketch the processes on a p–v diagram, and determine the total work of the combined process. *2.41 A gas undergoes two processes that are in series. The first process is an expansion that is carried out according to the relation pv = constant, and the second process is a constant-pressure process that returns the gas to the initial volume of the first process. The start of the first process is at 400 kPa and 0.025 m3 with the expansion to 200 kPa. Sketch the processes on a p–v diagram, and determine the work of the combined process. *2.42 A gas undergoes two processes in series. The first is a constant-pressure expansion that takes the gas from 100 psia and 1 to 2 ft.3. The second process is a ­constant-volume process during which the pressure decreases to 30 psia. Sketch the processes on a p–v diagram, and determine the work of the combined process. *2.43 A gas expands according to the equation, pv = 100, where p is the pressure in pounds force per square foot and v is the specific volume in cubic feet per pound mass. The initial pressure of the gas is 100 psfa, and the final pressure is 50 psfa. The gas is then heated at constant volume back to its original pressure of 100 psfa. Determine the work of the combined process. *2.44 A gas expands according to the equation p = –250V + 600, where V is in m3 and p is in kPa. If the initial pressure is 575 kPa, the initial volume is 0.1 m3, and the final volume is 0.4 m3, determine the work done. (Hint: Plot a p–V diagram.) *2.45 If the gas in Problem 2.44 expands at constant pressure from its initial pressure, determine the work done. Problems Involving the Nonflow Work Integral *2.46 A gas with a specific volume of 2.2 ft.3/lb. and a pressure of 10 psia is compressed slowly to 1.0 ft.3/lb. according to pv1.3 = constant. Find the work done per pound. *2.47 A gas with a specific volume of 1.5 ft.3/lb. and a pressure of 50 psia expands slowly to 2.5 ft.3/lb. according to pv1.4 = constant. Find the work done per pound. *2.48 A gas initially at 500 kPa and 0.20 m3 expands slowly according to pV1.4 = constant to 0.40 m3. Find the work done. *2.49 A gas expands slowly according to pV 1.4 = constant, starting at 1000 kPa and 0.2 m3. If the final volume is 0.5 m3, find the work done. *2.50 A gas initially at a pressure of 50 psia and a volume of 0.5 ft. is compressed slowly to 100 psia according to pV 1.3 = constant. Find the work done. *2.51 A gas in a piston-cylinder expands slowly from 500 kPa and 0.15 m3 to a final volume of 0.60 m3. Find the work done if the pressure varies according to (a) p = constant, (b) pV = constant, and (c) pV 1.3 = constant.

Work, Energy, and Heat

87

Cyclic Processes A cycle consists of a series of thermodynamic processes during which the working fluid can be made to undergo changes involving energy transitions and is subsequently returned to its original state. On a p–v diagram, it is a closed figure. *2.52 A cycle consists of three processes. The first is a constant-pressure compression at 200 kPa from an initial volume of 0.70 m3 to a final volume of 0.2 m3. The second process takes place at constant volume with the pressure increasing to 600 kPa. The third process completes the cycle and consists of a straight line from the end of the second process to the beginning of the first process. Sketch the cycle on p–v coordinates, and calculate the net work of the cycle. *2.53 A cycle consists of three processes. The first process consists of a constant-­ pressure compression from 14.7 psia and 26 to 10 ft.3. The second process is carried out at constant volume to a final pressure of 35 psia. The cycle is closed with a straight line from the end of the second process to the start of the first process. Sketch the cycle on p–v coordinates, and calculate the net work of the cycle. *2.54 A cycle consists of three processes. The first is an expansion that is carried out according to the relation pv = constant from an initial condition of 500 kPa and 0.2 m3 to a final pressure of 250 kPa. The second process is a constant-pressure compression that returns the gas to the volume that it had at the beginning of the first process. The cycle is closed with a constant-volume process that returns the gas to its state at the beginning of the first process. Sketch the cycle on p–v coordinates, and calculate the net work of the cycle.

3 First Law of Thermodynamics

L E A R N I NG G OA L S

After reading and studying the material in this chapter, you should be able to

1. State the first law of thermodynamics, or energy conservation, for both nonflow and flow systems 2. Define enthalpy and show that it is a property and therefore does not depend on whether a system is a nonflow or flow system 3. Apply the first law of thermodynamics to several nonflow systems, such as the adiabatic system, the constant-volume system, and the constant-pressure system 4. Derive and apply the continuity equation in its several forms to express the conservation of mass in a steady-flow system 5. Derive the energy equation from the first law of thermodynamics for a steady-flow system 6. Think of the area under the pressure–volume diagram as the work of compression or expansion and the area behind the pressure–volume diagram as the work of the compressor or expander 7. Understand the shortcomings of the Bernoulli equation 8. Define the term specific heat and show that the specific heats at constant volume and constant pressure are properties 9. Apply the first law of thermodynamics to the analysis of the steam or gas turbine, pipe flow, boilers, nozzles, throttling, heat exchangers, and the filling of a tank

3.1 Introduction We have discussed properties, state functions, systems, work, energy, and heat in the previous chapters. In this chapter, we will consider the conservation of energy as the basis for the first law of thermodynamics. Although Newton first proposed the equivalence of heat and work, it is only in relatively recent times, as a result of both observation and analysis, that the principle of conservation has become one of the cornerstones of thermodynamics. Most of this chapter will be concerned with the application of the first law of thermodynamics to both nonflow and flow systems and to develop energy equations applicable to these systems. The first law of thermodynamics will enable us to determine the energy 89

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quantities passing to or from a system as work and/or heat and also to determine the changes in the energy stored in the system.

3.2 First Law of Thermodynamics The first law of thermodynamics can be expressed in the following equivalent statements: 1. The first law of thermodynamics is essentially the statement of the principle of the conservation of energy for thermodynamical systems. As such, it may be expressed by stating that the variation of energy of a system during any transformation is equal to the amount of energy that the system receives from its environment (Fermi, 1956). 2. Energy can be neither created nor destroyed but only converted from one form to another (Obert, 1960). 3. If a system is caused to change from an initial state to a final state by adiabatic means only, the work done is the same for all adiabatic paths connecting the two states (Zemansky, 1957). In statement 3, by Zemansky, the term adiabatic is used. In general, we define an adiabatic transformation of a system as a process the system is caused to undergo, with no energy interchange as heat occurring during the process. For the purpose of this book, the concept of the conservation of energy, explicitly stated in the Fermi and Obert definitions, is essentially the first law of thermodynamics. By combining them, we have for the statement of the first law of thermodynamics that energy can be neither created nor destroyed but only converted from one form to another. Because we shall not concern ourselves with nuclear reactions at this time, it will not be necessary to invoke the interconvertibility of energy and mass in our present study. A system has already been defined as a grouping of matter taken in any convenient or arbitrary manner. However, when dealing with fluids in motion, it is more convenient to utilize the concept of an arbitrary volume in space, known as a control volume, that can be bounded by either a real or imaginary surface, known as a control surface. By correctly noting all the forces acting on the fluid within the control volume, the energies crossing the control surface, and the mass crossing the control surface, it is possible to derive mathematical expressions that will evaluate the flow of the fluid relative to the control volume. For a system in which fluids are flowing steadily, a monitoring station placed anywhere within the control volume will indicate no change in the fluid properties or energy quantities crossing the control surface with time, even though these quantities can and will vary from position to position within the control volume. As noted by Keenan (1941), “the first step in the solution of a problem in thermodynamics is the description of a system and its boundaries.”

3.3 Nonflow System The statements made in Section 3.2 about the first law of thermodynamics are, in essence, equivalent to each other in that they express the concept of energy conservation. To explore

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First Law of Thermodynamics

some of the implications and applications of the first law, let us examine the nonflow or closed system. This system will have boundaries across which both heat and work can penetrate, but no mass will be permitted to cross them. Note that the boundaries can move with the system as the process proceeds along if no mass flow crosses the boundaries. An example is a piston-and-cylinder arrangement in which the piston compresses the working fluid in the cylinder and heat may cross the boundary (e.g., by cooling of the cylinder) at the same time. This system is shown schematically in Figure 3.1. For convenience, it is assumed that there is a unit mass in the cylinder. Assuming also that there are no (or negligible) changes in elevation during the process and no directed (net) velocity of the working fluid, we may properly neglect energy terms relating to potential and kinetic energy. Writing the first law in words which state that the energy in state a plus or minus any additions or depletions from the system must equal the energy in state b yields the following: u1 + q – w = u2 (3.1) Rearranging yields

u2 – u1 = q – w (3.2a)

where both q and w are used to denote the net heat and net work, respectively, entering or leaving the system per unit mass of fluid and u denotes the internal energy per unit mass. Note that heat added is always positive and will increase the energy in the system. If work is added to the system from the surroundings, this will also increase the energy in the system. For consistency, because from Section 2.3 work added is considered negative, the work term in Equation 3.1 must have a negative sign. It is interesting and instructive to note that the piston–cylinder arrangement is treated as a nonflow process by the selection of the boundaries of the system, as shown by the

q (net in)

System

1 lb System

Work (net out)

1 lb Z1

a.

Z2

Reference plane

b.

2 a

b x

1

c.

FIGURE 3.1 Nonflow system. (a) Initial piston-cylinder system. (b) Final piston-cylinder system. (c) Work as a path function.

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dashed lines in Figures 3.1a and 3.1b. However, when the piston and cylinder are part of an internal combustion engine the selection of the system boundary at the exterior of the engine leads us to a steady-flow system where fuel and air enter while heat and work cross the boundary. This concept will be treated in further detail when we concern ourselves with power cycles in Chapters 8 and 9. Equation 3.2a is useful in establishing that internal energy is a property of a system and is not dependent on the path taken to place the system in a given configuration. This is true even though both q and w are path functions; that is, their values depend on the method of placing a system in a given configuration. For proof of the fact that internal energy is a property, the following reasoning is used.* Consider a system initially at state 1 that is caused to undergo a change to a second state 2 via path a. From Equation 3.2a and Figure 3.1c, we have u2 – u1 = qa – wa (3.2b) where the subscript a is used to denote path a. If path b is now followed between the same points 1 and 2, Equation 3.2a becomes u2 – u1 = qb – wb

(3.2c)

This procedure can be carried out for any path (x), and it must follow that when Equation 3.2a is applied, u2 – u1 = qx – wx

(3.2d)

Because the left sides of Equations 3.2b, 3.2c, and 3.2d are equal, it follows that the right sides of these equations

qx – wx = qa – wa = qb – wb (3.3)

are also equal, and that u2 – u1 is fixed only by the end states of the system and is independent of the process. It can therefore be concluded that internal energy is a property. As such, it is a state function and independent of the path of any process. There is one point about which students should make careful note. The proof of the fact that internal energy is a property is extremely important. In the calculus, an area can be obtained by integration. This process can be performed for those functions (paths) that can be evaluated as being continuous and dependent only on the end states. Such a function is said to be mathematically exact, and it is possible to perform all operations of the calculus on it. Opposed to this concept is the function whose value between two end states is determined not by the end states but by the path taken to achieve the end state. For example, the work done in moving a given block from one position on a plane to another position on the plane will depend on the amount of work done against friction. If the table is rough, more work is required to go from the initial to the final position than if the table were smooth. Mathematically, such a function is said to be inexact, and in general, it is not possible to evaluate this function directly by the methods of the calculus unless the path is defined. Work and heat are inexact (path functions), whereas internal energy is exact (a function of the end states only).

* This material is a modification of the proof in Keenan (1941, p. 12 and following).

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First Law of Thermodynamics

ILLUSTRATIVE PROBLEM 3.1 If a nonflow, constant-volume process has 10 Btu/lbm as heat added to the system, what is the change in internal energy per pound of working fluid? SOLUTION For a constant-volume process, we can consider that the piston in Figure 3.1 has not moved. Alternatively, we can consider that a tank having a fixed volume has heat added to it. Under these conditions, the mechanical work done on or by the system must be zero. The application of Equation 3.2a to this system yields u2 – u1 = q and it must be concluded that all the energy crossing the boundary as heat has been converted to internal energy of the working fluid. Therefore, u2 – u1 = 10 Btu/lbm

ILLUSTRATIVE PROBLEM 3.2 The working fluid in a nonflow system undergoes an adiabatic change. Determine the work done in this process. SOLUTION An adiabatic process is defined to be one during which no energy interchange as heat crosses the boundary of a system. As shown in Figure 3.2, this is the same as considering the system boundaries to be perfectly insulated. Note, however, that the piston can and does move. Application of Equation 3.2a to this situation yields u2 – u1 = –w Thus, the energy interchange as work to or from the system per unit mass of working substance equals the change in internal energy of the working fluid per unit

Movable, perfectly insulated piston

System

FIGURE 3.2 Illustrative Problem 3.2.

Perfect insulation Mass m

Q=0

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mass of fluid. The negative sign is taken to mean that work into the system (negative work by convention) will cause an increase in the internal energy of the working fluid and that work out of the system (positive work) will cause a decrease in the internal energy of the working fluid. In Chapter 2, we concluded that the work done in a quasi-static frictionless, nonflow process is the area under the p–v curve. Using this concept and Equation 2.21 for the work in Equation 3.2a gives us the following useful relation:

u2 – u1 = q – pΔv (3.4)

Equation 3.4 is written per unit mass of working fluid, and students are cautioned to understand the reasoning behind this equation fully so that it will not be misapplied. Either Equation 3.2a or Equation 3.4 is called the nonflow energy equation and expresses the first law as applied to a nonflow process. Equation 3.4 is more restrictive and, in the strictest sense, is applicable only to frictionless, quasi-static, nonflow processes. ILLUSTRATIVE PROBLEM 3.3 Solve Illustrative Problem 3.1 by the direct application of Equation 3.4. SOLUTION u2 – u1 = q – pΔv But v2 – vx (or Δv) is zero. Therefore, u2 – u1 = q (as before)

There is one nonflow process that will be found to be quite important in our subsequent discussion: the quasi-static, nonflow, constant-pressure process. Using Equation 3.4, we will now derive an expression relating heat, work, and internal energy for this process. Refer to the situation illustrated in Figures 3.1 and 3.3 where heat and work can cross the system boundary. Transposing terms in Equation 3.4 yields u2 – u1 + pΔv = q (3.4a) However, p, the pressure, has been defined to be constant. Therefore, u2 – u1 + p(v2 – v1) = q (3.4b) The condition of constant pressure permits us to write p = p1 = p2. Thus, u2 – u1 + p2v2 – p1v1 = q (3.4c)

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First Law of Thermodynamics

p p = Constant p

v1

(a)

(b)

v2

v

FIGURE 3.3 Quasi-static, nonflow, constant-pressure process. (a) Closed piston-cylinder. (b) Constant pressure process.

Equation 3.4c is consistent in terms of SI units. If the internal energy is in Btu per pound, pressure is in pounds per square foot, and specific volume is in cubic feet per pound, we can regroup terms and place them into consistent thermal units of Btu per pound as follows:

u2 +

p2 v2 pv − u1 + 1 1 = q (3.4d) J J

The composite term u + pv/J is a property that we will find to have great utility when flow processes are considered. At present, we will simply define h to be enthalpy expressed in Btu/lbm and to be given by

h = u+

pv (3.5) J

The conversion factor J is carried along as a reminder to students of the necessity to use consistent units in the English system at all times. Returning to Equation 3.4d, we now have the following energy equation for the nonflow, quasi-static, constant-pressure process: q = h2 – h1 = Δh

(3.4e)

So far, three nonflow, quasi-static processes have been considered. To summarize the energy equations for these processes,

1. Constant-volume process

q = u2 – u1 = Δu

(3.6)

2. Adiabatic process

–w = u2 – u1 = Δu

(3.7)

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Thermodynamics and Heat Power

3. Constant-pressure process q = h2 – h1 = Δh



(3.4e)

Further, the work of a quasi-static, nonflow process is w = pΔv

(2.21)

Enthalpy is defined as

h = u+

pv J

(3.5)

or



h2 − h1 = u2 +

p2 v2 pv − u1 + 1 1 J J

(3.8)

In all the foregoing, it has been assumed that the mass of fluid was unity. However, the equations derived can be used for any mass simply by multiplying each term in the energy equation by m, the mass involved. The enthalpy definition used in this book will include the conversion factor J for convenience and consistency, especially when using English units.

ILLUSTRATIVE PROBLEM 3.4 A rigid container contains 10 lb. of water. (a) If 100 Btu as heat is added to the water, what is its change in internal energy per pound of water? (b) If the 100 Btu is added by the mechanical friction of a paddle wheel stirring the water, what is the change in internal energy of the water? Discuss both processes. Refer to Figure 3.4. Win

Qin

FIGURE 3.4 Illustrative Problem 3.4.

m = 10 lbm

m = 10 lbm

(a)

(b)

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First Law of Thermodynamics

SOLUTION a. The nonflow energy equation applied to this process yields q = u2 – u1. Per pound mass of working substance, q = 100/10, or 10 Btu/lbm. Therefore, u2 – u1 = 10 Btu/lbm. b. In this process, energy crosses the boundary of the system by means of frictional work. As far as the system is concerned, we note only that energy has crossed its boundaries. The similarity of the terms work and heat lies in the fact that both are energy in transition. Thus, for the present problem, the contents of the tank will not distinguish between the energy if it is added as heat or the energy added as frictional work. As for part (a), u2 – u1 = 10 Btu/lbm.

3.4 Steady-Flow System 3.4.1 Conservation of Mass—Continuity Equation In the steady-flow system, both mass and energy are permitted to cross the boundaries of the system, but by denoting the process to be steady, we limit ourselves to those systems that are not time dependent. Because we are considering steady-flow systems, we can express the principle of conservation of mass for these systems as requiring the mass of fluid in the control volume at any time be constant. In turn, this requires that the net mass flowing into the control volume must equal the net mass flowing out of the control volume at any instant of time. To express these concepts in terms of a given system, let us consider the system schematically in Figure 3.5. Let us assume that at a certain time, fluid starts to enter the control volume by crossing the control surface at ① and that, after a small interval of time, the flowing fluid fills the pipe for a short distance Δx. If it is further assumed that, in this short section of uniform pipe, no heat is added or work is exchanged and that the fluid density stays constant, we can evaluate the amount of fluid that flowed between ① and ②. The mass contained between these sections is equal to the volume contained between the sections multiplied by the density of the fluid. The volume is AΔx, and the density is ρ. Therefore, the contained mass is ρAΔx. The distance between stations, Δx, is simply VΔt, where V is the

Control suface

x 1

Pressure p+ p

Uniform density

p1

FIGURE 3.5 Elementary flow system.

2

Velocity V

Control volume Pressure p

p2

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velocity of the fluid and Δt is the flow time required to fill the pipe between ① and ②. Substituting this for Δx yields m = ρAVΔt

(3.9a)

or  = ρAV = ρ1 A1V1 = ρ2 A2V2 (3.9b) m



 is the mass rate of flow per unit time, m/Δt. Also, where m  = m



AV v

(3.9c)

where the specific volume replaces the density, v = 1/ρ. Equation 3.9b is known as the continuity equation, and as written for a pipe or duct, we have made the assumption that the flow is normal to the pipe cross-section and that the velocity V either is constant across the section or is the average value over the cross-section of the pipe. We shall use the continuity equation quite frequently in our study, and it is important to note that it expresses the fact that the mass flow into the control volume must equal the mass flow out of the control volume in steady flow.

ILLUSTRATIVE PROBLEM 3.5 At the entrance to a steady-flow device, it is found that the pressure is 100 psia and that the density of the fluid is constant at 62.4 lbm/ft.3. If 10 000 ft.3/min of this fluid enters the system and the exit area is 2 ft.2, determine the mass flow rate and the exit velocity (see Figure 3.6). SOLUTION  = ρ1 A1V1. Let us first calculate the mass flow into the system. From Equation 3.9b, m We are told that 10 000 ft.3/min of this fluid enters the system, which is the same as

1

p1 = 100 psia 3 1 = 62.4 lbm/ft. 10 000 ft.3/min = A1V1 FIGURE 3.6 Illustrative Problem 3.5.

2

A2 = 2 ft.2

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First Law of Thermodynamics

 = ρ1 A1V1 = 62.4 × 10 000 = 624 000 lbm/min. saying A1V1 = 10 000 ft.3/min. Therefore, m Because this mass flow must also leave the system,  = ρ2 A2V2 m

Thus,



624 000

lbm lb ft. = 62.4 m3 × 2 ft.2 × V2 min min ft. V2 = 5000 ft./min

ILLUSTRATIVE PROBLEM 3.6 If the fluid entering the system shown in Figure 3.6 has a density of 1000 kg/m3 and 2000 m3/min enters the system, determine the mass flow rate and the exit velocity if the exit area is 0.5 m2. Assume that the density is constant. SOLUTION  = ρ1 A1V1. Therefore, Proceeding as in Illustrative Problem 3.5, m = ρAV; m

 = 1000 m

kg m3 × 2000 3 min m

= 2 × 106

kg min



 = ρ2 A2V2, Because m

2 × 106

kg kg = 1000 3 × 0.5 m 2 × V2 min m

and

V2 = 4000 m/min

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ILLUSTRATIVE PROBLEM 3.7 A hose is 1 in. in diameter and has water the density of which is 62.4 lbm/ft.3 flowing steadily in it at a velocity of 100 ft./s. Determine the mass flow of water in the hose (see Figure 3.7). SOLUTION From the continuity equation,

 = ρAV = 62.4 m

π(1 in.)2 lbm ft. × × 100 = 34.0 lbm/s 3 2 s ft. in. 4 × 144 2 ft.

Note that the dimension of the area has been used in square feet for dimensional consistency.

1 V1 = 100 ft./s 3 1 = 62.4 lbm/ft.

FIGURE 3.7 Illustrative Problem 3.7.

Consider a steam turbine as a flow system. Our present interest is in the flow of steam into and out of the noted boundaries of this system. The actions and interactions within the boundaries of this system will be studied later, but for us at this time, the boundaries can be thought of as defining a “black box.” Only the fluid (steam) interfaces are considered. The continuity equation is applied to the inlet and outlet steam flow, as in the following example.

ILLUSTRATIVE PROBLEM 3.8 A steam turbine has an inlet steam flow of 50 000 lbm/h of steam whose specific volume is 0.831 ft.3/lbm. The inlet diameter is 6 in. At the outlet, the pipe diameter is 8 in., and the specific volume of the steam is 1.825 ft.3/lbm. Determine the velocity at inlet and outlet of the turbine in ft./s.

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First Law of Thermodynamics

SOLUTION  1 = 50 000 lbm/h and v1 = 0.831 ft.3/lbm. Therefore, We have at the inlet m 1 = m

A1V1 v1

ft.3  v m lbm V1 = 1 1 = = 58.8 ft./s × min s A1 π(6 in.)2 60 × 60 min 4(144 in.2/ft.2 ) h 50 000



lbm h

0.8831



 2 is the same, that is, 50 000 lbm/h. Therefore, At the outlet, the value of m  v m V2 = 2 2 = A2



50 000 60

lbm h

min s × 60 min h

×

1.825 ft.3/ lbm π 8 in. 4 12 in./ft.

V2 = 72.6 ft./s

2



Again note the conversion factors of (12 in.)2/ft.2 and 60 min/h × 60 s/min to obtain the desired units of velocity.

ILLUSTRATIVE PROBLEM 3.9 A steam turbine has an inlet steam flow of 104 kg/h whose specific volume is 0.05 m3/kg. The inlet diameter is 100 mm, and the outlet diameter is 200 mm. If the outlet specific volume is 0.10 m3/kg, determine the inlet and outlet velocities.  

SOLUTION 1 =m  2 = 10 4 kg/h m



 1 = AV/v , V = m  v/A. Therefore, Because m 0.05



V1 =

m3 kg

 1v1 m 10 4 kg/h = × = 17.68 m/s A1 (60 × 60) s/h π (0.1)2 m 2 4

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At the outlet,

V2 =



0.10

4

m3 kg

 2 v2 m 10 kg/h = × = 8.84 m/s A2 (60 × 60) s/h π (0.2)2 m 2 4

3.4.2 Steady-Flow Energy Equation Figure 3.8 shows a steady-flow system in which it is assumed that each form of energy can  lb. of fluid per second enters and the same enter and leave the system. At the entrance, m amount leaves at the exit. At the entrance, the fluid has a pressure of p1, a specific volume of v1, an internal energy of u1, and a velocity of V1. At the exit, we have similar quantities expressed as p2, v2, and V2. The fluid enters and leaves at different elevations, and work and heat cross the boundary in both directions. In applying the first law to a system in which both mass and energy can cross the boundaries, it is necessary to adhere to the mathematical conventions chosen for positive and negative quantities of energy. It is also imperative that all pertinent energy terms be included in any analysis. To summarize, Table 3.1 identifies six energy terms that apply to various situations for steady-flow systems. We express the first law for the system shown in Figure 3.8 by stating that all the energy entering the system must equal all the energy leaving the system. This energy balance is set up in Table 3.2. By equating all the terms in Table 3.2 in English units, we obtain pv Z1 g V2 w + 1 + u1 + 1 1 + in + qin J gc 2 gc J J J



=

Z2 J

pv g wout V + + u2 + 2 2 + + qout 2 gc J J J gc

Work out

Work in m p1 v1 u1 V1

Z1

qin

qout Reference plane

FIGURE 3.8 Steady-flow system.

(3.10)

2 2

Z2

m p2 v2 u2 V2

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First Law of Thermodynamics

TABLE 3.1 Energy Terms Value Item

Btu/Unit Mass

kJ/Unit Mass

Zg Jg c

Zg

Kinetic energy

V2 2 gc J

V2 2

Internal energy

u

u

Flow work

pv J

pv

Work

w J

w

Heat

q

q

Potential energy

TABLE 3.2 Energy Balance Energy in

Energy out

Btu/lbm

kJ/kg

Btu/lbm

kJ/kg

Potential energy

Z1 g Jg c

Z1g

Z2 g

Z2g

Kinetic energy

V12 2 gc J

V12 2

V22 2 gc J

V22 2

Internal energy

u1

u1

u2

u2

Flow work

p1 v1 J

p1v1

p2 v2 J

p2v2

Work

w in J

win

w out J

wout

Heat

qin

qin

qout

qout

Jg c

In SI units, Z1 g +

V12 + u1 + p1 v1 + win + qin 2

V2 = Z2 g + 2 + u2 + p2 v2 + wout + qout 2

(3.10a)

Equation 3.10 is quite general and expresses the first law for this system. It is sometimes called the steady-flow energy or the general energy equation. We note that it is also quite proper to call it the energy equation applied to a steady-flow system.

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If at this point we note that both the heat and the work terms can be combined to form individual terms of net heat and net work, and being careful of the mathematical signs of these net terms, we can write for English units,

pv Z1 g V2 Z + 1 + u1 + 1 1 + q = 2 J gc 2 gc J J J

g pv V2 w + 2 + u2 + 2 2 + (3.11) gc 2g c J J J

In SI units,

Z1 g +  

V 12 V2 + u1 +   p1 v1 + q =   Z2 g +   2 +   u2 +   p2 v2 + w. (3.11a) 2 2

In Equation 3.11, all terms are written as Btu/lbm, and q and w represent net values per unit mass of working fluid. If we now note further that the grouping of terms u + pv/J appears on both sides of Equation 3.11, and that this combined term is a property that we have already called enthalpy, then from the definition of the term enthalpy we have

h = u+

pv J

(3.5)

(or h = u + pv in SI units). Using Equations 3.5 and 3.11 yields, for English units,

Z1 g V2 Z + 1 + h1 + q = 2 J gc 2 gc J J

g V2 w + 2 + h2 + (3.12) gc 2 gc J J

By regrouping the terms in Equation 3.12, we obtain



q−

V 2 − V 12 w Z − Z1 g = ( h2 − h1 ) + 2 + 2 (3.13) 2 gc J J J gc

where each quantity is in Btu/lbm. In terms of SI units,

q − w = h2 − h1 + g(Z2 − Z1 ) +

V 22 − V 12 (3.13a) 2

where each quantity is in terms of J/kg or kJ/kg. Note that when Z is in meters and V is in meters per second, the potential energy and kinetic energy terms will be in J/kg, the equivalent of m2/s2. Heat, work, and enthalpy per unit mass are usually given in kJ/kg. Thus, a factor of 1000 is often needed to make all the terms in Equation 3.13a compatible. Students should note that Equations 3.10 through 3.13 are essentially the same. To apply these equations intelligently, it is important that each of the terms be completely

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First Law of Thermodynamics

understood. Although they are not difficult, students may encounter trouble at this point because of a lack of understanding of these energy equations and the basis for each of the terms in them. Before illustrating the use of these energy equations, let us consider the following situation. A fluid is flowing steadily in a device in which it undergoes a compression. Let us further assume that this process is frictionless and quasi-static. Its work term can be written as the sum of the work done on the fluid plus the flow work. Kinetic and potential energy terms are assumed to be negligible. Thus, the work for this process becomes w = p1v1 – p2v2 – pΔv

(3.14)

Let us now plot a pv diagram for the fluid, as shown in Figure 3.9. As shown in Figure 3.9a, the term pΔv is the area under the curve between the limits 1 and 2. Subtracting p1v1 and adding p2v2 (graphically) results in vΔp and is shown in Figure 3.9b. Mathematically, –vΔp = p2v2 – p1v1 + pΔv

(3.15)

It will be recalled that for the quasi-static, frictionless, nonflow system, pΔv evaluated the work done on the working fluid. For the flow system, flow work of an amount of p1v1 enters the system, and flow work of an amount p2v2 leaves the system. We can therefore interpret the meaning of the areas on Figure 3.9 or the terms of Equation 3.15 as follows: The work of the quasi-static, frictionless flow system (neglecting the kinetic and potential energy terms) is the algebraic sum of the work to induct the fluid into the system plus the work of compression (or expansion) less the flow work to deliver the fluid to the downstream exit. It is sometimes convenient to think of pΔv as the work of compression (or expansion) and vΔp as the work of the compressor (or expander). It is extremely important to note that both pΔv and vΔp evaluate work only for a quasi-static process or system. For systems that are real, they do not evaluate work. However, for a large class of systems, they approximate the work terms, and their use is justified both from this approximation and the relative ease with which they can be evaluated. p

p 2

p2

2

p2

p

p

p

v

1

p1

1

p1

p v v2

v1 (a)

FIGURE 3.9 A p–v diagram. (a) Work as pΔv. (b) Work as vΔp.

v

v2

v1 (b)

v

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Thermodynamics and Heat Power

The form of Equations 3.11 through 3.13a, where work is expressed per unit mass, is helpful when determining the power associated with a given process. The work per unit mass times the mass flow rate is the power. Work out is associated with power out and likewise for work in. Expressed as an equation,  =m  w (3.16) W



 in Btu/s. Power  in lbm/s, w in Btu/lbm, and W Typical units are, in the English system, m may be expressed in horsepower using the conversion factor in Table 1.8. In the SI system,  in kJ/s, or kilowatts.  may be in kg/s, w in kJ/kg, and W m There is a similar relationship between heat transfer per unit mass, q, the mass flow rate,  and the rate of heat transfer per unit time. This is given by m,  q (3.17) Q = m



CALCULUS ENRICHMENT From the general energy equation (Equations 3.13 and 3.13a), we can write δq – δw = dh + d(K.E.) + d(P.E.) (a) where δ (delta) denotes an inexact quantity, that is, one that is a function of the path. Because h, enthalpy, is defined to equal u + pv,

h = u + pv; dh = du + p dv + v dp (b)

Substitute Equation b into Equation a, and δq – δw = du + p dv + v dp + d(K.E.) + d(P.E.) (c) From the energy equation for the nonflow system, δq – δu = p dv (d) Using Equations d and c, δq – δw = du + δq – δu + v dp + d(K.E.) + d(P.E.) (e) and δw = –v dp (f) if the K.E. and P.E. terms are negligible. From Equation f, we conclude that the work of a quasi-static flow process is the area behind the p–v curve. 3.4.3 Bernoulli Equation In fluid mechanics, use is sometimes made of the Bernoulli equation. Because of the frequent misapplication of this equation, a brief discussion of it will now be undertaken. Let

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First Law of Thermodynamics

us consider a system in which the flow is steady, there is no change in internal energy, no work is done on or by the system, no energy as heat crosses the boundaries of the system, and the fluid is incompressible. We further assume that all processes are ideal in the sense that they are frictionless. For this system, the energy equation reduces to the following in mechanical units of foot-pounds per pound mass:



Z1

g V 12 g V 22 + + p1 v1 = Z2 + + p2 v2 (3.18) gc 2 gc gc 2 gc

or in SI units,



Z1 g +

V 12 V2 + p1 v1 = Z2 g + 2 + p2 v2 (3.18a) 2 2

Note that for an incompressible fluid, v1 = v2. Equation 3.18 is the usual form of the Bernoulli equation found in elementary physics and fluid mechanics texts. Each term can represent a height, because the dimension of foot-pounds per pound corresponds numerically (and dimensionally) to a height. Hence, the term head is frequently used to denote each of the terms in Equation 3.18. From the derivation of this equation, we note that its use is restricted to situations in which the flow is steady, there is no friction, no shaft work is done on or by the fluid, the flow is incompressible, and there is no change in internal energy during the process. These restrictions are severe, and only under the simplest situations can we hope to apply the Bernoulli equation successfully. It becomes even more difficult to justify the procedure of adding heat and work terms to this equation while maintaining all the other restrictions. Students are cautioned against the use of this equation without a thorough understanding of its restrictions. In every case, it is preferable to write the complete and correct form of the energy equation first and then to make those assumptions that can be justified for each problem. 3.4.4 Specific Heat The term specific heat is defined as the ratio of energy as heat transferred during a particular process per unit mass of fluid involved divided by the corresponding change of temperature of the fluid that occurs during this process. Because heat can be transferred to or from a fluid and algebraic signs have been adopted for the direction of heat transfer, it is entirely possible for a process to have a negative specific heat. Students should not confuse the specific heat of a process with the specific heat property. This definition of specific heat is important for two processes, because they serve to define a new property of a fluid. These processes are the constant-pressure process (flow or nonflow) and the constant-volume process. Recall from earlier work that the constant-pressure, nonflow process is characterized by the energy equation that q = h2 – h1 = Δh. For the steady-flow process without change in elevation, in the absence of external work, and with negligible changes in kinetic energy, the steady-flow energy equation leads to the same result. Thus, for any constant-­ pressure process (flow or nonflow with the conditions noted), the specific heat is defined as

cp =

q ∆T

= p

∆h ∆T

p

(3.19)

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Thermodynamics and Heat Power

or (cp ΔT = Δh)p (3.19a) where the subscript p indicates a constant-pressure process. For the constant-volume process (which can only be a nonflow process), q = u2 – u1 = Δu. Therefore,

cv =

q ∆T

= v

∆u ∆T

(3.20) v

or (cvΔT = Δu)v (3.20a) where the subscript v indicates a constant-volume process.* These specific heats are the properties of the fluid and depend only on the state of the fluid. Typical units of specific heat are Btu/lbm·°R in English units and kJ/kg·K in SI units. A further discussion of specific heats is given in Chapter 6, where the internal energy and enthalpy of the ideal gas are functions of temperature only, making the definition of Equations 3.19 and 3.20 general for the ideal gas and not restricted to only constantpressure or constant-volume processes. ILLUSTRATIVE PROBLEM 3.10 A gas initially of 100°F and having cp = 0.22 Btu/lbm·°R and cv = 0.17 Btu/lbm·°R is placed within a cylinder. If 800 Btu as heat is added to 10 lbm of the gas in a nonflow, constant-pressure process, determine the final gas temperature. Also, determine the work done on or by the gas. Refer to Figure 3.10. SOLUTION For the nonflow, constant-pressure process, q = Δh = h2 – h1. However, Equation 3.19 allows us to evaluate Δh in terms of temperature and the specific heat at constant pressure. Thus, q = h2 – h1 = cp(T2 – T1) Using the data given and q on a unit mass basis,

q=

800 Btu = 0.22(T2 − T1 ) 10 lbm

* Equations 3.19 and 3.20 are more correctly written mathematically as



cp ≡

∂h ∂t

and c v ≡ p

∂u ∂t

v



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First Law of Thermodynamics

Qin = 800 Btu

m = 10 lbm cp = 0.22 Btu/lbm °R cv = 0.17 Btu/lbm °R

FIGURE 3.10 Illustrative Problem 3.10.

so T2 – T1 = 363.6°F. Because the initial temperature is 100°F, the final temperature is 363.6°F + 100 = 463.6°F. To obtain the work, we apply Equation 3.2 to the nonflow process: q – w = u2 – u1



The term u2 – u1 can be evaluated in terms of temperature and the specific heat at constant volume from Equation 3.20. Using this, we obtain –w = (u2 – ux) – q = cv(T2 – T1) – q Using q on a unit mass basis and noting that T2 – T1 = 363.6°F,

or

– w = 0.17 Btu/lbm⋅ °R(363.6°R) −

800 Btu 10 lbm

– w = 61.8 – 80 = –18.2 Btu/lbm w = 18.2 Btu/lbm



Thus, 18.2 Btu/lbm or 182 Btu as work is taken out of the system due to work done by the gas, because there is 10 lbm in the system.

3.5 Applications of First Law of Thermodynamics At this point in our study, we will apply the first law to several steady-flow situations that we will have applications for in later sections of this book. For the present, we restrict ourselves to seven steady-flow processes:

1. The steam or gas turbine 2. Pipe flow 3. The boiler

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Thermodynamics and Heat Power

4. The flow in nozzles 5. The throttling process 6. The heat exchanger 7. Filling a tank

3.5.1 Turbine As our first illustration of the applicability of the first law to steady-flow processes, let us consider the steam turbine shown in Figure 3.11. In this device, steam enters and expands in fixed nozzles to a high velocity. The high-velocity steam is then directed over the turbine blades, where it does work on the turbine wheel. The steam then exhausts from the turbine. The purpose of this machine is to obtain shaft work, and certain features about it should be noted. First, the shaft of the turbine is horizontal. Second, as the steam expands, its specific volume increases (see Chapter 5), and to keep the exit velocity nearly equal to the entering velocity, the exit pipe area is proportionally greater than the inlet pipe area. The turbine is suitably insulated to minimize heat losses to the surroundings and also to eliminate the possibility of injuring operating personnel working in the vicinity of the hot turbine casing. With the foregoing in mind, let us now apply the first law to the turbine (either steam or gas) shown schematically in Figure 3.12. The first law is given by q−



V2 − V21 w Z − Z1 g = h2 − h1 + 2 + 2 (3.21) 2 gc J J J gc

System boundary Steam in Shaft work

System boundary Steam out FIGURE 3.11 Single-stage turbine. (Courtesy of Worthington Corp., Columbus, Ohio.)

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First Law of Thermodynamics

1 m p1 v1 T1 u1 h1

2 m p2 v2 T2 u2 h2

System

Shaft work W

Boundary Z1

Z2

Insulation

Reference plane FIGURE 3.12 Schematic of a turbine.

or



q − w = h2 − h1 + g(Z2 − Z1 ) +

V 22 − V 12 (3.21a) 2

Because the shaft of the machine is horizontal, [(Z2 – Z1)/J] (g/gc) can be taken to be zero; that is,

where 0 is taken to mean goes to zero. Also as noted, the inlet and outlet velocities are kept nearly equal, leading us to conclude that the kinetic energy difference term goes to zero: Finally, the insulation of the turbine would effectively prevent heat losses to the surroundings:

q0 

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Thermodynamics and Heat Power

Equation 3.21, as applied to this device, becomes w = h1 − h2 J

or from Equation 3.21a,

w = h1 – h2 All the assumptions made for the steam turbine are equally applicable to the gas turbine. In this industrial unit, the turbine also drives the compressor. Exhaust gases leave at the right of the figure via an exhaust elbow. This unit will be discussed in detail later on as a prime mover in a power-producing cycle. ILLUSTRATIVE PROBLEM 3.11 A large steam turbine operates with a steam flow rate of 150 000 lbm/h. The conditions at inlet and outlet are tabulated below. Determine the power produced (a) if heat losses are negligible and (b) if heat losses equal 50 000 Btu/h.

Pressure (psia) Temperature (°F) Velocity (ft./s) Inlet position (ft.) Enthalpy (Bm/lbm)

Inlet

Outlet

1000 1000 125 +10 1505.4

1 101.74 430 0 940.0

SOLUTION Let us start this problem by referring to Figure 3.12 and using the form of energy equation given by Equation 3.12,

Z1 g V2 Z + 1 + h1 + q = 2 J gc 2 gc J J

g V2 w + 2 + h2 + gc 2 gc J J



where all terms are per unit mass, a. q = 0, and assuming that g = gc,



10 (125)2 + + 1505.4 + 0 778 2 × 32.17 × 778 w ( 430)2 + 940.0 + = 0+ 2 × 32.17 × 778 J

(a)

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First Law of Thermodynamics



0.013 + 0.312 + 1505.4 + 0 = 0 + 3.694 + 940.0 +

w (b) J

or w = 562.03 Btu/lbm J



(Had we neglected potential and kinetic terms, w/J = 565.4 Btu/lbm, a difference of 0.6%, which is quite small.) The total work of the turbine is 150 000 lbm/h × 562.03 Btu/lbm = 84 304 500 Btu/h. In terms of horsepower, 84 304 500 Btu/h × 778 ft. ⋅ lbf /Btu = 33 125.7 hp 60 min/h × 33 000 ft. ⋅ lbf /hp





In terms of kilowatts,

33 125.7 hp × 0.746 kW/hp = 24 711.8 kW

500 000 Btu/h b. = 0.333 Btu/lbm ( heat loss) 150 000 lbm/h Using this with Equation b, and noting that it is negative by convention, yields

0.013 + 0.312 + 15.5.4 − 0.333 = 0 + 3.694 + 940.0 +

w J

or

w = 561.70 Btu/lbm J which differs from part (a) by 0.06%. For all practical purposes, we could have neglected the potential, kinetic, and heat loss terms.

ILLUSTRATIVE PROBLEM 3.12 A steam turbine operates with an inlet velocity of 40 m/s and an inlet enthalpy of 3433.8 kJ/kg. At the outlet, which is 2 m lower than the inlet, the enthalpy is 2675.5 ­kJ/­kg­ and the velocity is 162 m/s. If the heat loss from the turbine is 1 kJ/kg, determine the work output per kilogram.

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SOLUTION If we refer to Illustrative Problem 3.11, it will be noted that these problems are similar except for units. Using Equation 3.11a yields



Z1 g +

V 21 V2 + h1 + q = Z2 g + 2 + h2 + w 2 2

For the units of this problem, 2 m × 9.81m/s 2 ( 40 m/s)2 kJ kJ + + 3433.8 −1 1000 J/kJ 2 × 1000 J/kJ kg kg = 0+ 0.02

(162 m/s)2 kJ + 2675.5 +w 2 × 1000 J/kJ kg

kJ kJ kJ kJ + 0.8 + 3433.8 −1 kg kg kg kg = 0 + 13.12

kJ kJ + 2675.5 +w kg kg



or

w = 745.0

kJ kg

ILLUSTRATIVE PROBLEM 3.13 A turbine (gas) receives air at 150 psia and 1000°R and discharges to a pressure of 15 psia. The actual temperature at discharge is 600°R. If cp of the gas can be taken to be constant over this temperature range and equal to 0.24 Btu/lbm·°R, determine the work output of the turbine per pound of working fluid. At inlet conditions, the specific volume is 2.47 ft.3/lbm, and at outlet conditions, it is 14.8 ft.3/lbm. The data are also shown in Figure 3.13. SOLUTION We have already discussed the turbine in detail and concluded that the first law yields

w = h1 − h2 J

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First Law of Thermodynamics

p1 = 150 psia

2

T1 = 1000ºR

1

v1 = 2.47 ft.3/lb.

p2 = 15 psia

T2 = 600ºR

v2 = 14.8 ft.3/lb.

Z1

Z2 Reference plane

FIGURE 3.13 Illustrative Problem 3.13.

Equation 3.19 enables us to obtain h1 – h2, because for the gas, h1 – h2 = cp(T1 – T2) Therefore,

w = h1 − h2 = c p (T1 − T2 ) = (0.24)(1000 − 600) J

and

w = 96 Btu/lbm J

Note that the specific volume and pressure given do not enter the solution of the problem. However, a pressure differential is required to cause the gas to flow.

ILLUSTRATIVE PROBLEM 3.14 Even though the turbine of Illustrative Problem 3.13 may be well insulated, there will be some heat loss. If the heat loss is found by experiment to be equal to 1.1 Btu/lbm of gas, determine the work output of the turbine per pound mass of gas. SOLUTION We must again return to the point in our discussion where we took  q 0 and not make this assumption. Doing this gives us

q−

w = h2 − h1 J

or

w = q + ( h1 − h2 ) J

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Thermodynamics and Heat Power

Because q is out of the system, it is a negative quantity, and h1 – h2 is the same as for Illustrative Problem 3.13. Thus, w = −1.1 + 96.0 = 94.9 Btu/lbm J



In other words, a heat loss decreases the work output of the turbine, as we have seen earlier.

3.5.2 Pipe Flow As our next illustration of the first law, we will apply the law to the flow of fluids in pipes. ILLUSTRATIVE PROBLEM 3.15 A gas flows in a pipe whose pressure and temperature at one section are 100 psia and 950°F. At a second section of the pipe, the pressure is 76 psia and the temperature is 580°F. The specific volume of the inlet gas is 4.0 ft.3/lbm, and at the second section, it is 3.86 ft.3/lbm. Assume that the specific heat at constant volume is 0.32 Btu/lb·°R. If no shaft work is done and the velocities are small, determine the magnitude and direction of the heat transfer. Assume the pipe to be horizontal, and neglect velocity terms. The data are also shown in Figure 3.14. SOLUTION We first write out the equation of the first law and then apply it to this process:

pv pv Z1 g V2 Z g V2 w + 1 + u1 + 1 1 + q = 2 + 2 + u2 + 2 2 + J gc 2 gc J J J gc 2 gc J J J Boundary

1

2

System

p1 = 100 psia



p2 = 76 psia

v1 = 4 ft.3/lbm

v2 = 3.86 ft.3/lbm

t1 = 950°F

t2 = 580°F

T1 = 1410°R

Z2

Z1 Reference plane

FIGURE 3.14 Illustrative Problem 3.15.

T2 = 1040°R

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First Law of Thermodynamics

Because the pipe is horizontal and velocity terms are to be neglected,

Also, , no work crosses the boundaries of the system. The energy equation is reduced to



u1 +

p1 v1 p v + q = u2 + 2 2 J J

However, Equation 3.20 permits us to express the internal energy change for the gas in terms of the temperature change as u2 − u1 = cv(T2 − T1)  for constant cv Therefore,



q = c v (T2 − T1 ) +

p2 v2 p1 v1 − J J

By inserting numerical quantities, we obtain



76 × 144 × 3.86 100(144)( 4) − 778 778 = −118.4 + 54.3 − 74.0 = −138.1 Btu/lbm

q = 0.32(1040 − 1410) +



Thus, 138.1 Btu/lbm is transferred from the gas.

ILLUSTRATIVE PROBLEM 3.16 If the pipe referred to in Illustrative Problem 3.15 was a vertical run of pipe such that section ② was 100 ft. above section ①, determine the direction and magnitude of the heat transfer.

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Thermodynamics and Heat Power

SOLUTION Using the reference plane of Figure 3.19 to coincide with the elevation of the pipe at section 1 makes Z1 = 0. The energy equation becomes



u1 +

p1 v1 p v Z + q = u2 + 2 2 + 2 J J J

g gc

p2 v2 p1 v1 Z2 − + J J J

g gc



and



q = u2 − u1 +



Using u2 – u1 = cv(T2 – T1) and Z2 = 100 ft. gives us



q = 0.32(1040 − 1410) +

76 × 144 × 3.86 100(144)( 4) 100 g − + 778 778 778 g c



Letting g/gc = 1 yields q = –118.4 + 54.3 – 74.0 + 0.13 = –138.0 Btu/lbm For this problem, neglecting the elevation term leads to an insignificant error.

3.5.3 Boiler The next application of the first law will be to the boiler or steam generator. The basic purpose of the steam generator is the turning of water into steam by the application of heat. It consists of a combination of many elements. In this unit, pulverized coal is burned in the furnace with air that has been preheated in the air heater. In addition to generating superheated steam, this unit reheats steam from the high-pressure turbine exhaust and returns it to the low-pressure turbine. The energy input to this system comes from the fuel, air, and feed water, and the useful output is steam. Because the purpose of the unit is to generate steam, the energy in the stack gas, unburned fuel, and heat transfer to the surroundings all represent losses that decrease the useful steam output. Again, we shall return to the steam generator in Chapter 8, where it is studied in some detail. For the present, the following problem will serve to illustrate the application of the first law to this unit.

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First Law of Thermodynamics

ILLUSTRATIVE PROBLEM 3.17 A steam boiler is required to produce 10 000 lbm/h of superheated steam at 1000°F and 1000 psia (h = 1505.9 Btu/lbm) from feed water supplied at 1000 psia and 100°F (h = 70.68 Btu/lbm). How much energy has been added to the water to convert it to steam at these conditions? The data are shown in Figure 3.15. SOLUTION As indicated in Figure 3.15, we can consider this system as a single unit with feed water entering and steam leaving. If well designed, this unit will be thoroughly insulated, and heat losses will be reduced to a negligible amount. Also, no work will be added to the fluid during the time it is passing through the unit, and kinetic energy differences will be assumed to be negligibly small. In large units, the inlet and outlet may be as much as 100 ft. apart. However, 100/778 is 0.129 Btu/lbm, which is quite small compared to the 1000 Btu/lbm or more involved in this problem. On this basis, differences in elevation will also be considered negligible. Once again, the energy equation is



pv Z1 g V2 pv Z g V2 w + 1 + u1 + 1 1 + q = 2 + 2 + u2 + 2 2 + 2 gc J 2g c J J J J gc J J gc

and for this problem –



–

Therefore,

u1 +

p1 v1 p v + q = u2 + 2 2 J J Boundary

System Feed in 10 000 lbm/h p1 = 1000 psia t1 = 100ºF h1 = 70.68 Btu/lbm

FIGURE 3.15 Illustrative Problem 3.17.

q

Steam out 10 000 lbm/h p2 = 1000 psia t2 = 1000ºF h2 = 1505.9 Btu/lbm

Z2 Z1

Reference plane



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Thermodynamics and Heat Power

or because

h = u+

pv J

q = h2 – h1 (this is the net value, because we assumed no heat losses). Using the data given, we have q = (1505.9 – 70.68) = 1435.2 Btu/lbm

For 10 000 lbm/h

10 000 × 1435.2 = 14.35 × 106 Btu/h

are required. Note that the working fluid (water) is our system and that the solution gives us the energy added to the water. This is not the energy released by combustion.

3.5.4 Nozzle A nozzle is a static device that is used to convert the energy of a fluid into kinetic energy. Basically, the fluid enters the nozzle at a high pressure and leaves at a lower pressure. In the process of expanding, velocity is gained as the fluid progresses through the nozzle. No work is done on or by the fluid in its passage through the nozzle. ILLUSTRATIVE PROBLEM 3.18 Steam is expanded in a nozzle from an initial enthalpy of 1220 Btu/lbm, to a final enthalpy of 1100 Btu/lbm. (a) If the initial velocity of the steam is negligible, what is the final velocity? (b) If the initial velocity is 1000 ft./s, what is the final velocity? See Figure 3.16.

1

System

Boundary 2 h2 = 1100 Btu/lbm

h1 = 1220 Btu/lbm

Z1

FIGURE 3.16 Illustrative Problem 3.18.

Reference plane

Z2

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First Law of Thermodynamics

SOLUTION The energy equation for a steady-flow device is pv Z1 g V2 Z + 1 + u1 + 1 1 + q = 2 J gc 2 gc J J J



g pv V2 w + 2 + u2 + 2 2 + gc 2g c J J J



For this device, differences in elevation are negligible. No work is done on or by the fluid, friction is negligible, and due to the speed of the fluid flowing and the short length of the nozzle, heat transfer to or from the surroundings is also negligible. Under these circumstances, –



Therefore,

u1 +

p1 v1 pv V2 V2 + 1 = u2 + 2 2 + 2 2 gc J 2 gc J J J



or

h1 − h2 =

V 22 − V 12 2 gc J

a. For negligible entering velocity and



h1 − h2 =

V22 2 gc J



and

V2 = 2 g c J ( h1 − h2 )



Substituting the data of the problem gives us



V2 = 2 × 32.17 lbm⋅ ft./lbf ⋅ s 2 × 778 ft. ⋅ lbf/Btu × (1220 − 1100) = 2451 ft./s



Btu lbm

b. If the initial velocity is appreciable, h1 − h2 +

V 12 V2 = 2 2 gc J 2 gc J



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Thermodynamics and Heat Power

Again, inserting numerical values yields

(1220 − 1100)

Btu + lbm

2

2 × 32.17 lbm⋅s 2 × 778 V22



ft. s

(1000)2

=

ft. lbf Btu

2

ft s

2 × 32.17 lbm⋅ft./lbf ⋅s 2 × 778

ft.⋅lbf Btu

V 22 2 × 32.17 × 778 V2 = 2647 ft./s

120 + 19.98 =



Note that in this part of the problem, the entering velocity was nearly 40% of the final velocity, yet neglecting the entering velocity makes approximately a 7 1/2% error in the answer. It is quite common to neglect the entering velocity in many of these problems.

ILLUSTRATIVE PROBLEM 3.19 Assume steam enters a nozzle with an enthalpy of 3450 kJ/kg and leaves with an enthalpy of 2800 kJ/kg. If the initial velocity of the steam is negligible, what is the final velocity? SOLUTION Refer to Illustrative Problem 3.18, and note that in SI units, V 22 = h1 − h2 2

and

V2 = 2 h1 − h2





Substitution yields

V2 =

(

)

2 × 1000 J/kJ 3450 − 2800 = 1140.2 m/s

(Note the need for 1000 J/kJ to obtain m/s.)



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First Law of Thermodynamics

Orifice plate System

Boundary

Static taps to manometer FIGURE 3.17 Orifice as a meter.

3.5.5 Throttling Process The next device that we consider is the case of an obstruction placed in a pipe (deliberately or as a result of the presence of a valve). One deliberate local obstruction that is often placed in a pipe is an orifice that is used to meter the quantity of fluid flowing. When used in this manner, the orifice usually consists of a thin plate inserted into a pipe and clamped between flanges. The hole in the orifice plate is concentric with the pipe, and static pressure taps are provided upstream and downstream of the orifice. Because of the presence of the orifice, the flow is locally constricted, and a measurable drop in static pressure occurs across the orifice. Static taps placed as shown in Figure 3.17 are usually used to measure the flow. The advantages of this device are its relatively small size, the ease of installation in a pipe, and the fact that standard installations can be used without the need for calibration. However, the orifice meter behaves in the same manner as a partly open valve and causes a relatively high pressure drop. This effect leads to the descriptive term of throttling for partly open valves, orifices, or other obstructions in pipes. In effect, the full flow is throttled back to some lesser flow by the obstruction. ILLUSTRATIVE PROBLEM 3.20 A fluid is flowing in a pipe. At some section of the pipe, there is an obstruction that causes an appreciable local pressure loss. Derive the energy equation for this process after flow has become uniform in the downstream section of the pipe. As noted earlier, this process is known as a throttling process and is characteristic of valves and orifices in pipelines. Refer to Figure 3.18. SOLUTION For the conditions of this problem, we can take differences in elevation to be negligible, differences in kinetic energy terms to be relatively small, and no work or heat to cross the system boundary. The complete energy equation is

pv Z1 g V2 pv Z g V2 w + 1 + u1 + 1 1 + q = 2 + 2 + u2 + 2 2 + 2 gc J 2g c J J J J gc J J gc



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1

2 System

Z1

Boundary

Throttle

Reference plane

Z2

FIGURE 3.18 Illustrative Problem 3.20.

and, with the assumption made for this process,

u1 +

p1 v1 p v = u2 + 2 2 J J

or

h1 = h2

In words, a throttling process is carried out at constant enthalpy. One assumption should be verified; that is, the kinetic energy differences at inlet and outlet are indeed negligible. This can easily be done by using the constant-enthalpy condition and using the final properties of the fluid and the cross-sectional area of the duct to determine an approximate final velocity. The throttling process is discussed again in Chapter 5, where we will find a very useful application of throttling.

3.5.6 Heat Exchanger The heat exchanger, as its name implies, is used to transfer heat from one fluid to another when the fluids are not mixed. In Chapter 11, the heat exchanger is considered in detail, when the problem of calculating the heat transfer is studied. Figure 3.19 shows a typical shell-and-tube heat exchanger. The “tube-side” fluid flows inside the tubes, and the “shellside” fluid flows outside the tubes but is contained by the shell of the heat exchanger. Let us now analyze the heat exchanger by referring to the sketch of Figure 3.20. The  1 and m  2, respectively. The temperatures at inlet and outlet are as two fluids flow at rates m shown. For the purposes of our present study, we will assume that potential and kinetic terms in the energy equation are negligible. Also, we will assume that there are no heat losses from the unit. This requires all of the heat transferred from one fluid to be received by the other. That is,

Q 1 = Q 2 (3.22)

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First Law of Thermodynamics

FIGURE 3.19 Shell-and-tube heat exchanger. (Courtesy of Patterson-Kelly Co., Division of Harsco Corp., East Stroudsburg, Pennsylvania.)

But

 1c p 1 (t12 − t11 ) (3.22a) Q 1 = H 12 − H 11 = m

and

 2 c p 2 (t22 − t21 ) (3.22b) Q 2 = H 22 − H 21 = m

Equating Equations 3.22a and 3.22b yields a “heat balance” for the exchanger:

 1c p 1 (t12 − t11 ) = m  2 c p 2 (t22 − t21 ) m

(3.23)

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m1, cp1 t11

m2, cp2

t21

t22

Heat exchanger

t12 FIGURE 3.20 Analysis of heat exchanger.

ILLUSTRATIVE PROBLEM 3.21 A heat exchange is used to cool 400 lbm/mm of lubricating oil. Hot oil enters at 215°F and leaves at 125°F. The specific heat of the oil is 0.85 Btu/lbm·°R. Cooling water enters the unit at 60°F and leaves at 90°F. If the specific heat of the water is 1.0 Btu/lbm·°R, determine the required water flow rate if heat losses are negligible. SOLUTION Refer to Figure 3.20:  p ∆t Q oil = mc = 400 lbm/min × 0.85 Btu/lbm ·°R × (125 − 215)°R

= − 30 600 Btu/min (out of oil)



Because the heat out of the oil is the heat into the water,  w c pw (∆t)w = 30 600 Btu/min m

 w × 1 × (90 − 60) = 30 600 m  w = 1020 lbm/min m



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First Law of Thermodynamics

3.5.7 Filling a Tank Consider the following situation, namely, that an evacuated tank is connected to a large steam source, as shown in Figure 3.21. The valve is opened, and steam is allowed to flow into the tank until the pressure in the tank equals the pressure in the line. Assume that the tank is perfectly insulated and that no shaft work occurs during the process. Also, assume that the kinetic and potential energy terms are negligible. In order to write the energy equation for this process, we will first define our system as consisting of the tank and the valve up to the supply side of the valve. The process of charging the closed tank is really an example of an open or flow system in transient flow that can be solved using the information that we have already developed. The supply steam is throttled through the valve, and its enthalpy remains constant during the process. This assumes that the mass of steam withdrawn from the supply line is small enough to leave the conditions in the supply line constant. The change in energy of the mass in the tank will be m2u2 – m1u1, where m1 and m2 are the initial and final masses in the tank and u1 and u2 are the initial and final internal energy, respectively. The initial mass in the tank, m1, is taken as zero, because the tank was specified as being evacuated at the start of the process. The total energy into the tank will equal m2hi, where hi is the enthalpy of the source. Equating these energy terms gives us m2u2 = m2hi (3.24) or

u2 = hi (3.25)

From Equation 3.25, we see that the final internal energy of the mass in the tank equals the enthalpy of the steam in the supply line. As we will see in Chapters 5 and 6, the final temperature in the tank will be greater than the temperature in the supply line.

Steam supply line Valve

Insulated tank

FIGURE 3.21 Filling a tank.

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Thermodynamics and Heat Power

3.6 Review Using the material developed in Chapter 2, namely, the concepts of energy, work, heat, and the statement of the first law of thermodynamics as being the conservation of energy, we analyzed both nonflow and steady-flow mechanical systems. For the nonflow or closed system, one in which no mass crosses the boundary, we were able to write an energy equation that related the internal energy and heat entering a system to the internal energy and work leaving a system. This equation then permitted us to analyze several nonflow situations, including the adiabatic, constant-volume, and constant-pressure systems. As a consequence of our analysis of the constant-pressure system, we defined a new property, which we called enthalpy, to be the sum of the internal energy plus the product of the pressure and the specific volume of a substance. We also showed that the work of a nonflow, quasi-static process can be taken to be the area under the p–v curve. The term steady implies a system that does not vary with time. For the steady-flow system, this requires that the rate at which mass enters must equal the rate at which mass leaves the system. We then developed the continuity equation, which expresses this fact mathematically. Then we considered the energy terms required to write the first law of thermodynamics for the steady-flow system. These terms were potential energy, kinetic energy, and flow work, which we considered in Chapter 2. Using these terms with the already developed concepts of internal energy, heat, and work enabled us to write an energy equation that we called the steady-flow energy equation or, more simply, the general energy equation. Before we applied this equation to several industrial situations, we developed two new properties from the definition of the term specific heat. These properties were the specific heat at constant pressure and the specific heat at constant volume, and we were able to show their relation to the properties enthalpy and internal energy, respectively. Our final part of this chapter was the application of the general energy equation to several common industrial situations: the boiler, the turbine, the nozzle, throttling, pipe flow, the heat exchanger, and the filling of a tank. By making certain simplifications, it was possible to analyze each system quantitatively. In addition to the foregoing, it should be apparent that the successful application of the material of this chapter requires a systematic approach to problem solving. It is strongly suggested that the following procedure be followed to analyze all problems:

1. Read, visualize, and understand the problem. 2. Draw a schematic sketch of the problem, and indicate all known quantities. 3. Write out the full energy equation. 4. On the basis of the statement of the problem or knowledge of the device in question, determine those terms that can be omitted or neglected. 5. Solve the problem by performing the necessary algebraic and arithmetic steps. Check carefully for dimensional consistency. 6. Using the solution as a first approximation, check the validity of the assumptions made in step 4. There are no shortcuts to an understanding of thermodynamics, and it will be found that the procedure outlined here will prove to be invaluable.

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First Law of Thermodynamics

Key Terms Terms used for the first time in this chapter are as follows: adiabatic process: A process in which no energy as heat enters or leaves during the specified state change. Bernoulli equation: A very restrictive form of the energy equation that is frequently used in fluid mechanics. boiler: A device used to convert the chemical energy in a fuel to an increase in the energy of a working fluid by the combustion of the fuel. continuity equation: An equation expressing the conservation of mass in a steady-flow system. energy equation: See general energy equation. enthalpy: The sum of the internal energy and the pv term. first law of thermodynamics: An expression of the conservation of energy in a system. general energy equation: The quantitative statement of the first law of thermodynamics applied to a steady-flow system. nonflow energy equation: The quantitative expression of the first law of thermodynamics applied to a nonflow system. nozzle: A static device used to increase the velocity of a fluid. specific heat: The ratio of the energy transferred as heat to the corresponding temperature change of the substance. The specific heat at constant volume and the specific heat at constant pressure are both properties. steady-flow energy equation: See general energy equation. throttling: An irreversible, adiabatic, steady-flow process in which the fluid is caused to flow through an obstruction in a pipe with a resulting drop in pressure. turbine: A machine consisting of a rotor and stator whose purpose is to convert the energy in a working fluid to useful work.

Equations Developed in This Chapter Nonflow energy equation Nonflow energy equation Enthalpy

u2 – u1 – q – w (3.2a) u2 – u1 – q – pΔv (3.4) pv h = u+ (3.5) J

Continuity equation

 = pAV = p1 A1V1 = p2 A2 V2 (3.9b) m

Continuity equation

 = AV (3.9c) m v

General energy equation

pv w Z1 g V2 + 1 + u1 + 1 1 + in + qin 2 gc J J gc J J =

Z2 J

pv g V2 w + 2 + u2 + 2 2 + out + qout 2 gc J J J gc

(3.10)

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General energy equation

General energy equation

Thermodynamics and Heat Power

V 12 + u1 + p1v1 + w in + qin 2 V2 = Z2 g + 2 + u2 + p2 v2 + w out + qout 2

Z1 g +

pv Z1 g V2 + 1 + u1 + 1 1 + q 2 gc J J gc J =

General energy equation

(3.10a)

Z2 J

pv g w V2 + 2 + u2 + 2 2 + 2g c J J J gc

V 12 + u1 + p1v1 + q 2 V2 = Z2 g + 2 + u2 + p2 v2 + w 2

(3.11)

Z1 g +

(3.11a)

w Z − Z1 g V 2 − V 12 (3.13) = ( h2 − h1 ) + 2 + 2 J J gc 2 gc J

General energy equation

q−

General energy equation

q − w = h2 − h1 + g(Z2 − Z1 ) +

Power

 =m  w (3.16) W

Heat transfer rate

 (3.17) Q = mq

Specific heat at constant pressure

cp =

Specific heat at constant volume

cv =

q ∆T q ∆T

= p

= v

∆h ∆T

p

∆u ∆T

v

V 22 − V 12 2 gc J

V 22 − V 12 (3.13a) 2

(3.19)

(3.20) Illustrative Problem 3.23

Nozzle

h1 − h2 =

Throttling

h1 = h2

Filling a tank

u2 = hi (3.25)

Illustrative Problem 3.26

QUESTIONS 3.1 Does the first law of thermodynamics apply to each of the following situations? (a) An atom bomb; (b) a system that is time dependent; (c) a chemical system that is exothermic, that is, giving off heat as the reaction proceeds; (d) the tides on the Earth; (e) the sun and the reactions that occur on the sun; (f) a permanent magnet. 3.2 An automobile engine consists of a number of pistons and cylinders. If a complete cycle of the events that occur in each cylinder can be considered to consist of a number of nonflow events, can the engine be considered a nonflow device? 3.3 Can you name or describe some adiabatic processes? 3.4 What is unique about the nonflow, constant-pressure process? 3.5 Is enthalpy the sum of internal energy plus flow work? 3.6 In words, what does the continuity equation express? 3.7 What are the limitations of the continuity equation? 3.8 All substances are subjected to pressure and have a specific volume. Because this means that they all have the product pv, do they all have flow work?

First Law of Thermodynamics

131

3.9 Do all substances have enthalpy? 3.10 The term pΔv is the area under a p–v curve, and the term –vΔp is the area behind the p–v curve. How do you interpret each of these areas? 3.11 Discuss the problems associated with the Bernoulli equation. 3.12 With all of the problems associated with the Bernoulli equation, why is it still used? 3.13 When a fluid is vaporized, the temperature does not change during the process as heat is added. What is the specific heat for this process? 3.14 Can you name another common process that is carried out at constant temperature and therefore has a specific heat that is similar to the one in Question 3.13? 3.15 What is the importance of the fact that cp and cv are properties? 3.16 A number of assumptions were made when the seven applications of the energy equation were discussed. Is it always necessary to make these assumptions when any of these situations are analyzed? 3.17 In all seven applications, we took the difference in elevations to be negligible. Would this also be true if you were analyzing the hydroelectric power plants at Niagara Falls? PROBLEMS Unless indicated otherwise, use gc = 32.174 lbm·ft./lbf·s2 and g = 32.174 ft./s2 or 9.81 m/s2. Problems Involving Nonflow Systems 3.1 The internal energy of a nonflow system increases by 70 Btu when 82 Btu of work is done by the system on its surroundings. How much heat has been transferred to or from the system? 3.2 If the internal energy of a nonflow system increases by 90 kJ while the system does 125 kJ of work on the surroundings, determine the heat transfer to or from the system. 3.3 A nonflow process is carried out when 1000 Btu as heat are added to 10 lbm of hydrogen at constant volume. What is the change in specific internal energy? How much work is done by the gas? 3.4 If a nonflow process is carried out so that 30 Btu/lbm of work is removed from the process while 100 Btu/lbm is added as heat, determine the change (increase or decrease) in the specific internal energy of the fluid. 3.5 If 10 kg of a gas is heated by the addition of >5 kJ in a nonflow process, what is the change in its specific internal energy if the process is carried out at constant volume? 3.6 If a nonflow process is carried out so that 30 kJ/kg of work is removed while 75 kJ/kg is added as heat, determine the change in internal energy of the fluid. 3.7 A constant-pressure, nonflow process is carried out at 125 kPa. During the process, the volume changes from 0.15 to 0.05 m3, and 25 kJ of heat is rejected. Evaluate (a) the work done and (b) the change in internal energy of the system. 3.8 A closed gaseous system undergoes a reversible process during which 20 Btu/ lbm is rejected as heat and the specific volume changes from 0.5 to 0.2 ft.3/lbm. If the pressure is constant at a value of 40 psia, determine the change in specific internal energy.

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3.9 In a constant-pressure, nonflow process, 10 lbm of gas has 500 Btu added to it. During the process, the internal energy decreases by 25 Btu/lbm. How much work was done by the gas per pound of gas? 3.10 A constant-pressure, nonflow system receives heat at a constant pressure of 350 kPa. The internal energy of the system increases by 180 kJ while the temperature increases by 170°C, and the work done is 75 kJ. Determine cp and the change in volume if there is 1.5 kg in the cylinder. 3.11 A constant-pressure, nonflow process is carried out at a pressure of 200 kPa. If 50 kJ of heat is removed while the volume changes from 0.2 to 0.1 m3, what is the change in specific internal energy of the working fluid? Assume 0.5 kg of fluid. 3.12 A gas that is contained in a cylinder is made to undergo a constant-pressure expansion from a volume of 0.1 m3 to a volume of 0.4 m3. If the piston moves to keep the pressure constant at 400 kPa, determine the work in kilojoules. 3.13 A nonflow system has a mass of working fluid of 5 kg. The system undergoes a process in which 140 kJ as heat is rejected to the surroundings and the system does 80 kJ of work. Assuming that the initial specific internal energy of the system is 500 kJ/kg, determine the final specific internal energy in kJ/kg. 3.14 A nonflow system has a mass of 5 lb. in it. The system undergoes a process during which 200 ft.·lbf of heat is transferred to the surroundings. If the system does 1000 ft.·lbf of work on the surroundings, determine the change in specific internal energy of the fluid. 3.15 A nonflow process is carried out adiabatically. If 55 kJ of work is removed from 4 kg of fluid, what is the change in the total internal energy and the specific internal energy of the fluid? 3.16 A nonflow process is carried out adiabatically. What is the change in specific internal energy of the fluid if 55 000 ft.·lbf of work is removed from 8 lbm of fluid in this process? 3.17 During a certain nonflow process, 100 Btu/lbm is added as heat to the working fluid while 25 000 ft.·lbf/lbm is extracted as work. Determine the change in internal specific energy of the fluid. 3.18 If the enthalpy of a gas is 240 Btu/lbm when the pressure is 100 psia and the specific volume is 3.70 ft.3/lbm, determine the specific internal energy of the gas. 3.19 What is the specific internal energy of a gas whose enthalpy is 500 kJ/kg? At this condition, the pressure is 100 kPa and the specific volume 0.1 m3/kg. 3.20 A closed system receives 1 kJ as heat, and its temperature rise is 10 K. If 20 kg is in the system, what is the specific heat of the process? 3.21 Determine the specific heat of an adiabatic process. Is this the specific heat at a constant volume or the specific heat at constant pressure? 3.22 Two kilograms of a gas receive 200 kJ as heat at constant volume. If the temperature of the gas increases by 100°C, determine the cv of the process. 3.23 Heat is supplied to a gas in a rigid container. If the container has 0.6 lbm of gas in it and 100 Btu is added as heat, determine the change in temperature of the gas and the change in its specific internal energy. For this gas, cv is 0.35 Btu/lbm·°R. 3.24 If 100 kJ/kg of heat is added to 10 kg of a fluid while 25 kJ/kg is extracted as work, determine the change in the specific internal energy of the fluid for a nonflow process.

133

First Law of Thermodynamics

3.25 Heat is supplied to a gas that is contained in a rigid container. If 0.2 kg of gas has 100 kJ as heat added to it, determine the change in temperature of the gas and the change in its specific internal energy. Use cv = 0.7186 kJ/kg·K and cp = 1.0062 kJ/ kg·K. 3.26 If cp and cv of air are, respectively, 1.0062 and 0.7186 kJ/kg·°K and 1 MJ as heat is added to 10 kg in a nonflow, constant-pressure process, what is the final temperature of the gas, and how much work is done by the gas? Assume that the initial temperature of the gas is 50°C. 3.27 The cp and cv of air are 0.24 and 0.17 Btu/lbm·°R, respectively. If 1000 Btu is added as heat to 20 lbm of air in a nonflow, constant-pressure process, what is the final temperature? How much work is done by the gas? The initial temperature is 100°F. 3.28 In a certain process, the working fluid is cooled until 100 Btu/lbm has been extracted as heat. During this process, 100 ft.·lbf/lbm of fluid is added as work. If the working substance undergoes a change in temperature from 100°F to 50°F, what is the specific heat of the process? 3.29 Air is adiabatically compressed in a nonflow process from a pressure and temperature of 14.7 psia and 70°F to 200 psia and 350°F. If cv of the air is 0.171 Btu/lbm·°R, determine the change in specific internal energy of the air and the work done. 3.30 If a nonflow system has 6 kg in it and undergoes a process in which 175 kJ as heat is transferred to its surroundings, determine the final specific internal energy in kJ/kg if the work done by the system is 100 kJ. Assume that the initial specific internal energy is 400 kJ/kg. 3.31 A nonflow, cylinder-piston apparatus contains 0.5 lbm of a gas. If 10 Btu is supplied as work to compress the gas as its temperature increases from 70°F to 150°F, determine the energy interchange as heat. For the gas, cv can be taken as 0.22 Btu/ lbm·°R. 3.32 A nonflow system undergoes a process in which 42 kJ of heat is rejected. If the pressure is kept constant at 125 kPa while the volume changes from 0.20 to 0.06 m3, determine the work done and the change in internal energy. *3.33 Four individual nonflow processes numbered as 1, 2, 3, and 4 are carried out. For each of the processes, fill in the following table. Assume all values are in kJ. q

w

15 22 –20

8

Process 1 2 3 4

18

u2 16 20 14

u1

Δu

6 4 15 4

*3.34 A closed cycle consists of the three processes listed in the table below. Fill in the missing values if all the quantities are in Btu/lbm. (Hint: A closed cycle returns to its starting point.) Process l→2 2→3 3→l

q

w

Δu

200 z y

x 100 –150

100 t 300

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Problems Involving the Continuity Equation 3.35 Ten cubic feet of fluid per second flows in a pipe 1 in. in diameter. If the fluid is water whose density is 62.4 lbm/ft.3, determine the weight rate of flow in pounds per hour. 3.36 A gallon is a volume measure of 231 in3. Determine the velocity in a pipe 2 in. in diameter when water flows at the rate of 20 gal./min in the pipe. 3.37 When a fluid of constant density flows in a pipe, show that for a given mass flow the velocity is inversely proportional to the square of the pipe diameter. 3.38 Water having a density of 1000 kg/m3 flows in a pipe that has an internal diameter of 50 mm. If 0.5 m3/s flows in the pipe, determine the mass flow rate in kilograms per hour. 3.39 What is the velocity of the water flowing in Problem 3.38? 3.40 Air flows through a 12 in. × 12 in. duct at a rate of 800 cfm. Determine the mean flow velocity in the duct. 3.41 Air flows through a rectangular duct 0.5 m × 0.75 m at the rate of 200 m3/min. Determine the average velocity of the air. 3.42 Water flows through the pipe shown at the rate of 30 ft.3/s. Determine the velocity at sections 1 and 2. Also calculate the mass flow rate per second in the pipe at these sections. The diameters shown in Figure P3.42 are internal diameters. 2 1

Flow

10 in. dia

15 in. dia = 62.4 lbm/ft.3

FIGURE P3.42 Sudden expansion pipe problem.

3.43 Air, having a specific weight of 11.8 N/m3, flows in the pipe shown in Figure P3.43 with a velocity of 10 m/s at section 1. Calculate the weight flow rate per second of the air and its specific weight at section 2 if the air has a velocity of 3 m/s at section 2. 2 1

Flow dia = 0.1 m dia = 0.25 m FIGURE P3.43 Gradual expansion pipe problem.

3.44 If the water level in the tank remains constant, determine the velocity at section 2 as shown in Figure P3.44. Assume the water to be incompressible.

135

First Law of Thermodynamics

Q3 = A3V3 = 0.4 ft.3/s

3

Water level 2 V2 V1 = 12 ft./s

dia = 3 in.

1

dia = 2 in. FIGURE P3.44 Water tank flow problem.

3.45 Water flows through a pipe at the rate of 1500 L/min. At one section, the pipe is 250 mm in diameter, and later on, it decreases to a diameter of 100 mm. What is the average velocity in each section of the pipe? 3.46 A pump can fill a tank in 1 min. If the tank has a capacity of 18 gal., determine the average velocity in the 1.25-in. diameter pipe that is attached to the pump. 3.47 For the liquid rocket shown in Figure P3.47, calculate V2 for steady operation. Liquid oxygen, 20 lbm/s Exhaust dia = 6 in. Exhaust gases Specific weight = 0.023 lbf/ft.3

1

2 Liquid fuel, 6.5 lbm/s FIGURE P3.47 Nozzle problem.

3.48 Water flows through the nozzle shown in Figure P3.48 at the rate of 100 lbm/s. Calculate the velocity at sections 1 and 2.

p = 62.4 lbm/ft.3

Flow 1 8 in. dia FIGURE P3.48 Nozzle problem.

2 2.5 in. dia

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Thermodynamics and Heat Power

Problems Involving the Steady-Flow Energy Equation 3.49 A water turbine operates from a water supply that is 100 ft. above the turbine inlet. It discharges to the atmosphere through a 6-in.-diameter pipe with a velocity of 25 ft./s. If the reservoir is infinite in size, determine the power out of the turbine if the density of water is 62.4 lbm/ft.3. 3.50 A water pump is placed at the bottom of a well. If it is to pump 1.0 ft.3/s to the surface, 100 ft. away, through a 4-in.-inside-diameter pipe, determine the power required in foot-pounds per second and horsepower if the density of water is 62.4 lbm/ft.3. 3.51 Air is compressed until its final volume is half its initial volume. The initial pressure is 100 psia, and the final pressure is 35 psia. If the initial specific volume is 1 ft.3/lbm, determine the difference in the pv/J term in Btu/lbm. Is this difference “flow work” for this process? 3.52 Determine the power of a pump if 2000 kg/min of water is compressed from 100 kPa to 1 MPa. The water density can be taken to be 1000 kg/m3, and its temperature does not change. The inlet to the pump is 100 mm in diameter, and the outlet is 150 mm in diameter. The inlet is 50 m below the outlet. 3.53 A steady-flow device is operated with an entering pressure of 50 psia and a specific volume of 0.8 ft.3/lbm. At the exit of the device, the pressure is 15 psia and the specific volume 3.2 ft.3/lbm. Determine the change in flow work in this device. 3.54 If a fluid flows past a section of pipe with a pressure of 100 kPa and having a specific volume of 10 –3 m3/kg, determine its flow work at this section. 3.55 At the entrance to a steady-flow device, the pressure is 350 kPa and the specific volume 0.04 m3/kg. At the outlet, the pressure is 1 MPa and the specific volume 0.02 m3/kg. Determine the flow work change in this device. 3.56 The enthalpy of a substance is found to be 1000 Btu/lbm at 1000°F above an arbitrary datum of 0°F. If cv is a constant and equal to 0.5 Btu/lbm·°R, determine the difference in the pv/J terms at zero and 1000°F. Does this difference represent flow work? *3.57 A steam turbine is supplied with steam at 700°F and 500 psia. The steam is expanded adiabatically until the final condition is saturated vapor at 300°F. If the properties of steam at the initial and final states are as given here, determine the work output of the turbine per pound of steam. 500 psia and 700°F

300°F (saturated vapor)

h = 1356.7 Btu/lbm v = 1.3040 ft.3/lbm u = 1236.0 Btu/lbm

h = 1180.2 Btu/lbm v = 6.472 ft.3/lbm u = 1100.0 Btu/lbm

*3.58 A fluid at 1 MPa has a specific volume of 0.2 m3/kg and an entering velocity of 200 m/s. The heat loss is 10 kJ/kg, and the fluid does 180 kJ/kg of work. The fluid leaves the device with a pressure of 200 kPa, a specific volume of 1 m3/kg, and a velocity of 600 m/s. What is the change in the specific internal energy of the fluid? *3.59 A steam turbine operates adiabatically with inlet and other conditions as given here. Determine the work out of the turbine. State all assumptions.

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First Law of Thermodynamics

At 0.5 MPa and 500°C

At 0.1 MPa (saturated vapor)

h = 3483.9 kJ/kg v = 0.7109 m3/kg u = 3128.4 kJ/kg

h = 2675.5 kJ/kg v = 1.6940 m3/kg u = 2506.1 kJ/kg

3.60 A steam turbine receives steam at 110 ft./s velocity and 1525 Btu/lbm enthalpy. The steam leaves at 810 ft./s and 1300 Btu/lbm enthalpy. What is the work out in Btu per pound mass flowing? 3.61 A turbine is operated with an enthalpy at entrance of 1340 Btu/lbm and an exit enthalpy of 1285 Btu/lbm. If the entrance velocity of the turbine is 150 ft./s and the exit velocity is 500 ft./s, determine the work out of the turbine. 3.62 Solve Problem 3.61 if there is a heat loss of 5.5 Btu/lbm of fluid by heat transfer from the turbine casing. 3.63 A gas turbine receives an air–fuel mixture having an enthalpy of 550 Btu/lbm of gas. If 10 Btu/lbm is lost by heat transfer from the turbine and the enthalpy of the leaving gas is 50 Btu/lbm, how much work can be obtained from the turbine? 3.64 An air compressor takes in air having an enthalpy of 100 kJ/kg. The air is compressed to a final condition in which the enthalpy is 180 kJ/kg. As the air travels through the compressor, it loses 20 kJ/kg as heat. Determine the work per kilogram of the compressor. *3.65 Air having the following properties passes through a steady-flow device. Determine the work in kJ/kg if the heat loss is 20 kJ/kg.

Pressure Density Velocity Internal energy

Inlet

Outlet

700 kPa 3.0 kg/m3 70 m/s 2100 kJ/kg

170 kPa 0.60 kg/m3 200 m/s 2025 kJ/kg

3.66 A gas turbine has gas entering it at 1100°F and leaving at 800°F. If the specific heat cp = 0.265 Btu/lbm·°R, determine the work out of the turbine. Neglect losses and velocity effects. 3.67 Solve Problem 3.61 if the entering velocity is 100 ft./s, the leaving velocity is 300 ft./s, and there is a heat loss of 4.8 Btu/lbm from the turbine. *3.68 Assume 4.8 kg/s of steam enters a turbine. The inlet of the turbine is 2.5 m higher than the outlet. The inlet velocity is 132 m/s, and the outlet velocity is 327 m/s. Heat is lost from the casing of the turbine at the rate of 9.2 kJ/s. At the inlet of the unit, the enthalpy is 3127.4 kJ/kg, and at the outlet, the enthalpy is 2512 kJ/kg. Determine the power out of the turbine in kilowatts. 3.69 Gas enters a turbine at 600°C and leaves at 350°C. If the specific heats of the gas are cp = 0.8452 kJ/kg·K and cv = 0.6561 kJ/kg·K, determine the work out of the turbine. State all assumptions. 3.70 Assume the entering velocity in Problem 3.69 is 86 m/s and the leaving velocity is 232 m/s. If the outlet of the turbine is 3.2 m higher than the inlet, determine the work out of the turbine if the process is adiabatic.

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3.71 Air flows in a compressor at the rate of 1.1 kg/s. The air enters the compressor at a pressure of 100 kPa, a temperature of 25°C, and a velocity of 72 m/s. It leaves with a pressure of 225 kPa, a temperature of 84°C, and a velocity of 125 m/s. A cooling jacket surrounds the compressor to cool the air, and it removes 15 kJ/kg as heat from the air. If cp = 1.0041 kJ/kg·K and cv = 0.7172 kJ/kg·K, calculate the power to operate the compressor. 3.72 Air expands through a nozzle from 1000 psia and 500°F to 600 psia and 0°F. If cp of air can be taken to be constant and equal to 0.24 Btu/lbm·°R, what is the final velocity? Assume that the initial velocity is zero. 3.73 If the initial velocity in Problem 3.72 is 9.25 ft./s, what is the final velocity? 3.74 Steam expands in a nozzle from an initial enthalpy of 1300 Btu/lbm to a final enthalpy of 980 Btu/lbm. Determine the final velocity if the entering velocity and heat losses are negligible. 3.75 Solve Problem 3.74 if the initial velocity is 1100 ft./s. 3.76 Air expands in a nozzle from 7 MPa and 250°C to 3.5 MPa and 50°C. If cp = 1.0062 kJ/kg·K and cv = 0.7186 kJ/kg·K, determine the velocity out of the nozzle. State all assumptions. 3.77 Solve Problem 3.76 if the initial velocity is 325 m/s. 3.78 A nozzle has steam flowing through it. The steam enters the nozzle at 250 psia with a velocity of 100 ft./s. The initial specific volume is 2.31 ft.3/lbm and the initial internal energy is 1114.1 Btu/lbm. The steam expands to 15.0 psia with a specific volume of 27.34 ft.3/lbm and a final internal energy of 1080.1 Btu/lbm. Calculate the velocity at the exit of the nozzle. 3.79 Steam flows through a nozzle. If the properties are as given here, determine the exit velocity if the nozzle is well insulated. Neglect the inlet velocity.

Pressure Temperature Internal energy Enthalpy

Inlet

Outlet

300 psia 500°F 1159.5 Btu/lbm 1257.5 Btu/lbm

100 psia 350°F 1115.4 Btu/lbm 1200.4 Btu/lbm

3.80 Solve Problem 3.79 for an initial velocity of 600 ft./s. 3.81 Steam is generated in a boiler. If the initial water enters the boiler as saturated water at 1000 psia (h = 542.4 Btu/lbm) and leaves as superheated steam at 950 psia and 1000°F (h = 1507.4 Btu/lbm), how much heat is added to the steam to generate 1 lb. of steam at these conditions? 3.82 Steam is generated in a boiler. Water enters the boiler as saturated liquid at 7 MPa (h = 1267.00 kJ/kg) and leaves as superheated steam at 6 MPa and 500°C (h = 3422.2 kJ/kg). Neglecting potential and kinetic terms, determine the amount of heat that is added to generate 1 kg of steam under these conditions. Assume that there are no heat losses. *3.83 Water flows in a heat exchanger, and heat is transferred from the water to heat air. At the inlet, the pressure of the water is 100 psia, and at the outlet, it is 80 psia. The initial specific volume is 0.017 736 ft.3/lbm, and the final specific volume is

First Law of Thermodynamics

*3.84

*3.85

*3.86

*3.87

139

0.017 57 ft.3/lbm. The initial enthalpy is 298.61 Btu/lbm, the initial internal energy is 298.28 Btu/lbm, the final enthalpy is 282.21 Btu/lbm, and the final internal energy is 281.95 Btu/lbm. Determine the heat transferred from the water. State all assumptions. Air flows in steady flow in a pipeline whose internal diameter is constant. At a particular section of the pipe, the pressure, temperature, and velocity are 150 psia, 500°R, and 30 ft./s. The specific volume corresponding to these conditions is 1.24 ft.3/lbm. At a section farther downstream, the pressure is 300 psia, the velocity is 45 ft./s, and the temperature is 1500°R. Determine the specific volume of the air at the downstream section and also the magnitude and direction of the heat transfer in Btu per pound mass. Assume that cp is 0.24 Btu/lbm·°R and that it is constant. Dry saturated steam at 200 psia flows adiabatically in a pipe. At the outlet of the pipe, the pressure is 100 psia and the temperature 400°F. The initial specific volume of the steam is 2.289 ft.3/lbm, and its internal energy is 1114.6 Btu/lbm. The final enthalpy is 1227.5 Btu/lbm, and the final specific volume is 4.934 ft.3/lbm. How much energy per pound mass was transferred? Was this into or out of the system? Was this heat or work? A heat exchanger is used to heat petroleum distillates for use in a chemical process. Hot water enters the unit at 180°F and leaves at 105°F. The distillate enters at 85°F and leaves at 148°F. If the specific heat of water is taken to be 1.0 Btu/lbm·°R and the distillate has a specific heat of 0.82 Btu/lbm· °R, determine the pounds of water required per pound of distillate flowing. A hydro-electric turbine at the base of a 6 m tall dam receives 130 m3/s of water (density = 1000 kg/m3) from a large reservoir. Turbine discharge velocity is 5 m/s. Neglecting friction, determine the following: (a) turbine specific work and direction, in kJ/kg (b) turbine power, in kW and (c) discharge pipe diameter in m.

4 The Second Law of Thermodynamics

L E A R N I NG G OA L S

After reading and studying the material in this chapter, you should be able to



1. Understand that work can be converted into heat, but that the conversion of heat into useful work may not always be possible 2. Define a heat engine as a continuously operating system across whose boundaries flow only heat and work 3. Define thermal efficiency as the ratio of the useful work delivered by a heat engine or cycle to the heat input to the engine or cycle 4. Understand what is meant by the statement that a reversible process is any process performed so that the system and all its surroundings can be restored to their initial states by performing the process in reverse 5. State the second law of thermodynamics as “Heat cannot of itself pass from a lower temperature to a higher temperature” 6. Understand that all natural processes are irreversible, and cite some of the effects that cause irreversibility 7. Explain the four processes that constitute the Carnot cycle 8. Deduce from the Carnot cycle three important general conclusions concerning the limits of the efficiency of a heat engine 9. Define the new property that is introduced in this chapter that we have called entropy 10. Understand that entropy is also a measure of the unavailability of energy that occurs in an irreversible process 11. Calculate the change in entropy for a process in which there is a temperature change, such as the mixing of two fluids 12. Understand that the entropy of an isolated system increases or, in the limit, remains the same, which, for a given internal energy, we interpret to mean that the state having the greatest entropy will be the most probable state that the system will assume. This state is called stable equilibrium

141

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4.1 Introduction Thus far, we have considered various forms of energy (including energy in transition as both work and heat) without regard to any limitations on these quantities. It has been assumed that work and heat are mutually interchangeable forms of energy, and it may have appeared to students that the distinction made between these quantities was arbitrary and possibly not necessary. In this chapter, the interconvertibility of these quantities is explored with the object of determining any possible limitations and to express these limitations quantitatively, if they exist. As an example of the point in question, consider the motion of a block sliding along a rough horizontal plane. For motion to proceed along the plane, it is necessary that work be done on the body. All this work subsequently appears as heat at the interface between the block and the plane. There is no question that work has been converted into heat, but can the heat generated in this process be converted into an equivalent amount of work? Let us assume (incorrectly) that this heat can be converted into work without any losses in the process. We know that the energy as heat increases the motion of the individual molecules of the body. By increasing the molecular motion within the body, we have, in a general sense, done work, but it is also possible to distinguish that this form of work is not the same as the external work put into the process. The original transitional energy as work has been converted into heat, and this heat can be expressed as molecular work. However, this form of energy will not be available to return the body to its original state. From this simple example, we note that work can be converted into heat, but that the conversion of heat into useful work may not always be possible. Even though the first law states that energy is conserved, it does not furnish the necessary information to enable us to determine whether energy has become unavailable. It is now necessary to define certain terms. The first of these is the concept of a heat engine. As defined by Keenan (1941, p. 58): A heat engine may be defined as a continuously operating system across whose boundaries flow only heat and work. It may be used to deliver work to external devices, or it may receive work from external devices and cause heat to flow from a low level of temperature to a high level of temperature. This latter type of heat engine is known as a refrigerator.

In essence, this definition of a heat engine can be taken to be the definition of a thermodynamic cycle, which we shall understand to be a series of thermodynamic processes during which the working fluid can be made to undergo changes involving only heat and work interchanges and is then returned to its original state. The purpose of the conventional engineering thermodynamic cycle is, of course, to convert heat into work. In an air-conditioning or refrigeration cycle, work is used to remove heat from an area in which it is undesirable. Other special cycles exist but are not treated in this text. Associated with the concept of a cycle is the term efficiency. Because the usual purpose of a cycle is to produce useful work, the thermal efficiency of a cycle is defined as the ratio of the net work of the cycle to the heat added to the cycle, that is,

η=

net work output × 100 (4.1) heat added

Note that the heat term is the heat added and not the net heat of the cycle. For powerproducing cycles, the heat is usually added from some high-temperature source. Using the

The Second Law of Thermodynamics

143

notation that Qin is the heat added to the cycle and that Qr is the heat rejected by the cycle, the first law applied to the cycle will yield W/J = Qin – Qr. Therefore,

η=

Qin − Qr Q × 100 = 1 − r × 100 (4.2) Qin Qin

For cycles whose purpose is not the production of useful work, other standards of comparison have been devised and are in use. If we consider the large central station plant, the importance of obtaining high thermal efficiencies is at once obvious. An examination of Equation 4.2 leads us to the conclusion that minimizing the heat rejection of a cycle leads to the maximum conversion of heat to work. This leads us to two questions: (1) Must there be a rejection of heat from a cycle, and if so, (2) what is the best mode of cycle operation to minimize the heat rejected in order to obtain maximum thermal efficiency? These questions will be partially answered in this chapter, and we shall return to them when we study practical engine cycles.

4.2 Reversibility—Second Law of Thermodynamics In Section 4.1, the illustration of a block sliding along a horizontal plane was used to introduce the concept that heat and work are not always mutually convertible without losses. This same body moving along the plane will also serve to answer the following question: By reversing each step of the process that caused the body to move along the plane, is it possible to restore the body to its original state, and at the same time, will the surroundings also be restored to the condition that existed before the start of the original process? To answer this question, let us once again consider the forward motion of the body along the plane. We have stated that as the block moves, heat is generated at the interface between the block and the plane. This energy is transferred to the body and the plane and will tend to raise the temperature of the body and its surroundings. When the block reaches the end of the plane, let us reverse the force system acting on the body and attempt to restore it to its original position. As the body moves back along the path, heat will again be generated at the interface between the body and the plane. Obviously, the heat generated on the return path is in addition to the heat generated at the interface during forward motion of the body. To a casual observer who viewed the block before the beginning of motion and then viewed it some time after motion had ceased, it would appear that the body had not moved and that it, as well as the surroundings, had been restored to its original state. This is not true. A net transfer of energy has taken place to the body and its surroundings, and they are not in their original state. Even though the net effect has been an infinitesimal change in the temperature of the body and its surroundings, it is a real effect that precludes us from saying that the system and its surroundings have been restored to their original state. We also notice that each step of the forward motion of the body was not identically reversed because of this effect on the surroundings. The heat generated during the forward motion of the block was not returned to the system as work during the return motion. On the contrary, more heat was generated during the return motion, and even if both the plane and the body were perfectly insulated from their surroundings, none of the heat generated would have been returned to the system as work.

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The process we have considered is illustrative of an irreversible process. To formalize the concepts of reversibility and irreversibility, the following definition of reversible process is used: A reversible process is any process performed so that the system and all its surroundings can be restored to their initial states by performing the process in reverse.

All processes of a reversible cycle must, therefore, also be reversible. Students should note that the concept of the frictionless, quasi-static process introduced earlier basically implies that such a process is reversible. The second law of thermodynamics is an expression of empirical fact that all forms of energy are not necessarily equivalent in their ability to perform useful work. There are many statements and corollaries of the second law that can be found in the literature on thermodynamics. For the present, the statements of Clausius and Kelvin–Planck will serve to express the second law fully (Howell and Buckius 1992). It is impossible to construct a device that operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body. (Heat cannot, of itself, pass from a lower temperature to a higher temperature.) The Clausius Statement It is impossible to construct a device that operates in a cycle and produces no other effect than the production of work and exchange of heat with a single reservoir. The Kelvin–Planck Statement

One of the many consequences of the second law of thermodynamics is the conclusion that all natural processes are irreversible. It has already been shown that the presence of friction will cause a process to be irreversible. Some processes that are irreversible are the following:

1. Any process in which work is transformed into internal energy via the agency of friction or inelastic action. 2. Any process in which inelastic molecular action occurs. 3. Any process that transfers heat from one portion of a system to another by virtue of a finite temperature difference. 4. Any process that causes temperature differences between parts of the same system. 5. Any process involving combustion or chemical reactions. 6. Any process that is not performed quasi-statically; thus, to be reversible, a process must proceed at an infinitesimally slow rate.

It is important for students to fully understand where the irreversibilities occur in the listed processes. Also, by observing the effects on the environment, other irreversible processes will become apparent. The next question we ask is, under what conditions will a process be reversible? The answer is that in reality, no process is reversible. However, as an abstract ideal, the reversible process is extremely useful, and this ideal can be achieved only if the process is frictionless and quasi-static—and then only for an isothermal or adiabatic process. The quasi-static process is always in thermodynamic equilibrium and is carried out with infinite slowness so that at any step in the process, it can be reversed and all steps retraced.

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Also, when such a process is specified to be either isothermal or adiabatic, temperature differences within the system or in parts of the system are precluded. To be general, we must exclude other irreversible effects such as magnetic hysteresis and electrical currents.

4.3 The Carnot Cycle The material discussed so far in this chapter has served to define a cycle, its efficiency, and the concept of a reversible process. It would appear quite natural at this point to combine all these concepts and to discuss reversible cycles and their efficiency. Historically, these concepts were first enunciated by Nicolas Leonard Sadi Carnot in 1824, and the reversible thermodynamic cycle that he proposed now bears his name. It is interesting to note that Carnot did his work approximately 175 years ago. In this short span of human history, scientific thermodynamics has become a reality. Figure 4.1 shows some important names and dates in the development of the science of thermodynamics. As noted in Section 4.2, the two frictionless, quasi-static processes that are reversible are the isothermal (constant temperature) and adiabatic (no energy as heat crosses the boundary). Carnot proposed a reversible cycle composed of two reversible isothermal processes and two reversible adiabatic processes, and on the basis of this cycle, he was able to reach certain general conclusions. Let us consider the cycle that has been named for him by describing each step of the cycle. Figure 4.2 (solid line) is a schematic of a direct engine cycle. For the Carnot cycle, we define the following sequence of events:



1. Heat is taken from an infinite reservoir (source) at T1 isothermally and reversibly. Basically, this is equivalent to a quasi-static reception of heat into the cycle without temperature differences. 2. The energy received from step 1 is permitted to produce work by expanding reversibly and adiabatically in an ideal frictionless engine. During this step, net

1750

Date 1850

1800

1900

Joule Watt

Clausius

Thomson/Rumford

Kelvin Maxwell

Fourier

Stefan Rayleigh

Poisson

Boltzmann

Carnot FIGURE 4.1 Some important dates and persons in the development of thermodynamics.

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T1 Source Qin W

Win

Network

Qr Reversed cycle

T2

Direct cycle

Sink

FIGURE 4.2 Elements of Carnot cycle.





work is produced, but no energy as heat is permitted to cross the boundaries of the system even though the pressure and temperature of the working fluid may have changed. 3. At this point in the cycle, the working fluid is at temperature T2, and we shall want to return it to its starting point. To do this, we first reject heat at constant temperature (T2) reversibly and isothermally to an infinite sink. 4. The final step in the cycle is to cause the working fluid to be adiabatically and reversibly compressed to its initial state.

Note that in every analysis of the Carnot cycle, T1 always represents the higher temperature and T2 always represents the lower temperature. For a noncondensing gas, the steps of the cycle are portrayed on pressure–volume coordinates in Figure 4.3. p

Isothermal (constant temperature)

Isentropic (reversible adiabatic) Work in

Qin 1 4 2 3 Qout

T1

Work out Isentropic (reversible adiabatic) T2

Isothermal (constant temperature) v FIGURE 4.3 Carnot cycle on p–v coordinates; noncondensible gas.

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The Second Law of Thermodynamics

1

2

3

4

FIGURE 4.4 Visualized Carnot engine.

To visualize what a real engine working on the Carnot cycle could look like, consider a gas contained within a piston cylinder as in Figure 4.4. The numbers refer to the steps in Figure 4.3. Initially, the gas is heated while the piston rises, with just enough heat added to maintain the gas at a constant temperature TH. Normally, this expanding gas would tend to lose temperature as its pressure drops. This is an isothermal expansion process. Next, the piston continues to rise but no heat is transferred, causing the temperature and pressure to fall. This is an adiabatic expansion process. Next, the gas is cooled as heat is removed and the piston is allowed to fall, increasing the gas pressure sufficiently to keep its temperature constant at TC. This is an isothermal compression process. Finally, the cold sink is removed and the piston continues to fall while the temperature and pressure increase back to the condition at the start of the cycle. This is an adiabatic compression process. The Carnot cycle just described is a reversible cycle, and it is therefore possible to reverse each step in turn and thus reverse the cycle. Such a reversed cycle would effectively take work as an input and pump heat from T2 to T1. The reversed cycle is known as a heat pump and is discussed further in Chapter 10. It should be noted that the Carnot cycle is not unique, and it is not the only reversible cycle that can be devised. Actually, many reversible cycles have been proposed as prototypes of real cycles. The power of the Carnot cycle is that the following general conclusions can be deduced from it:

1. No engine operating between fixed source (T1) and sink (T2) temperatures and continuously delivering work can be more efficient than a reversible Carnot engine operating between these same temperature limits. To prove this proposition, let us take two engines, engine 1 with an efficiency greater than the efficiency of a reversible Carnot engine, and engine 2, which is a reversible Carnot engine, and operate them between a hot reservoir at T1 and a cold reservoir at T2. If these engines are arranged as shown in Figure 4.5, we have engine 1 operating directly to produce 100 units of work. The output of engine 1 is now used to drive engine 2, the reversible engine, in the reversed direction. This reversed engine will take the same energy values used in the heat engine (heat in, work out, heat out) and reverse their direction (heat out, work in, heat in). Thus, the efficiency of the heat engine will equal the work in divided by the heat out when this engine is operated in reverse. Because the work of engine 1 is used as the input to engine 2, there is no net work out of the combined system. Assuming that

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T1 200

1

250

100

100

Zero net work

2

150 T2

FIGURE 4.5 Proof of Carnot principle 1.

engine 1 has an efficiency of 50% and engine 2 has an efficiency of 40%, we find that the input to engine 1 is 200 units and that it rejects 100 units of heat. Engine 2, the reversible engine with an assumed efficiency of 40%, has 150 units of heat entering from the cold reservoir at T2 and rejects 250 units to the hot reservoir at T1. Therefore, we have 50 units of heat being delivered from T2, the lower temperature, to T1, the higher temperature, with no net work being put into the combined cycle. This directly violates the Clausius statement of the second law of thermodynamics, which states that heat cannot of itself pass from a lower to a higher temperature. Therefore, we may reject the assumption that an engine can be more efficient than a reversible engine operating between the same temperature limits. Thus, Carnot principle 1 is proved. 2. The efficiency of all reversible cycles operating between the same temperature limits is the same. The proof of Carnot principle 2 is essentially the same as that used for Carnot principle 1 and is not given in detail. Students should note that this principle, combined with the first, proves that the reversible cycle and its associated processes indeed serve to establish the index of performance for heat engine cycles. 3. The thermal efficiency of a reversible engine is a function solely of the upper and lower temperatures of the cycle and is not a function of the working substances used in the cycle. This third principle is somewhat different in its viewpoint, and part of the mathematical reasoning is quite abstract. We can argue this point qualitatively in the following manner. Let us assume that the efficiency of a reversible engine is a function of the working substance used in the cycle. By using two reversible cycles, as for principle 1, we can place a different working fluid in each of the cycles. One reversible cycle would be more efficient than the other, and by the identical reasoning used in principle 1, we would arrive at a violation of the Clausius statement. Thus, the efficiency of a reversible engine cycle cannot be a function of the working substance used in the cycle. By continuing this line of reasoning, we are also directed to the conclusion that the efficiency of a reversible engine is a function only of the upper and lower temperatures used in the cycle.

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The Second Law of Thermodynamics

t1 Q1 Q1

Q2 t2 Q2

Q3

Q3 t3

FIGURE 4.6 Derivation of the absolute temperature.

To establish the temperature function, we can resort to reasoning similar to that used by Fermi (1956) and Dodge (1944). Consider the three heat reservoirs shown in Figure 4.6 and maintained at temperatures t1, t2, and t3, respectively, on some arbitrary absolute temperature scale. Assume that three Carnot heat engines operate between these temperatures. Because the efficiency of the cycle is assumed to be some function of the temperature limits of the cycle, it follows from Equation 4.2 that for each engine, Qr /Qin is also a function of t1 and t2 for the respective temperatures and heat quantities associated with each engine. Therefore,

Q1 = φ1 (t1 , t2 ) Q2



Q2 = φ2 (t2 , t3 ) (4.3b) Q3



Q1 = φ3 (t1 , t3 ) Q3

(4.3a)

(4.3c)

The symbol ϕ is interpreted to mean “a function of”; thus, from Equation 4.3a, Q1/Q2 is a function of t1 and t2. Dividing Equation 4.3c by Equation 4.3b and comparing with Equation 4.3a yields

Q1 φ (t , t ) = φ1 (t1 , t2 ) = 3 1 3 Q2 φ2 (t2 , t3 )

(4.4)

The left side of Equation 4.4 indicates that ϕ3 /ϕ2 is a function only of t1 and t2. Thus, the function of t3 must cancel out of Equation 4.4, and we obtain

Q1 φ (t ) = φ1 (t1 , t2 ) = 3 1 Q2 φ2 (t2 )

(4.5)

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At this point, it becomes impossible to determine the function in Equation 4.5 analytically, because it is entirely arbitrary and many temperature functions can satisfy it. Kelvin proposed that the temperature function in Equation 4.5 be taken as Q1 T1 = Q2 T2



(4.6)

Equation 4.6 is taken to be the definition of the absolute thermodynamic temperature scale. This temperature scale is the same as the absolute temperature scale that was defined by the ideal gas (see Chapters 1 and 6). Thus, the temperature functions given by Equations 4.5 and 4.6 are simply the absolute temperatures. If Equation 4.6 is inverted, Q2 T2 = Q1 T1



(4.6a)

Subtracting unity from each side of Equation 4.6a gives us Q1 T −1= 2 −1 Q2 T1



(4.7)

Simplifying Equation 4.7 yields Q1 − Q2 T1 − T2 T = = 1 − 2 (4.7a) Q1 T1 T1



In terms of the previous notation,



η=

Qin − Qr T −T T × 100 = 1 2 × 100 = 1 − 2 × 100 Qin T1 T1

(4.7b)

From Equation 4.7b, we conclude the following:

1. The efficiency of a reversible-engine cycle is a function only of the upper and lower temperatures of the cycle. 2. Increasing the upper temperature while the lower temperature is kept constant increases the efficiency of the cycle. 3. Decreasing the temperature at which heat is rejected while keeping the upper temperature of the cycle constant increases the efficiency of the cycle.

As noted before, the temperature scale that is defined by Equation 4.6 is called the absolute thermodynamic scale, because it does not depend on the working substance.

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The Second Law of Thermodynamics

The Carnot cycle would make for a most efficient engine if it could be utilized as such. The problem is the difficulty of devising heat transfer processes that are constant temperature. The only known system that may be considered equivalent to a Carnot engine is in nature: the hurricane. Both the heat addition to the storm with the evaporation of ocean water and the cooling of the storm in the upper atmosphere occur at approximately constant temperatures. See the list of references (Bluestein 2006) for an understanding of this phenomenon.

ILLUSTRATIVE PROBLEM 4.1 A reversible engine operates between 1000°F and 80°F. (a) What is the efficiency of the engine? (b) If the upper temperature is increased to 2000°F while the lower temperature is kept constant, what is the efficiency of the engine? (c) If the lower temperature of the cycle is increased to 160°F while the upper temperature is kept at 1000°F, what is the efficiency of the cycle? SOLUTION Referring to Figure 4.7 and converting all temperatures to absolute temperatures, we obtain the following:

T −T 1460 − 540 = 0.63 = 63% a. 1 2 = T1 1460 T −T 2460 − 540 = 0.78 = 78% b. 1 2 = T1 2460 T −T 1460 − 620 = 0.575 = 57.5% c. 1 2 = T1 1460 T1 = 1000 + 460 = 1460

T1 = 2000 + 460 = 2460

Qin

T2 = 80 + 460 = 540 FIGURE 4.7 Illustrative Problem 4.1.

Qin

Qin W J

Qr

T1 = 1000 + 460 = 1460

W J Qr

T2 = 80 + 460 = 540

W J Qr

T2 = 160 + 460 = 620

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ILLUSTRATIVE PROBLEM 4.2 Assume that 100 units of heat enter the reversible engine in Illustrative Problem 4.1. If the cycle is reversed, determine the amount of work into the cycle and the heat removed from the reservoir at T2. SOLUTION The quantities of energy in the reversed cycle must equal those of the direct cycle. Several approaches are possible in solving this problem. We can use the efficiency obtained in Illustrative Problem 4.1. Therefore,



W/J W = 0.63 and = 100(0.63) = 63 units out Qin J Qin − Qr =

W J



Therefore,

100 – 63 = 37 = Qr

For the reversed cycle, we have only to note that Qr (or 37 units) is taken into the system from the low-temperature reservoir, 63 units of work enter the system, and 100 units are returned to the high-temperature reservoir.

ILLUSTRATIVE PROBLEM 4.3 It is desired to heat a house in the winter with a heat pump when the outside air is at 15°F. If the inside of the house is maintained at 70°F while the house loses 125 000 Btu/h, what is the minimum horsepower input required? SOLUTION Refer to Figure 4.8 and note that the reversed cycle is evaluated by considering the direct cycle first. From Equation 4.6, Qin Qr = T1 T2



where Qin = 125 000 Btu/h, T1 = 70 + 460 = 530°R, and T2 = 15 + 460 = 475°R: Qr = Qin ×

T2 475 = 125 000 × T1 530

= 112 028 Btu/h work = Qin − Qr = 125 000 − 112 028 = 12 972 Btu/h



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The Second Law of Thermodynamics

t1 = 70oF

70oF

Qin = 125 000 Btu/hr Wout

Direct

125 000 Btu/hr Win

Reversed

Qr t2 = 15oF

t2 = 15oF

FIGURE 4.8 Illustrative Problem 4.3.

Therefore, the reversed cycle (heat pump) requires at least 12 972 Btu/h of work input. This is

Btu ft. ⋅ lbf × 778 h Btu = 5.1 hp ft. ⋅ lbf min 60 × 33 000 h min⋅⋅ hp 12 972





ILLUSTRATIVE PROBLEM 4.4 A Carnot engine operates between a source temperature of 1000°F and a sink temperature of 100°F. If the engine is to have an output of 50 hp, determine the heat supplied, the efficiency of the engine, and the heat rejected. Refer to Figure 4.9.

1000oF = 1460oR

50 hp

100oF = 560oR FIGURE 4.9 Illustrative Problem 4.4.

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Thermodynamics and Heat Power

SOLUTION



50 hp =

50 × 33 000 = 2120.8 Btu/min as output 778 ( because 1 hp is equivalent to 33 000 ft.·lbf /min )

η = 1− =

T2 560 × 100 = 1 − × 100 = 61.6% T1 1460

W/JJ 2120.8 = Qin Qin





Qin =



2120.8 = 3443 Btu/min 0.616

Qr = 3443(1 − 0.616) = 1322 Btu/min

ILLUSTRATIVE PROBLEM 4.5 A Carnot engine operates between a source temperature of 700°C and a sink temperature of 20°C. Assuming that the engine will have an output of 65 hp, determine the heat supplied, the efficiency of the engine, and the heat rejected. SOLUTION We can also refer to Figure 4.9, noting that T1 = 700 + 273 = 973 K and T2 = 20 + 273 = 293 K. The efficiency of the Carnot engine is

η=

T1 − T2 973 − 293 × 100 = × 100 = 69.9% T1 973

The work output of the engine is 65 × 0.746 = 48.49 kJ/s. Because efficiency is work out/heat in, heat in = Qin =

48.49 = 69.37 kJ/s 0.699

heat rejected = Qout − work out = 69.37 − 48.49 = 20.88 kJ/s

As a check, Qr = Qin(l – η) = 69.37(1 – 0.699) = 20.88 kJ/s

The Second Law of Thermodynamics

155

ILLUSTRATIVE PROBLEM 4.6 USING CALCULUS ENRICHMENT If you have the choice of lowering the lowest temperature in a Carnot cycle by 1° or of raising the upper temperature by 1°, which would you do? Base your answer on the one that will yield the higher efficiency. SOLUTION We start the solution to this problem by writing the efficiency of the Carnot cycle as η = (1 – T2/T1) Differentiating the efficiency, first with respect to T1 while holding T2 constant and then with respect to T2 while holding T1 constant, yields

dη = –(T2 ) – dT1/(T1 )2 = (dT1/T1 )(T2 /T1 ) (a)

and dη = –dT2 /T1 (b) If we now refer to Equation b, we see that a 1° decrease in T2 gives us an efficiency increase of 1/T1. From Equation a, we see that a 1° increase in T1 gives us an increase in efficiency of (1/T1) (T2/T1). This is always smaller than the result that we obtained for the 1° decrease in T2, because the ratio of (T2/T1) is always less than unity. Thus, we conclude that if it is feasible, we should strive to decrease the lower temperature of the cycle as much as possible to increase the cycle efficiency. In most cases, the lower temperature is determined by ambient conditions, and it may not be possible to lower it to any extent.

ILLUSTRATIVE PROBLEM 4.7 Two Carnot engines are operated in series with the exhaust of the first engine being the input to the second engine. The upper temperature of this combination is 700°F, and the lower temperature is 200°F. If each engine has the same thermal efficiency, determine the exhaust temperature of the first engine (the inlet temperature to the second engine). Refer to Figure 4.10. SOLUTION The statement of the problem has the efficiency of both engines being equal. Denoting the efficacy of each engine as ηl and η2, respectively, η1 = (T1 – Ti)T1,

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Thermodynamics and Heat Power

700°F

Equally efficient Carnot engines

Ti

200°F FIGURE 4.10 Illustrative Problem 4.7.

and η2 = (Ti – T2)/Ti Equating these efficiencies and using the given data,

(1160 – Ti)/1160 = (Ti – 660)/Ti

Solving,

1160Ti − Ti2 = 1160Ti − (660)(1160)

or

Ti2 = (660)(1160)

We can generalize this result as

Ti = T1T2





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The Second Law of Thermodynamics

Finally, for this problem,

Ti = (660)(1160)



and Ti = 875°R = 415°F

4.4 Entropy If we refer to the working fluid and the changes that occur to it (for any reversible cycle operating between the same temperature limits), we have established that Qin Qr = T1 T2



In other words, the heat reception or rejection for the fluid in any reversible cycle divided by the temperature at which the heat is interchanged is a constant. The specific reversible paths that constitute the cycle do not change the value of these quantities. If the value of these quantities was a function of the specific reversible paths chosen, we could readily show that a violation of the second law would result. The uniqueness of these ratios leads us to the conclusion that they may represent state functions of the fluid, and as such, we may define them for a reversible process as properties. In fact, it is correct to make this assumption. To generalize the foregoing conclusion, we define the quantity S as referring to this new property and call it entropy. On a unit mass basis, the specific entropy is s. The defining equation for entropy is given by

∆S =

Q reversible process ∆S in Btu/°R or kJ/K T

q kg ⋅ K ∆s = reversible process ∆s in Btu/lbm ⋅ °R or kJ/k T



(4.8)

Entropy is defined as a differential because it is associated with a transfer of heat, which changes the state of the substance. Thus, the absolute value of the entropy of a substance may be assigned a zero value at any arbitrary state, as has been done in the development of the tables in Appendix 2. To show that entropy is a property of the state and not a function of the path chosen, let us consider the following situation: A reversible cycle operates between states a and b as

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Thermodynamics and Heat Power

b

1 2 3 a FIGURE 4.11 Proof that entropy is a property.

indicated by the path a, 1, b, 2, a in Figure 4.11. Let us also indicate a second possible return path, b, 3, a. For the first path (a, 1, b, 2, a),

∆S1, 2



Q = T

path 1 a ,b

Q + T

path 2



(4.9)

b,a

path 1

where the symbol indicates the sum of the Q/T items from a to b via path 1, and a ,b path 2 denotes the same from b to a via path 2. For path b, 3, a, as the return path, b,a

∆S1, 3 =

Q T

path 1

+ a ,b

Q T

path 3



(4.10)

b,a

All the processes in these two cycles are reversible, which permits us to write the foregoing relations for known paths. Let us once again repeat that the two frictionless, quasi-static processes that are reversible are the adiabatic and isothermal. For the reversible isothermal process, Q is not a function of T, and the reversible adiabatic process requires Q to be zero. Thus, if a cycle is composed of these reversible processes, ΔS of the cycle is zero. We may generalize this statement for all reversible cycles and say that the summation of ΔS around the reversible cycle must equal zero. Using this fact and equating Equations 4.9 and 4.10 yields



Q T

path 2

b,a

Q = T

path 3

(4.11) b,a

Thus, we can conclude that the function (Q/ T)reversible represents a property that is a function only of the state of the fluid and is independent of the reversible path taken to reach the particular state. The importance of this statement is not just in the proof of the fact that entropy is a state function; it is important also in that it provides a means of calculating the change in entropy for any process. All that is necessary is a knowledge of the initial and final states of the process, because we can always (at least in principle) consider a reversible process between the same initial and final states. It must be emphasized that Q/T can be used to evaluate only the entropy change for a reversible process.

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The Second Law of Thermodynamics

CALCULUS ENRICHMENT In order to establish entropy as a property, let us first consider a mathematical relation known as the inequality of Clausius. Consider the figure, which shows a reversible engine operating in a cycle with a constant upper temperature reservoir of T0 and rejecting heat as a temperature of T to a second engine operating in a cycle. The second engine converts all of the rejected heat of the first engine into useful work. If we take both engines as our system, the total work output will equal the sum of the work outputs of the individual engines. Thus, Reservoir at T0 Heat input Q0

Reversible engine

Work out WR

R

Heat rejected QR Temperature T Second engine

E

WR + WE

Work out WE

δW = δWR + δWE (a) For the work of the first engine, we have δWR = δQ 0(l – T/T0) (b) and for the second engine, δWE = δQR (c) Adding Equations b and c and simplifying yields the total work, δW = (T0 /T)δQR (d) We can write Equation d for the complete cycle using the notation that § indicates an integration around the complete cycle as

∫ δW = T ∫ (δQ /T ) (e) 0

R

If the figure is studied, it will be seen that this arrangement cannot produce the net work output, because it would violate the Kelvin–Planck statement of the second

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Thermodynamics and Heat Power

law. We therefore conclude that the only way this arrangement can operate is with a net work input and a heat flow into the reservoir. Equation e, with T0 constant, leads us to conclude



∫ δW ≤ 0 (f)

Combining this conclusion with Equation e yields



∫ (δQ/T ) ≤ 0 (g)

This relation, Equation g, is known as the inequality of Clausius. For a reversible cycle, it is readily shown that the equality in Equation g holds. Thus,

∫ (δQ/T )

rev

= 0 (h)

In Chapter 1, we showed that a quantity that is a property is a function only of the state of a system. Such a quantity is also an exact differential and can be represented mathematically as

∫ dx = 0 (i)

We therefore conclude that Equation h defines a property, S, that we have called entropy, where the property entropy is defined as dS = (δQ/T)rev (j) Therefore, for a reversible process, we have 2



∆S = S2 − S, =

∫ (dQ/T )

rev

(k)

1

Because entropy is a state function, we may use it to portray graphically any equilibrium state of a fluid. Let us plot on temperature–entropy coordinates the reversible processes constituting the Carnot cycle. For convenience, we use a unit mass of working fluid, and the entropy coordinate becomes the specific entropy s. Let us consider each step of the cycle and interpret each step with the aid of Figure 4.12.

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The Second Law of Thermodynamics

T B

T1

qin C

Net work (per pound of working fluid) A

T2

D

q rejected

A´ s1

s

D´ s2

s

FIGURE 4.12 Direct Carnot cycle.

Energy as heat enters the cycle at the constant upper temperature T1 with an increase in entropy from B to C. This is represented by the horizontal line BC. Because Δs = qin / T1, qin = T1Δs, which is equivalent to the area under the line BC or area A′BCD′. The fluid is then expanded via a reversible adiabatic process, which cannot give rise to an increase in entropy because no heat enters or leaves the system during its course. The reversible adiabatic process is therefore carried out at constant entropy. Because of this fact, it is called an isentropic process. A reversible adiabatic process is isentropic, but not all isentropic processes are reversible adiabatic processes. Therefore, the expansion of this step is the vertical line CD. The next step in the cycle is the isothermal rejection of heat represented by the horizontal line DA. Because Δs = qr/T2, T2Δs = qr, and the heat rejected by the cycle is represented by area A′ADD′, which is the area under the line DA. The final step in the cycle is the isentropic (reversible adiabatic) compression along path AB to return the cycle to its starting point. Because the area A′BCD′ is the heat into the cycle and area A′ADD′ is the heat rejected, the net work of the cycle is the area ABCD, or the area enclosed by the paths of the cycle on T–s coordinates. It should be noted that we have considered 1 lb. of working fluid because s is the specific entropy.

ILLUSTRATIVE PROBLEM 4.8 To vaporize 1 lbm of saturated water into saturated steam at 200 psia, 843.7 Btu is required. If the temperature of this process is constant and equal to 381.86°F, what is the change in entropy for the process? SOLUTION For the reversible isothermal process, we can write Δs – q/T. Thus,



∆s =

843.7 Btu or ∆s = 1.002 381.86 + 460 lbm ⋅ °R

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Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 4.9 If the process described in Illustrative Problem 4.8 is the heat reception portion of a Carnot cycle, what is the efficiency of the cycle if the lowest temperature of the cycle is 50°F? How much work is done per pound of fluid? How much energy is rejected? SOLUTION

η=

T1 − T2 T × 100 = 1 − 2 × 100 T1 T1

= 1−



460 + 50 × 100 460 + 381.886

= (1 − 0.606) × 100 = 39.4%







w = η qin = (0.394)(843.7 ) = 332.4 Btu/lbm J

qr = qin −

w = 843.7 − 332.4 = 511.3 Btu/lbm J

As an alternative solution and referring to Figure 4.12, we can write the following: qin = T1Δs (4.12a) qr = T2Δs (4.12b)

w = qin − qr = (T1 − T2 )∆s J qr = T2 ∆s = ( 460 + 50)(1.002) = 511 Btu/lbm

w = qin − qr = 843.7 − 511 = 332.7 Btu/lbm J η=

332.7 w/J × 100 = × 100 = 39.4% 843.7 qin

(4.12c)

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The Second Law of Thermodynamics

ILLUSTRATIVE PROBLEM 4.10 Determine the change in entropy at 1.4 MPa for the vaporization of 1 kg of saturated water to saturated steam. Compare your answers to the Steam Tables in Appendix 2 (hfg = 1959.7 kJ/kg, sfg = 4.1850 kJ/kg·K, t = 195.07°C). SOLUTION As in Illustrative Problem 4.9, we can consider the vaporization process to be isothermal. Therefore,



hfg

1959.7 = 195.07 + 273 T = 4.1867 kJ/kg ⋅ K

∆s =



If we use 273.16 to obtain temperature in degrees Kelvin, Δs = 4.1853 kJ/kg · K This compares very closely to the Steam Tables value. It has already been noted that the cycle efficiency can be improved by raising the upper temperature of the cycle or lowering its lowest temperature. From Equation 4.12b, it is noted that the heat rejected during this cycle is equal to the change in entropy during the heat rejection process multiplied by the temperature at which the heat is rejected. In a general sense, the entropy change of the process becomes a measure of the amount of heat that becomes unavailable (rejected) during the cycle. For an irreversible process, we have already indicated that some energy becomes unavailable because of friction during the process. If it is assumed that the irreversible process can be restored to its original state by the input of additional work to the system via a reversible path, it can be shown that the increase in entropy during the irreversible process can be used to evaluate the least amount of work necessary to restore the system to its original state. Thus, a greater entropy change requires more work to restore the system. In this sense, entropy is also a measure of the unavailability of energy that occurs in an irreversible process. ILLUSTRATIVE PROBLEM 4.11 One hundred Btu enters a system as heat at 1000°F. How much of this energy is unavailable with respect to a receiver at 50°F? Also, how much of this energy is unavailable with respect to a receiver at 0°F? SOLUTION Let us assume that a Carnot engine cycle operates between the two temperatures in each case. Figure 4.13 shows this problem on T–S coordinates. The shaded area under the 1460°R line represents the input of 100 Btu. Thus, T1ΔS = Qin

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Thermodynamics and Heat Power

T

1000°F

50°F 0°F

1460 R

510 R 460 R

S

S

FIGURE 4.13 Illustrative Problem 4.11.



∆S =

100 Btu Qin = = 0.0685 1460 T1 °R

The crosshatched area represents heat rejected or

Qr = T2 ∆S = (510)(0.0685) = 34.9 Btu



The crosshatched area for a receiver at 0°F is Qr = (460)(0.0685) = 31.5 Btu Note from this problem that the maximum work output is

work (max.) = Qin – T2ΔS

and the unavailable energy is the difference between the heat into the cycle and the maximum work output, or Qr. Also, by lowering T2, we decrease the energy rejected and increase the energy available.

ILLUSTRATIVE PROBLEM 4.12 If 1 kJ enters a system as heat at 500°C, how much of this energy is unavailable with respect to (a) a receiver at 20°C and (b) a receiver at 0°C? SOLUTION Refer to Illustrative Problem 4.11.



∆S =

1000 J J Qin = = 1.2937 500 + 273 K T1

Qr = T2 ∆S



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The Second Law of Thermodynamics

Therefore, Qr = (273 + 20)(1.2937 ) a. = 379.05 J for the receiver at 20°C b. Qr = (273 + 0)(1.2937 ) = 353.18 J for the receiver at 0°C Note that ΔS for the process is independent of the receiver temperature.

The available energy for a process that receives heat is the amount of net work that would be obtained from the most efficient engine cycle of which the process could be made a part. Similarly, the unavailable energy for a process is the amount of energy that would be rejected from the most efficient engine cycle of which the process could be made a part. Because the atmosphere is essentially the lowest temperature reservoir to which heat is rejected, 77°F (25°C) and 1 atm is often taken as the heat rejection condition. This has been called the dead state. If a state is in equilibrium with the dead state, it can no longer be used to obtain useful work. Any process can be considered to have a characteristic specific heat associated with it. Therefore, the heat transfer during such a process can be written as

(4.13)

q = cΔT

where it is reversible or irreversible. Using Equation 4.13 and the definition of entropy given in Equation 4.8, s2 – s1 = summation of cΔT/T for a reversible process between its temperature limits. This relation can be used to evaluate the change in entropy for a process taking place between temperatures T1 and T2, and it will correctly evaluate the change in entropy for any process between the prescribed limits as long as we restrict it to apply to the system and not to the surroundings. Thus, for a constant c, it can be shown that the summation of cΔT/T between the limits of T1 and T2 yields

s2 − s1 = c ln

T2 (4.14) T1

where the symbol ln is the natural logarithm to the base e.

ILLUSTRATIVE PROBLEM 4.13 If 6 lb. of a gas undergoes a constant pressure change from 1440°F to some second temperature, determine the final temperature if the entropy change is −0.7062 Btu/°R. Assume the specific heat, cp = 0.361 Btu/lbm·°R for this gas.

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SOLUTION If we multiply both sides of Equation 4.14 by the mass m, m∆s = ∆S = mc p ln



T2 T1

For this problem,

−0.7062

T2 Btu Btu = 6 lbm × 0.361 × ln °R lbm °R 1440 + 460

or

ln

T2 −0.7062 = = −0.3260 1440 + 460 6 × 0.361

From the definition of ln,



T2 = e −0.3260 1440 + 460 T2 = (1440 + 460)(0.7218)



and T2 = 1371.4ºR or 911.4ºF

ILLUSTRATIVE PROBLEM 4.14 If 1 lbm of water at 500°F is adiabatically mixed with 1 lbm of water at 100°F, determine the change in entropy. Assume that the specific heat of the hot and cold streams can be considered constant and equal to unity. Also, the specific heat of the mixture can be taken to be unity. Refer to Figure 4.14.

m1 at t1

m2 at t2

(m1 FIGURE 4.14 Illustrative Problem 4.14.

m2) at t

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The Second Law of Thermodynamics

SOLUTION To solve this problem, it is necessary first to establish the equilibrium temperature of the final mixture. Applying the first law to the closed system of 2 lb. of water, there is no work done and no heat transfer into or out of the system. Thus, total ΔU = 0, and so m1c1(t – t1) + m2c2(t – t2) = 0. Solving for t, (1)(1)(t – 500) + (1)(1)(t – 100) = 0 yielding t = 300°F For this problem, the hot stream is cooled from 500°F to 300°F. Because we may state that heat Q was removed during this process, Δs would be expected to be negative. By applying Equation 4.14,



∆s = 1 ln

300 + 460 760 960 = − ln 1.263 = ln = − ln 760 500 + 460 960

= −0.233 Btu/lbm ⋅ °R



The cold stream is heated from 100°F to 300°F; therefore,

∆s = 1 ln

760 = ln 1.357 = 0.305 Btu/lbm ⋅ °R 560



The net change is 0.305 – 0.233 = +0.072 Btu/lbm·°R. An alternative solution to this problem is found by assuming an arbitrary temperature lower than any other temperature in the system. The change in entropy of each fluid is determined with respect to this arbitrary temperature, and the net change in entropy is the algebraic sum of the values found in this manner. An illustration of the procedure is found in Chapter 7, as well as in Illustrative Problem 4.15. If the specific heat of the substances being mixed varies with temperature, the appropriate average specific heats for the temperature intervals should be used.

ILLUSTRATIVE PROBLEM 4.15 Solve Illustrative Problem 4.14 using 0°F as a reference temperature for entropy. SOLUTION As a first step, we calculate the final mixture temperature as was done in Illustrative Problem 4.14 and find it to be 300°F. Next, let us calculate the initial entropy of each fluid above the 0°F base. For the “hot” fluid,



∆s = c ln

T2 500 + 460 = 1 ln T1 0 + 460

= 1 ln 2.087 = 0.736 Btu/lbm ⋅°R



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Thermodynamics and Heat Power

For the “cold” fluid, s = c ln



T2 100 + 460 = 1 ln T1 0 + 460

= 1 ln 1.217 = 0.196 Btu/lbm ⋅°R



At the final mixture temperature of 300°F, the entropy of each stream above 0°F is, for the “hot” fluid, s = c ln



T2 300 + 460 = 1 ln T1 0 + 460

= 1 ln 1.652 = 0.502 Btu/lbm ⋅°R



and for the “cold” fluid,



s = c ln

T2 300 + 460 = 1 ln T1 0 + 460

= 1 ln 1.652 = 0.502 Btu/lbm ⋅°R



The change in entropy of the “hot” fluid is 0.502 – 0.736 = –0.234 Btu/lbm·°R. The change in entropy of the “cold” fluid is 0.502 – 0.196 = 0.306 Btu/lbm·°R.

total change = 0.306 – 0.234 = 0.072 Btu/lbm·°R

The advantage of this alternative procedure is that by using a convenient, arbitrary datum below the lowest temperature in the system, we avoid negative logarithms. Either method is correct, and the choice of one over the other is purely personal preference.

The fact that entropy is a property leads us to inquire whether there are possible relations between entropy and other properties of a fluid. If they exist, they should prove to be very valuable, because it would then be possible to compute one from the other without resorting to experiment. Let us recall the energy equation applied to the reversible nonflow process:



q = ∆u +

p∆v J

(4.15)

Because the process is assumed to be reversible, we may replace q by TΔs. Thus,

T∆s = ∆u +

p∆v J

(4.16)

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The Second Law of Thermodynamics

In Equation 4.16, TΔs evaluates the energy as heat only if the process is reversible, and similarly, pΔv/J evaluates only the work of a reversible process. However, each term of this equation consists of properties of the fluid that are not functions of the path. Thus, by applying the energy equation and the second law to a reversible, nonflow process, we have been able to arrive at a general equation involving only property terms. The only restriction on this equation occurs when each of the various terms is interpreted as either heat or work. By referring to the reversible steady-flow process, we can arrive at another relationship between the properties. Alternatively, the same result can be obtained as follows. By definition,

h2 − h1 = (u2 − u1 ) +

p2 v2 − p1 v1 J

(4.17)

or

∆h = ∆u +

∆( pv) (4.18) J

The change in the product pv/J equals

( p + ∆p)( v + ∆v) − pv J

(4.19)

Carrying out the multiplication of the terms of Equation 4.19 yields

∆( pv) = ∆pv + ∆vp + ∆p∆v J

(4.20)

The product (ΔpΔv) is the product of two small terms and can be considered negligible. Thus,

∆( pv) ∆pv + p∆v = (4.21) J J

Replacing Δ(pv)/J in Equation 4.18 with its equivalent from Equation 4.21 yields

∆h = ∆u +

∆pv + ∆vp (4.22) J

By the substitution of Equation 4.22 into Equation 4.16 and rearranging, we have the desired result:

T∆s = ∆h −

v∆p (4.23) J

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Thermodynamics and Heat Power

We can thus relate entropy to enthalpy by means of Equation 4.23. Once again, each term in this equation is a property, but the interpretation of such terms as TΔs as a heat quantity or vΔp as a work quantity can be valid only for a reversible process. The student should note that Equations 4.15 through 4.23 can be written in terms of SI units simply by omitting the conversion factor J wherever it appears. The final result would be TΔs = Δh − vΔp (4.23a)



CALCULUS ENRICHMENT Applying the first and second laws to a nonflow system undergoing an internally reversible process, we obtain the following relation: δq = δw + du

(a)

For this process, δw = p dv

(b)

For the heat transfer, dq, we can write dq = T ds

(c)

Substitution of Equations b and c into Equation a yields T ds = du + p dv

(d)

Equation d is known as the first of the Gibbs or T ds equations. Starting with the definition of enthalpy, we can obtain the second T ds equation: du = d(h – pv) = dh – p dv – v dp

(e)

Equating du in Equation d with du in Equation e gives us the desired second T ds relation, namely, T ds = dh – v dp

(f)

The T ds equations involve only properties, and even though they were obtained by considering a nonflow, internally reversible system, they are valid for all systems and processes. Solving these equations for ds gives us ds = du/T + p dv/T

(g)

and ds = dh/T – v dp/T

(h)

By integration of either ds equation, we can obtain the change in entropy for a process knowing the p, v, T relation and the relation of temperature to either h or u.

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The Second Law of Thermodynamics

It has been established that entropy is a property and can be evaluated by considering reversible paths connecting the given end states of a process. Let us consider the situation in which two processes start out from a given state. The first one is carried out reversibly until a second state is reached. The second process is carried out irreversibly until the same pressure as the first process has stopped at is reached. These processes operate between a fixed source at T1 and a fixed sink at T2 as part of a Carnot cycle. For the reversible process, Qin Qr = T1 T2



For the irreversible process, less net work is produced, with the consequence that more energy must be rejected as heat. Thus, Qr/T2 for the irreversible process can at best equal the equivalent ratio of the reversible process, or as is the case in all instances, it must be greater. Using this qualitative argument, we can arrive at another important consequence of the second law: The entropy of an isolated system increases or in the limit remains the same. Keenan 1941

This principle of the increase of entropy also serves as a criterion of irreversibility. Thus, if we find during a process that the entropy of an isolated system increases, we must conclude that the process is irreversible. Another consequence of the principle of the increase of entropy is that at a given internal energy, that state having the greatest entropy will be the most probable state that the system will assume. At this most probable state, the system is said to be in stable equilibrium. The foregoing can be summarized by the following simple equation: ΔS ≥ 0 for isolated systems



(4.24)

which is interpreted to state that for airy reversible change in an isolated system, the total entropy remains unchanged, and for any irreversible change, the total entropy increases. CALCULUS ENRICHMENT From the inequality of Clausius, we can now develop the principle of the increase of entropy. Consider points A and B in the figure that are connected by two processes, one reversible and the other irreversible. From the inequality of Clausius, we can write that

∫

B

(δQ/T ) =

∫

A

∫

(δQ/T ) + (δQ/T ) < 0 (a)

A

B

because the cycle is irreversible. For the reversible path, we can use the definition of entropy to give us B



∫ (δQ/T ) + S

A

A

− SB < 0 (b)

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Transposing terms, B

∫

SB − SA ≥ (δQ/T ) (c)



A

B Irreversible path 1

2 Reversible path A

Complete cycle = paths 1 + 2

Note that the equality holds for a reversible process and that the inequality holds for an irreversible process. Equation c is the general statement of the principle of the increase of entropy. For a reversible adiabatic process, the change in entropy will be zero, while for an irreversible adiabatic process, the entropy will increase. For a system that is isolated, SB – SA ≥ 0

(d)

and we conclude that the entropy of an isolated system increases or in the limit remains the same. Thus, if the changes in an isolated system are entirely reversible, the entropy will remain constant.

Many researchers have also referred to entropy as an indication of the arrow of time. Since entropy is never decreasing in a system, it relates to the progress of time. Thus, the universe is considered to be a very low entropy state in its formation and the increase in entropy follows our progress in time. Another aspect of entropy is its relationship to the amount of disorder or randomness in a system. As entropy must always increase in real systems, so do systems favor disorder. Thus, solids have lower entropy than liquids and liquids lower entropy than gases. As an example, if ice is left at its freezing point, 32°F (0°C) in 14.7 psia (101 kPa) air, it will melt into liquid water with the more disorderly molecules. Likewise, water left to stand in street puddles after a rain will eventually evaporate into water vapor. In general, processes occur that result in increased entropy and randomness. As shown in Illustrated Problem 4.14, when heat is transferred from a hot body to a cold body until an equilibrium temperature is reached, the increase in entropy of the cold body exceeds the decrease in entropy of the hot body so the net entropy has increased.

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4.5 Review The reasoning in this chapter is more abstract than in previous chapters and therefore may present more difficulty for students. Starting with the definition of thermal efficiency, we then continued with the statement of the second law of thermodynamics. For our purposes, the second law of thermodynamics can be stated as “Heat cannot, of itself, flow from a lower temperature to a higher temperature.” Based on the second law and the concept of reversibility, we were able to reason out the three general conclusions that Carnot arrived at:



1. No engine operating between fixed source (T1) and sink (T2) temperatures and continuously delivering work can be more efficient than a reversible engine operating between these same temperature limits. 2. The efficiency of all reversible cycles operating between the same temperature limits is the same. 3. The thermal efficiency of a reversible engine is a function solely of the upper and lower temperatures of the cycle and is not a function of the working substance used in the cycle.

In 1824, Sadi Carnot proposed a reversible cycle consisting of two constant-temperature and two adiabatic processes. The utility of this cycle lies in the ease with which we were able to calculate its thermal efficiency using the temperature function proposed by Kelvin. This is the absolute thermodynamic temperature, which coincides with our earlier definition of absolute temperature. We thus became able to determine the limiting efficiency of any cycle operating between upper and lower temperature limits by calculating the thermal efficiency of the Carnot cycle between the same temperature limits. This definition of the absolute thermodynamic temperature combined with the Carnot cycle also enabled us to define a new property called entropy. The property entropy was also shown to be a measure of the unavailability of energy that occurs in an irreversible process. Using the energy equation for a reversible, nonflow process enabled us to derive some general relations among entropy, enthalpy, and internal energy.

Key Terms Terms used for the first time in this chapter are as follows: absolute thermodynamic temperature: An arbitrary temperature function used with the Carnot cycle. For practical purposes, it is identical to the absolute temperature scales of Kelvin or Rankine. Carnot cycle: A reversible cycle proposed by Sadi Carnot in 1824 that consists of two constant-temperature and two adiabatic processes. cycle: A series of thermodynamic processes during which the working fluid can be made to undergo changes involving energy transitions and is subsequently returned to its original state.

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entropy: A property of a substance; also a measure of the unavailability that occurs in an irreversible process. heat engine: A continuously operating system across whose boundaries flow only heat and work. isentropic: A process carried out at constant entropy. A reversible adiabatic process is isentropic. isothermal: A process carried out at constant temperature. principle of the increase of entropy: The entropy of an isolated system increases or in the limit remains the same. reversible process: Any process performed so that the system and all its surroundings can be restored to their initial states by performing the process in reverse. second law of thermodynamics: Heat cannot, of itself, pass from a lower temperature to a higher temperature. thermal efficiency: The ratio of the net work of a cycle to the heat added to the cycle.

Equations Developed in This Chapter Net work output Thermal efficiency

net work output × 100 heat added

(4.1)

Qin − Qr Q × 100 = 1 − r × 100 Qin Qin

(4.2)

η= η=

Q1 T1 = Q2 T2

Kelvin temperature function Efficiency of a reversible cycle Entropy Entropy change General property relation General property relation General property relation (SI) Entropy increase principle

η= ∆S =

(4.6)

T1 − T2 T × 100 = 1 − 2 × 100 T1 T1

q Q or ∆s = T T

reversible process

(4.7a) (4.8)

T2 T1

(4.14)

T∆ s = ∆u +

p∆v J

(4.16)

T∆ s = ∆h +

v∆p J

(4.23)

TΔs = Δh – vΔp

(4.23a)

ΔS ≥ 0 for all isolated systems

(4.24)

s2 − s1 = c ln

QUESTIONS

4.1 Can a heat engine do anything other than deliver work? 4.2 Define a cycle. 4.3 Thermal efficiency is defined to be the ratio of net work to heat added in a cycle. Would you think that this is an appropriate definition to be used when a refrigerator is being discussed?

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4.4 Do you know of any process in nature that is reversible? 4.5 There are four distinct events that occur in the Carnot cycle. Starting with the heat reception event, name and describe each one. 4.6 There are three conclusions reached from the Carnot cycle regarding reversible cycles. What are they? 4.7 What was the contribution by Kelvin? 4.8 What two factors determine the limiting efficiency of any cycle? 4.9 How does the combination of the work of Kelvin and Carnot help in the design of power cycles? 4.10 The statement has been made that entropy is a property. What does this mean to you? 4.11 Other than being a property, what else does entropy represent? 4.12 It is possible to derive a relation among entropy, enthalpy, and internal energy that is perfectly general. Under what conditions can you associate heat and work to these terms? 4.13 What is the principle of the increase of entropy? 4.14 Why is the principle of the increase of entropy important? PROBLEMS Problems Involving Thermal Efficiency 4.1 An engine cycle is operated to produce 12.5 Btu/min as work. If 100 Btu/min as heat enters the cycle, determine the heat rejected and the efficiency of the cycle. 4.2 A reversible engine produces 10 hp as work while 1270 Btu/min enter the engine as heat. Determine the energy rejected and the thermal efficiency of the cycle. 4.3 A heat engine produces 75 hp for a heat addition of 9000 Btu/min. Determine the thermal efficiency and heat rejected by this engine. 4.4 A Carnot power plant operates between a high-temperature reservoir at 1500°F and a low-temperature reservoir at 70°F. Determine the heat addition if the plant produces 1000 MW of power. 4.5 An engine produces 10 kJ of work while 80 kJ enters the engine cycle as heat. Determine the energy rejected and the thermal efficiency of the cycle if it is reversible. 4.6 An inventor claims to have an engine that has a thermal efficiency of 90%. Comment on the claim. 4.7 A diesel engine uses 450 lbm of fuel per hour. If the burning of the fuel releases 18 000 Btu/lbm and the engine produces 840 hp, determine its thermal efficiency. 4.8 An internal combustion engine uses 0.38 lbm/h of gasoline for each horsepower that it produces. If the gasoline has an energy content of 19 500 Btu/lbm, determine the thermal efficiency of the engine. *4.9 An automobile engine has an efficiency of 23%. If the engine produces 100 hp as its output, determine the heat input to the engine. If gasoline has a heat content

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of 20 750 Btu/lbm and a specific gravity of 0.74, determine the gallons of gasoline used per hour at this rating. *4.10 An automobile has an efficiency of 22%. It is rated to give an output of 100 kW. Determine the heat input to the engine and the fuel consumption in liters per hour if the gasoline has a heat content of 4.9 × 104 kJ/kg and a specific gravity of 0.82. 4.11 A gas turbine has a thermal efficiency of 25% and develops 10 000 hp. If the fuel releases 18 500 Btu/lbm, determine the rate of fuel usage. 4.12 A power plant burns 900 kg of coal per hour and produces 480 kW of power. If each kilogram of coal releases 5.9 MJ, determine the efficiency of the plant. 4.13 A gas expands isothermally in a cylinder, and it is found to deliver 1 kJ of work. During the process, it is found that 1 kJ of heat is added to the gas to keep it isothermal. It would appear that all the heat has been converted to useful work in this process. Is this possible? Base your answer on both the first and second laws of thermodynamics. Problems Involving Reversible Heat Engines and the Carnot Cycle 4.14 A Carnot cycle is operated between 1000°F and 500°F. If the upper temperature is increased to 1100°F, what is the efficiency of the cycle? If the lower temperature is decreased to 400°F, what is the efficiency of the cycle? 4.15 A Carnot cycle operates between 900°C and 100°C. Determine the efficiency of the cycle, the heat rejected, and the useful work output if 100 kJ enters the cycle as heat. 4.16 A Carnot engine operates between 940°F and 60°F and produces 80 hp. How much heat is supplied to the engine, how much heat is rejected by the engine, and what is the thermal efficiency of the engine? 4.17 A reversible power cycle has a lower reservoir temperature of 300 K. The cycle produces 42 kW as power and rejects 180 kW to the cold reservoir. Determine the temperature of the high temperature reservoir. 4.18 A Carnot engine operates between 1350°F and 125°F. If it rejects 55 Btu as heat, determine the work output. 4.19 A Carnot engine produces 40 hp when operated between temperatures of 1500°R and 500°R. Calculate the heat supplied per hour to the engine. 4.20 A Carnot cycle operates between 1800°F and 200°F. Determine the efficiency of the cycle, the heat rejected, and the useful work output if 500 Btu/min enters the cycle as heat. 4.21 Is it possible for a reversible engine cycle to produce 100 hp if it receives 300 Btu/s at 1000°F and rejects heat at 500°F? 4.22 An inventor tests an engine cycle that she has built and finds that its thermal efficiency is 58%. If the engine operates between 540°F and 60°F, should she release her findings to the press or retest the engine? 4.23 An inventor claims that he can obtain 155 hp as work from an engine with a heat input equivalent to 500 hp. Comment on the validity of his claim if the engine is to operate between 250°F and 10°F. Also comment on the probability of achieving these conditions.

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*4.24 Two engines are operated between the same temperature limits, and each engine rejects 1000 kJ as heat to the sink. If engine A is irreversible and has a claimed efficiency of 50% and engine B is reversible and has a claimed efficiency of 40%, prove numerically that a violation of the second law will occur under these conditions. *4.25 Two reversible engines operate in series between temperatures of 1000°F and 100°F. If the first engine receives 1000 Btu, determine the total work output of this arrangement and the temperature at the inlet to the second engine. Assume that both engines have the same thermal efficiency. *4.26 A Carnot cycle has an efficiency of 32%. Assuming that the lower temperature is kept constant, determine the percent increase of the upper temperature of the cycle if the cycle efficiency is raised to 48%. *4.27 A reversible cycle is shown on a T–S diagram in Figure P4.27. Calculate the efficiency of this cycle. T B

1200°R

400°R

C A

S

S

FIGURE P4.27

*4.28 A house is cooled by the removal of 68 000 Btu/h using a reversed Carnot cycle. Assume that the house is kept at 72°F and that the outside temperature is 90°F. If the motor used is rated at 6.5 hp and electricity costs 14 cents/kW·h, determine the cost per day to operate this cycle. Repeat this problem for a 4-hp motor, and compare your results. Note that this is an ideal cycle and that all processes are ideal. *4.29 A reversible engine has an efficiency of 40%. If it is operated in such a manner that 15% of the work is lost as friction in its moving parts, what would the efficiency be? 4.30 A reversible engine operates between 900°F and 200°F. What is the maximum efficiency of this cycle? If the rating of this engine is 1 hp, determine the heat rejected per minute. 4.31 If the cycle in Problem 4.30 is reversed, how much heat is rejected to the upper temperature reservoir? 4.32 A reversible engine operates between 750°C and 80°C. Determine the maximum efficiency of the cycle and the heat rejected if the engine is rated at 1 hp. 4.33 If the cycle in Problem 4.32 is reversed, how much heat is rejected to the upper temperature reservoir?

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4.34 In order to keep a freezer at 20°F while the room temperature is 72°F, 13 500 Btu/h must be removed. If the freezer operates as a reversible cycle, determine the minimum work input required. 4.35 A Carnot engine operates between a source temperature of 900°F and a sink temperature of 100°F. If the engine produces 100 000 ft.-lb. of work, determine its thermal efficiency, the heat supplied, and the heat rejected. 4.36 The ocean is an almost infinite energy source. Off the coast of Hawaii, the surface temperature is 86°F, while at a depth of 2200 ft., the temperature is 43°F. Determine the maximum efficiency of a reversible power plant that is operated between these temperature limits. This cycle is described in Chapter 9 as the ocean thermal energy conversion (OTEC) plant. 4.37 A Carnot engine receives 1000 Btu as heat at 1000°F and operates with a sink temperature of 150°F. Determine the efficiency, work out, and heat rejected by this engine. 4.38 A Carnot engine operates between an upper temperature of 700°C and a lower temperature of 30°C. If the engine can produce 150 kJ of work, determine its thermal efficiency, the heat supplied, and the heat rejected. 4.39 A Carnot engine develops 30 hp while rejecting 100 MJ/h as heat to a receiver at 20°C. Determine the upper temperature of the cycle and its efficiency. 4.40 A Carnot engine develops 20 hp while rejecting 70 000 Btu/h as heat to a receiver at 80°F. Determine the efficiency of the engine and the source temperature. 4.41 A reversed Carnot engine operates between 150°F and 60°F; 100 Btu/min is extracted from the cold body. Determine the horsepower required to operate the engine. 4.42 A Carnot engine operates with an efficiency of 30% and, when reversed, removes 1000 Btu/h as heat from the cold sink. Compute the heat rejected to the hotter source. 4.43 A reversed Carnot engine operates between 80°C and 20°C; 100 kJ/min as heat is extracted from the cold body. Determine the horsepower required to operate the engine. 4.44 A reversed Carnot engine operates with an efficiency of 30%, removing 1 MJ as heat from the cold sink. Calculate the heat rejected to the hotter source. 4.45 A solar powered 10 kW Carnot power cycle is proposed drawing heat from 50°C solar collectors. Determine the required rate of heat rejection to the 20°C surrounding air. 4.46 A reversed Carnot cycle is used to heat a room. If 9000 Btu/h is required, how much energy must be put in electrically if the room is to be at 70°F and a deep well at 40°F is used as the source of working fluid for the cycle? 4.47 A reversed Carnot engine operates between 40°C and 5°C. If the motor input is 4 hp, determine the heat removed from the cold sink. 4.48 A reversed Carnot engine is used to heat a room. If 10 kW is required to replace heat losses from the room, how much energy must be put into the motor if the room is to be kept at 22°C and a deep well at 4°C is used as the source of the working fluid of the cycle?

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4.49 A solar powered 10 kW Carnot power cycle is proposed, drawing heat from 50°C solar collectors. Determine the required rate of heat rejection to the 20°C surrounding air, in kW. 4.50 A Carnot engine operates with an efficiency of 40%. If the upper temperature is 500°C, determine the lower temperature of the cycle. 4.51 A Carnot engine develops 25 hp while operating with an efficiency of 32%. If the engine rejects heat to the atmosphere at 70°F, determine the upper temperature of operation and the heat rejected. 4.52 A reversible engine cycle operates with an efficiency of 35%. If the engine develops 19 kW while rejecting heat to a reservoir at 5°C, determine the heat input, the heat rejected, and the upper temperature of the cycle. 4.53 A reversed Carnot engine is used to cool a large room in the summer. The room is to be kept at 24°C when the outside temperature is 35°C. It is estimated that 150 kJ/min is the heat transfer from the outside to the room. Calculate the power required to operate the engine. Problems Involving Entropy 4.54 A Carnot engine receives 5800 Btu/min as heat at a temperature of 400°F. If the engine develops 50 hp, what is the receiver temperature? What is the change in entropy during the heat input portion of the cycle? 4.55 What is the change in entropy during the heat rejection portion of the engine cycle described in Problem 4.54? *4.56 The Steam Tables show that at 100°F, the heat of vaporization, hfg, is 1037.0 Btu/ lbm. Determine the change in entropy, sfg, and compare the calculated value to the value given for sfg in the Steam Tables. (Note that the Steam Tables use –459.67°F as absolute zero.) 4.57 To change a pound of saturated water to saturated steam at 32°F, 1075.4 Btu/lbm is required. Determine the change in entropy for this process. 4.58 Water is heated from 32°F to 212°F. If the specific heat of this process is taken to be constant and equal to unity, what is the change in entropy for this process per pound of water? 4.59 If the process described in Problem 4.58 is reversed, what is the change in entropy per pound of water? 4.60 For the engine of Problem 4.35, determine the change in entropy for the heat reception and heat rejection portions of the cycle. *4.61 A Carnot engine cycle is operated as described in Problem 4.35. If there are irreversibilities in the cycle that cause an entropy change in the heat rejection portion of the cycle to be 10% greater than in the heat reception portion, determine the thermal efficiency of the cycle. 4.62 One kilogram of air is heated at constant volume from 100°C to 400°C. If cv is 0.7186 kJ/kg·K, determine the change in entropy of the air. 4.63 If 1 lbm of air is heated at constant volume from 70°F by the addition of 200 Btu as heat, calculate the change in entropy for the process. Assume that cv = 0.171 Btu/ lbm·°R and remains constant for the entire process.

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4.64 If 1 lbm of air is heated at constant pressure from 70°F by the addition of 200 Btu as heat, calculate the change in entropy for the process. Assume that cp = 0.24 Btu/lbm·°R and remains constant for the entire process. 4.65 If the process described in Problem 4.62 is carried out at constant pressure with cp = 1.0062 kJ/kg·K, determine the change in entropy of the process. *4.66 A Carnot engine has an entropy change during the isothermal heat addition portion of the cycle of 0.15 Btu/lbm·°R when it operates between the temperatures of 1500°F and 500°F. How much work does this engine deliver per pound of working fluid? 4.67 One pound of air is heated at constant volume. If the value of cv = 0.171 Btu/lbm·°R and is constant, determine the entropy change when the air is heated from 200°F to 800°F. 4.68 If the process in Problem 4.67 is carried out at constant pressure and cp = 0.24 Btu/lbm·°R, determine the entropy change. 4.69 A Carnot engine operates between 200°F and 1800°F. If the entropy change during the heat addition portion of the cycle equals 0.25 Btu/lbm·°R, calculate the work per lbm of working fluid. 4.70 A Carnot power cycle operates between 1200 K and 300 K. If 4.8 MJ of heat is supplied to the cycle, determine the heat rejected and the change in entropy during the heat reception portion of the cycle. 4.71 One lbm of air is heated at a constant temperature of 100°F by the addition of 250 Btu. Calculate the change in entropy for this process. 4.72 One kilogram of air is heated at a constant temperature of 40°C by the addition of 200 kJ. Determine the change in entropy for this process. *4.73 Five pounds of water at 200°F is mixed with 2 lb. at 100°F. What is the total change in entropy for this process? Assume that all specific heats are constant and equal to unity. Work this problem by considering each stream separately. 4.74 A process is carried out at constant volume. It is found that the change in entropy for the process is 0.05 Btu/lbm·°R. If cv is constant and equal to 0.171 Btu/lbm·°R and the upper temperature of the process is 250°F, determine the initial temperature of the process. 4.75 A gas is cooled from 250°C, and it is found that the entropy change is –0.1427 kJ/ kg·K. Assuming that the appropriate specific heat for the process is 1.4876 kJ/ kg·K, determine the temperature after cooling. 4.76 A gas is heated at constant pressure from 100°F. If cp = 0.31 Btu/lbm·°R and the entropy change is 0.2107 Btu/lbm·°R, determine the upper temperature. 4.77 A process is carried out at constant volume. It is found that the entropy change is 1 kJ/kg·°K. If cv is constant and equal to 0.7186 kJ/kg·K and the lower temperature of the process is 20°C, determine the upper temperature. *4.78 An isentropic process is carried out with the working fluid expanding from 700°F to 100°F. The specific heat at constant pressure is 0.24 Btu/lbm·°R. During the process, the internal energy changes by 102.6 Btu/lbm. Determine the change in entropy for this process. 4.79 A constant-temperature process is carried out with a concurrent change in entropy of 0.1 Btu/lbm·°R at 600°F. Determine the unavailable portion of the energy received with respect to a receiver at 50°F and at 100°F.

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181

4.80 A constant-temperature process is carried out with a concurrent change in entropy of 0.2 kJ/kg·K at 400°C. What is the unavailable portion of the energy received with respect to a receiver at 20°C and at 45°C? *4.81 During a constant-pressure process, it is found that the change in entropy is 1 equal to c p. If cp is constant and the initial temperature is 450°F, determine the 2 final temperature for the process. *4.82 One pound of air undergoes two processes that are in series. The first process consists of an isothermal expansion during which the air is supplied with 22 Btu at a temperature of 386°F. This process is then followed by a reversible adiabatic process that takes the gas to a temperature of 134°F. Determine the change in entropy for these combined processes.

5 Properties of Liquids and Gases L E A R N I NG G OA L S

After reading and studying the material in this chapter, you should be able to 1. Define the word phase and distinguish among the three phases of matter 2. Understand and use the fact that the vaporization process is carried out at constant temperature and that less heat is required to vaporize a unit mass of water as the pressure is raised 3. Define the state that is known as the critical state 4. Understand and use the nomenclature used in the Steam Tables 5. Understand the use of the triple point as the reference state for zero internal energy and zero entropy 6. Define the term quality and use it to determine the properties in the wet region 7. Obtain the properties of steam in the subcooled, saturated, and superheated states 8. Describe the various graphical representations of the properties of steam, especially the temperature–entropy and the enthalpy–entropy (Mollier) charts 9. Represent state paths for various processes on the Mollier chart 10. Show how the throttling process can be used to determine the quality of wet steam 11. Be aware that industry uses computer systems to determine the properties of steam either by use of equations or by use of readily available commercial programs, and be able to use the CRC Press website to obtain the properties of steam in both SI and USCS units

5.1 Introduction In Chapter 1, a brief, introductory study of the properties of a gas was presented. In this chapter, the properties of liquids and gases are investigated in some detail, because the state of a system can be described in terms of its properties. Based on the observable properties of pressure, temperature, and volume, it is possible to derive other properties that can also suffice to describe the state of a system. The relationship among the pressure, volume, and temperature of a system, when expressed mathematically, is called the equation of state for the substance in question. A state is an equilibrium state if no finite rate of change of state can occur without a finite change, temporary or permanent, in the state of the environment. The ideal gas relation derived in Chapter 1 and used extensively throughout Chapter 6 is an example of such an equation of state (see Equation 6.8).

183

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Thermodynamics and Heat Power

A phase of a substance can be defined as that part of a pure substance that consists of a single, homogeneous aggregate of matter. The three common phases that are usually spoken of are solid, liquid, and gaseous. When dealing with the gaseous phase, a distinction is made between a gas and a vapor that is somewhat artificial but in common usage. The term vapor is applied to the gaseous phase that is in contact with saturated liquid or is not far removed from the saturated state, and the term gas is used for the vapor that is either at very low pressure or far removed from the saturated state.

5.2 Liquids and Vapors The distinction between vapor and liquid is usually made (in an elementary manner) by stating that both will take up the shape of their containers, but that the liquid will present a free surface if it does not completely fill its container. The vapor (or gas) will always fill its container. With the foregoing in mind, let us consider the following system: a container is filled with water, and a movable, frictionless piston is placed on the container, as shown in Figure 5.1. As heat is added to the system, the temperature of the system will increase. Note that the pressure on the system is being kept constant by the fixed weight of the piston. The continued addition of heat will cause the temperature of the system to increase until the pressure of the vapor generated exactly balances the pressure of the atmosphere plus the pressure due to the weight of the piston. At this point, the vapor and liquid are said to be saturated. As more heat is added, the liquid that was at saturation will start to vaporize. The two-phase mixture of vapor and liquid has only one degree of freedom, and as long as liquid is present, vaporization will continue at a constant temperature. As long as liquid is present, the mixture is said to be wet, and both the liquid and vapor are saturated. After all the liquid is vaporized, only the vapor is present, and the further addition of heat will cause the temperature of the vapor to increase at constant system pressure. This state is called the superheat state, and the vapor is said to be superheated. If this process is carried out at various pressures, a singular curve of temperature of saturation as a function of pressure will be generated. Such a curve is called a vapor pressure or saturation curve for the substance. For a constant rate of heat input, it is possible to plot a curve of temperature as a function of time or heat added at a given system pressure, say, 100 psia. This curve is shown as a solid line in Figure 5.2. If the rate of heating is kept constant and the identical system is made to undergo this process again but with a system pressure of 1000 psia, the dashed W W

W

(a)

W

Liquid

(b)

(c)

(d)

FIGURE 5.1 Heating water and steam at constant pressure. (a) Water only. (b) Water and steam. (c) Steam only. (d) Super­heated steam.

185

Properties of Liquids and Gases

curve in Figure 5.2 will represent the heat-added temperature history of the system. The decreased slope at 1000 psia during the heating portion indicates an increased specific heat of the liquid (water) due to the increased pressure. At the end of the heating portion, the liquid is saturated at a higher temperature. The water is subsequently vaporized at constant temperature, and the length of the horizontal portions of the curves is proportional to the heat necessary to vaporize the fluid at constant pressure (the latent heat of vaporization). Recall that heat transfer during a change of phase at constant temperature is called latent heat, while heat transfer for a single phase with changing temperatures is called sensible heat. At 1000 psia, the figure shows that less heat is required to vaporize a unit mass of fluid than at 100 psia. After all the water is vaporized, the specific heat of the vapor at the higher pressure is higher. Repeating the experiment a number of times and measuring pressure, temperature, and specific volume enables us to plot curves of T–v, p–T, and p–v. Figure 5.3a shows a typical T–v diagram (not to scale) for a substance that expands on freezing, that is, when it goes from liquid to solid. From this diagram, we can see that the water can exist in several states:

1. A pure solid state, usually called ice 2. A pure liquid state 3. A pure gaseous state (vapor), usually called steam 4. Equilibrium mixtures of liquid and vapor states, liquid and solid states, and solid and vapor states

Figure 5.3b and c shows typical p–T and p–v diagrams (not to scale) for the vapor–liquid states of a typical substance such as water. The triple point is the state in which all three phases are in equilibrium. The critical point is the state in which it is impossible to distinguish between the liquid and vapor phases. At the critical point, the properties of the liquid and vapor phases are identical. The temperature and pressure at this point are known, respectively, as the critical temperature and the critical pressure. Heating

Vaporizing

Superheating

(Boiling)

Temperature

1000 psia 100 psia

Steam-water mixture Saturated liquid

Saturated vapor Heating (water only) Subcooled liquid

Heat addition FIGURE 5.2 Heating of water.

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Thermodynamics and Heat Power

(a) Critical point

ure ess r p ical Crit

+s Liquid

olid

or Vap

T

id

qu

Li

t stan Con

Liquid + vapor

re ssu pre

lin

e

lid

So

Solid + vapor

Solid

e g cur v Meltin cur ve Fusion

v (b) p

Critical point Liquid Vaporization curve

l Sub

c tion ima

Vapor

e urv

Triple point

T

(c) p Critical point

Constant temperature lines Liquid

Saturatedliquid line

Liquid-vapor mixture

Saturated-vapor line

Vapor

v

FIGURE 5.3 (a) A typical temperature-specific volume (T–v) diagram. (Not to scale.) (b) A typical pressure–temperature (p–T) diagram. (Not to scale.) (c) A typical pressure–volume (p–v) diagram. (Not to scale.)

187

Properties of Liquids and Gases

All the data can be presented as a single, three-dimensional figure, as shown in Figure 5.4 (not to scale). Figure 5.3a–c can be obtained from Figure 5.4a by projection onto the T–v, p–T, and p–v planes. Note that the triple line shown in Figure 5.4a projects as a point when it is viewed parallel to the v-axis. Because of this, the projection of the triple line is called the triple point. Water is a substance that expands upon freezing as shown in Figure 5.4a. Other substances that contract on freezing would have a three-dimensional figure such as that shown in Figure 5.4b.

(a)

id Liqu

Pressure

id -liqu Solid

Cr

id Sol

Liq u vap id or

Tri

ple

Sp

eci

fic

Critical point

So

lid

vol

lin

um

-va

e

iti c

al

tem p

C te ons m ta pe nt ra tu re Va po r

po

e

r

era t

ur e

e

tur

era

p Tem

(b) id Liqu Solid

id -liqu

Critical point

id

Pressure

Sol

Sp

So

eci

lid

Trip l line e

fic

vol

um

e

-va

Va

po

r

po

r

Te

re

atu

er mp

FIGURE 5.4 (a) A typical p–v–T figure for a substance that expands on freezing (not to scale). (b) A typical p–v–T figure for a substance that contracts on freezing (not to scale).

188

Thermodynamics and Heat Power

5.3 Thermodynamic Properties of Steam Water has been used as a thermodynamic working fluid for many centuries, and it has been the subject of extensive research to establish its thermodynamic properties in the past two centuries. The need to know the thermodynamic properties of water from the subcooled liquid state to states above the critical point is obvious if units such as a steam generator, shown in Figure 5.5, are to be properly designed. Research on thermodynamic properties of water has been carried out throughout the world, and as a result of this research, extensive tables of the properties of water have been published.* There are nine tables of thermodynamic properties in the Steam Tables (as this work is commonly called) that cover the properties of Gas outlet

Steam coil air heater Air inlet

Air heater Superheater

Economizer

Secondary air duct

Coal bunker

Feeder

Cyclone furnace

Primary air duct

FIGURE 5.5 Modern water-tube steam generator. Design pressure, 1575 psia; steam temperature 900°F; maximum continuous steam output, 550,000 lb./h. (Courtesy of Babcock and Wilcox Co.) * See Keenan et al. (1969). These tables are in English units. A separate volume bearing the same title with the additional parenthetical phrase (SI Units) has also been published by the same authors (Keenan et al. 1978).

189

Properties of Liquids and Gases

TABLE 5.1 Nomenclature Used in the Steam Tables t = temperature p = absolute pressure v = specific volume h = enthalpy s = entropy u = internal energy Subscripts f = property of the saturated liquid g = property of the saturated vapor fg = property change due to evaporation

English Units

SI Units

°F psia or in. Hg ft.3/lbm Btu/lbm Btu/lbm·°R Btu/lbm

°C MPa m3/kg kJ/kg kJ/kg K kJ/kg

ice, water, and steam. These tables include the transport properties, viscosity, and thermal conductivity. The triple point, that is, the state in which the solid, liquid, and vapor are in equilibrium, is used as the reference state for zero internal energy and zero entropy. The use of this reference state gives rise to negative values of internal energy, enthalpy, and entropy of the liquid state at 32°F. The fact that these properties are negative should not cause any difficulty, because we are invariably interested in differences in properties. Tables 1 and 2 of the Steam Tables are for the saturated state. Abstracts of these tables are given in Figures 5.6, 5.7, 5.10, and 5.11. Complete tables are given in Appendix 2. Table 1 presents the data with temperature as the independent variable; Table 2 presents essentially the same data with pressure as the independent variable. All the tabulated data are arranged to facilitate linear interpolation between values. The nomenclature used in the Steam Tables is shown in Table 5.1. It should be noted that all the tabulated properties are specific properties and are tabulated per unit mass. Table 1, the temperature table, goes to the critical temperature of 705.44°F, and Table 2 tabulates data up to the corresponding critical pressure of 3203.6 psia. Portions of these tables are shown in Figure 5.6a (Figure 5.6b for SI units) and Figure 5.7a (Figure 5.7b for SI units). The SI table goes to 374.136°C and 22.09 MPa. Note that the change in property going from saturated liquid to saturated vapor (the fg subscript) is given for internal energy, enthalpy, and entropy, but not for specific volume, but can easily be calculated from the equation for specific volume. The relation for the saturation state properties, that is, f, g, and fg, is given by hg = h f + h fg

v g = v f + v fg s g = s f + s fg

(5.1)

ug = u f + u fg and, in addition, the definition of enthalpy in terms of internal energy, pressure, and specific volume must also be satisfied. Thus,

h = u+

pv (5.2) J

0.6988 0.7211 0.7439 0.7674 0.8914 0.8162 0.8416 0.8677 0.8945 0.9220

Press. (lbf /s  q. in.) p

0.016099 0.016102 0.016105 0.016108 0.016111 0.016114 0.016117 0.016121 0.016124 0.016127

Sat. Liquid vf

467.7 454.0 440.9 428.2 415.9 404.0 392.4 381.3 370.5 360.1

Sat. Vapor vg

Specific Volume

58.07 59.06 60.06 61.06 62.06 63.06 64.05 65.05 66.05 67.05

Sat. Liquid uf 982.2 981.5 980.8 980.2 979.5 978.8 978.1 977.5 976.8 976.1

Evap. ufg

Internal Energy

1040.2 1040.6 1040.9 1041.2 1041.5 1041.9 1042.2 1042.5 1042.8 1043.2

Sat. Vapor ug 58.07 59.07 60.06 61.06 62.06 63.06 64.06 65.05 66.05 67.05

Sat. Liquid hf

Saturation Temperatures

1042.7 1042.1 1041.5 1041.0 1040.4 1039.8 1039.2 1038.7 1038.1 1037.5

Evap. hfg

Enthalpy

1100.7 1101.2 1101.6 1102.0 1102.4 1102.9 1103.3 1103.7 1104.2 1104.6

Sat. Vapor hg 0.11165 0.11346 0.11527 0.11708 0.11888 0.12068 0.12248 0.12427 0.12606 0.12785

Sat. Liquid sf

1.8966 1.8922 1.8877 1.8833 1.8788 1.8744 1.8700 1.8657 1.8613 1.8569

Evap. sfg

Entropy

2.0083 2.0056 2.0030 2.0003 1.9977 1.9951 1.9925 1.9899 1.9874 1.9848

Sat. Vapor sg

FIGURE 5.6 (a) Extract from saturation table. More detailed values are found in Appendix 2. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

90 91 92 93 94 95 96 97 98 99

Temp. (°F) t

(a)

190 Thermodynamics and Heat Power

0.004246 0.004496 0.004759 0.005034 0.005324 0.005628 0.005947 0.006281 0.006632 0.006999

Press. (MPa) p

1.0043 1.0046 1.0050 1.0053 1.0056 1.0060 1.0063 1.0067 1.0071 1.0074

Sat. Liquid 103 vf

32 894 31 165 29 540 28 011 26 571 25 216 23 940 22 737 21 602 20 533

Sat. Vapor 103 vg

Specific Volume

125.78 129.96 134.14 138.32 142.50 146.67 150.85 155.03 159.20 163.38

Sat. Liquid uf 2290.8 2288.0 2285.2 2282.4 2279.5 2276.7 2273.9 2271.1 2268.2 2265.4

Evap. ufg

Internal Energy

2416.6 2418.0 2419.3 2420.7 2422.0 2423.4 2424.7 2426.1 2427.4 2428.8

Sat. Vapor ug 125.79 129.97 134.15 138.33 142.50 146.68 150.86 155.03 159.21 163.39

Sat. Liquid hf

Saturation Temperatures

2430.5 2428.1 2425.7 2423.4 2421.0 2418.6 2416.2 2413.9 2411.5 2409.1

Evap. hfg

Enthalpy

2556.3 2558.1 2559.9 2561.7 2563.5 2565.3 2567.1 2568.9 2570.7 2572.5

Sat. Vapor hg 0.4369 0.4507 0.4644 0.4781 0.4917 0.5053 0.5188 0.5323 0.5458 0.5592

Sat. Liquid sf

8.0164 7.9822 7.9483 7.9146 7.8811 7.8478 7.8147 7.7819 7.7492 7.7167

Evap. sfg

Entropy

8.4533 8.4329 8.4127 8.3927 8.3728 8.3531 8.3336 8.3142 8.2950 8.2759

Sat. Vapor sg

FIGURE 5.6 (b) Extract from saturation table (SI units). (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. Sf Units Edition. 1978. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

30 31 32 33 34 35 36 37 38 39

Temp. (°C) t

(b)

Properties of Liquids and Gases 191

338.12 338.77 339.41 340.04 340.68 341.30 341.93 342.55 343.17 343.78

Temp. (°F) t

0.017850 0.017858 0.017865 0.017872 0.017879 0.017886 0.017894 0.017901 0.017908 0.017915

Sat. Liquid vf

3.884 3.852 3.821 3.790 3.760 3.730 3.701 3.672 3.644 3.616

Sat. Vapor vg

Specific Volume

308.95 309.62 310.29 310.96 311.62 312.27 312.92 313.57 314.21 314.85

Sat. Liquid uf 798.8 798.2 797.6 797.1 796.6 796.0 795.5 794.9 794.4 793.9

Evap. ufg

Internal Energy

1107.7 1107.8 1107.9 1108.1 1108.2 1108.3 1108.4 1108.5 1108.6 1108.7

Sat. Vapor ug 309.33 310.01 310.68 311.34 312.01 312.67 313.32 313.97 314.62 315.26

Sat. Liquid hf

Saturation Pressures

881.0 880.5 880.0 879.5 879.0 878.5 877.9 877.4 876.9 876.4

Evap. hfg

Enthalpy

1190.4 1190.5 1190.7 1190.8 1191.0 1191.1 1191.3 1191.4 1191.6 1191.7

Sat. Vapor hg 0.48786 0.48870 0.48954 0.49037 0.49119 0.49201 0.49282 0.49363 0.49443 0.49523

Sat. Liquid sf

1.1042 1.1027 1.1012 1.0996 1.0981 1.0966 1.0951 1.0937 1.0922 1.0907

Evap. sfg

Entropy

1.5921 1.5914 1.5907 1.5900 1.5893 1.5886 1.5880 1.5873 1.5866 1.5860

Sat. Vapor sg

FIGURE 5.7 (a) Extract from saturation table. More detailed values are found in Appendix 2. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

115 116 117 118 119 120 121 122 123 124

Press. (lbf / sq. in.) p

(a)

192 Thermodynamics and Heat Power

179.91 180.77 181.62 182.46 183.28 184.09 184.89 185.68 186.46 187.23

t

Temp. (°C)

194.44 190.80 187.30 183.92 180.67 177.53 174.49 171.56 168.73 165.99

103 vg

103 vf

1.1273 1.1284 1.1296 1.1308 1.1319 1.1330 1.1342 1.1353 1.1364 1.1375

Sat. Vapor

Sat. Liquid

Specific Volume

761.68 765.47 769.21 772.89 776.52 780.09 783.62 787.11 790.56 793.94

uf

Sat. Liquid 1822.0 1818.8 1815.6 1812.5 1809.4 1806.3 1803.3 1800.3 1797.4 1794.4

ufg

Evap.

Internal Energy

2583.6 2584.2 2584.8 2585.4 2585.9 2586.4 2586.9 2587.4 2587.9 2588.4

ug

Sat. Vapor 762.81 766.63 770.38 774.08 777.74 781.34 784.89 788.40 791.86 795.28

hf

Sat. Liquid

Saturation Pressures

2015.3 2012.2 2009.2 2006.2 2003.3 2000.4 1997.5 1994.6 1991.8 1989.0

hfg

Evap.

Enthalpy

2778.1 2778.9 2779.6 2780.3 2781.0 2781.7 2782.4 2783.0 2783.6 2784.2

hg

Sat. Vapor 2.1387 2.1471 2.1553 2.1634 2.1713 2.1792 2.1869 2.1945 2.2020 2.2093

sf

Sat. Liquid

4.4478 4.4326 4.4177 4.4030 4.3886 4.3744 4.3605 4.3467 4.3332 4.3199

sfg

Evap.

Entropy

6.5865 6.5796 6.5729 6.5664 6.5599 6.5536 6.5473 6.5412 6.5351 6.5292

sg

Sat. Vapor

FIGURE 5.7 (b) Extract from saturation table (SI units). (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. Sf Units Edition. 1978. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18

p

Press. (MPa)

(b)

Properties of Liquids and Gases 193

194

Thermodynamics and Heat Power

or in SI units,

h = u + pv (5.2a)

The following examples will serve to illustrate the use of Tables 1 and 2.

ILLUSTRATIVE PROBLEM 5.1 Determine the enthalpy of saturated steam at 90°F using the tabulated properties of pressure, specific volume, and internal energy in Table 1. Compare the result with the tabulated value of h. SOLUTION From Table 1 (Figure 5.6a),

p = 0.6988 psia



vg = 467.7 ft.3/lbm



ug = 1040.2 Btu/lbm

Because

h = u+

pv J

and hg = ug +

pv g J

therefore,



hg = 1040.2 Btu/lbm +

0.6988 lbf/in.2 × 144 in.2/ft.2 × 467.7 ft.3/lbm 778 ft. ⋅ lbf/Btu

= 1100.7 Btu/lbm This value is in agreement with 1100.7 Btu/lbm for hg from Table 1.

ILLUSTRATIVE PROBLEM 5.2 Determine the enthalpy of saturated steam at 30°C using the tabulated properties of pressure, specific volume, and internal energy in Table 1. Compare the result with the tabulated value of hg.

195

Properties of Liquids and Gases

SOLUTION From Table 1 (Figure 5.6a),

p = 0.004246 MPa = 4.246 kPa



vg = 32 894/103 m3/kg = 32.894 m3/kg



ug = 2416.6 kJ/kg

Because h = u + pv  and  hg = ug + pvg therefore,

hg = 2416.6 kJ/kg + 4.246 kN/m2 × 32.894 m3/kg = 2556.27 kJ/kg

The tabulated value of hg from Table 1 is 2556.3 kJ/kg. (Students should carefully note the units used.)

ILLUSTRATIVE PROBLEM 5.3 Determine the enthalpy, entropy, specific volume, and internal energy of saturated steam at 118 psia. Assume that the values for 115 and 120 psia are available, and perform the necessary interpolations. Compare the results with the tabulated values for 118 psia. SOLUTION The necessary interpolations are best done in tabular form as shown in the following: p 115 118 120

hg 1190.4 1190.8 1191.1

Table 2 (hg)118 = 1190.8

(3/5)(1191.1 – 1190.4) = 0.42 (hg)118 = 1190.4 + 0.42 = 1190.8 Btu/lbm p 115 118 120

vg 3.884 3.792 3.730

Table 2 (vg)118 = 3.792

(3/5)(3.884 – 3.730) = 0.092 (vg)118 = 3.884 – 0.092 = 3.792 ft.3/lbm

196

Thermodynamics and Heat Power

p

sg

115 118 120

1.5921 1.5900 1.5886

Table 2 (sg)118 = 1.5900

(3/5)(1.5921 – 1.5886) = 0.0021 (sg)118 = 1.5921 – 0.0021 = 1.5900 p

ug

115 118 120

1107.7 1108.06 1108.3

Table 2 (ug)118 = 1108.1

(3/5)(1108.3 – 1107.7) = 0.36 (ug)118 = 1107.7 – 0.36 = 1108.06

The interpolation process that was done in tabular form for this illustrative problem can also be demonstrated by referring to Figure 5.8 for the specific volume. It will be seen that the results of this problem and the tabulated values are essentially in exact agreement and that linear interpolation is satisfactory in these tables.

p psia 3.730

120 118

3.792

5 3

3

115

3.884

5

3.7 FIGURE 5.8 Illustrative Problem 5.3.

3.8

3.9

v ft3 lbm

197

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.4 Determine hfg for saturated steam at 115 psia using the pressure, volumes, and internal data given in Table 2 (Figure 5.7). SOLUTION By definition, hg = u g + hf = uf +

and

h fg = hg − h f = (ug − u f ) +

From Table 2 at 115 psia,

pv g J pv f J



p( v g − v f ) p( v g − v f ) = u fg + J J



ufg = 798.8 Btu/lbm



vg = 3.884 ft.3/lbm



vf = 0.017850 ft.3/lbm

Note that if the table had vfg, we could have read it directly because vg – vf = vfg. Proceeding gives



h fg = 798.8 Btu/lbm +

115 lbf /in.2 × 144 in.2 /ft.2 (3.884 − 0.017850) ft.3 /lbm 778 ft. ⋅ lbf/Btu

= 798.8 + 82.3 = 881.1 Btu/lbm The tabulated value is 881.0 Btu/lbm, and the agreement is satisfactory.

ILLUSTRATIVE PROBLEM 5.5 Determine hfg for saturated steam at 1.0 MPa using the pressure, volumes, and internal data given in Table 2 (Figure 5.7a). SOLUTION Refer to Illustrative Problem 5.4. From Table 2 at 1.0 MPa,

ufg = 1822.0 kJ/kg

198

Thermodynamics and Heat Power



vg = 194.44/103 = 0.19444 m3/kg



vf = 1.1273/103 = 0.0011273 m3/kg



p = 1.0 MPa

Because vfg = vg – vf,

vfg = 0.19444 – 0.0011273 = 0.1933127 m3/kg



hfg = ufg + p(vfg)



= 1822.0 kJ/kg + (1000 kN/m2)(0.1933127 m3/kg)



= 2015.3 kJ/kg

The tabulated value is 2015.3 kJ/kg, which is in exact agreement with the value calculated.

ILLUSTRATIVE PROBLEM 5.6 Determine hfg at 115 psia by considering this process to be a reversible, constant-­ temperature process where TΔs = Δh. SOLUTION For constant-temperature, reversible vaporization, hfg = Δh = TΔs = Tsfg. Therefore, (388.12 + 460)1.1042 = 881.3 Btu/lbm, which is also in good agreement with the tabular values. Use of –459.67°F for absolute zero, which is the value used in the table, gives almost exact agreement.

Between the saturated liquid and the saturated vapor, there exists a mixture of vapor plus liquid (the wet region). To denote the state of a liquid–vapor mixture, it is necessary to introduce a term describing the relative quantities of liquid and vapor in the mixture. The quality of a mixture (x) is defined as the ratio of the mass of vapor to the mass of the mixture. Thus, in 1 lb. of mixture, there must be (1 – x) lb. of liquid. Another term is used to describe the wet region: percent moisture. A mixture whose quality is 80% has 20% moisture by weight and is simply said to have 20% moisture. Consider a mixture weighing 1 lb. and having a quality x. In this mixture, there is x lb. of vapor and (1 – x) lb. of liquid. The enthalpy of this mixture per pound of mixture is the sum of the enthalpies of the components. Therefore, the enthalpy of the liquid portion of the mixture is

hl = (1 – x)hf

and the enthalpy of the vapor portion is

hv = xhg

199

Properties of Liquids and Gases

The sum of these terms is the enthalpy of the mixture hx:

hx = (1 – x)hf + xhg (5.3a)

By the same reasoning, the entropy, internal energy, and specific volume of the wet mixture are given as

sx = (1 – x)sf + xsg (5.3b)



ux = (1 – x)uf + xug (5.3c)



vx = (1 – x)vf + xvg (5.3d)

It is sometimes more convenient to express Equations 5.3a–5.3d in terms of the property change during vaporization. By noting that the fg property is equal to the g value minus the f value, it is possible to rewrite Equations 5.3a–5.3d as follows:

hx = hf + xhfg (5.4a)



sx = sf + xsfg (5.4b)



ux = uf + xufg (5.4c)



vx = vf + xvfg (5.4d)

The relationship among these quantities can be demonstrated by referring to Figure 5.9, which is a T–s diagram for water. The saturation curve is indicated, and a point below the saturation curve is in the wet region. The T–s diagram is discussed further later in this chapter, but for now, it should be noted that the expressions for entropy in Equations 5.3 and 5.4 can be directly determined from Figure 5.9. T

Temperature

sx

Saturated liquid

Wet mixture of quality x T = const Saturated vapor

xsfg

(1 _ x)sfg sfg

sf

Saturation line

sg

Entropy

s

FIGURE 5.9 T–s diagram showing relation of properties and quality. (From F. P. Durham, Thermodynamics, 2nd ed., Upper Saddle River, N.J.: Prentice Hall, Inc., 1959, p. 43. With permission.)

200

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.7 A wet steam mixture at 120 psia is found to have a quality of 80%. Determine its entropy, enthalpy, internal energy, and specific volume. SOLUTION Using Table 2 and a quality of 80% (x = 0.8), we have

sx = sf + xsfg = 0.49201 + 0.8(1.0966) = 1.3693 Btu/lbm·°R



hx = hf + xhfg = 312.67 + 0.8(878.5) = 1015.47 Btu/lbm



ux = uf + xufg = 312.27 + 0.8(796.0) = 949.07 Btu/lbm



vx = vf + xvfg = 0.017886 + 0.8(3.730 – 0.017886)



= 2.988 ft.3/lbm

As a check on the solution obtained, we calculate ux = hx −

px vx J 120



= 1015.47 Btu/lbm −

ft.3 lbf in.2 × 144 2 × 2.988 2 lbm in. ft. 778 ft. ⋅ lbf/Btu

= 949.10 Btu/lbm which agrees with the value 949.07 Btu/lbm.

ILLUSTRATIVE PROBLEM 5.8 A wet mixture at 1.0 MPa is found to have a quality of 85%. Determine its entropy, enthalpy, internal energy, and specific volume. SOLUTION Using x = 0.85 yields

sx = sf + xsfg = 2.1387 kJ/kg·K + (0.85)(4.4487 kJ/kg·K)

201

Properties of Liquids and Gases



= 5.9201 kJ/kg·K



hx = hf + xhfg = 762.81 kJ/kg + (0.85)(2015.3 kJ/kg)



= 2475.82 kJ/kg



ux = uf + xufg = 761.68 kJ/kg + (0.85)(1822.0 kJ/kg)



= 2310.38 kJ/kg



vx = vf + xvfg = [1.1273 m3/kg + (0.85)(194.44 m3/kg – 1.1273 m3/kg)] × 10 –3



= 165.44/103 = 0.16544 m3/kg

As a check,



ux = hx − px vx = 2475.82 kJ/kg −

1.0 × 106 (0.16544 m 3/kg) 103 kPa/MPa

= 2310.38 kJ/kg

Again, the agreement is exact. Note the units used for consistency.

ILLUSTRATIVE PROBLEM 5.9 A mixture of wet steam at 90°F is found to have an enthalpy of 900 Btu/lbm. What is its quality? SOLUTION For the wet mixture, hx = hf + xhfg. Solving for x gives us x=



hx − h f h fg



Using the data from Table 1 (Figure 5.6), we have

x=

900 Btu/lbm − 58.07 Btu/lbm = 0.807 = 80.7% 1042.7 Btu/lbm

202

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.10 A mixture of wet steam at 30°C is found to have an enthalpy of 2000.0 kJ/kg. Determine its quality. SOLUTION Because hx = hf + xhfg,

x=

hx − h f h fg

=

2000.0 kJ/kg − 125.79 kJ/kg = 0.771 or 77.1% 2430.5 kJ/kg



Steam quality is important in the usage of steam equipment such as a heat exchanger or a steam turbine. These devices require steam as free from moisture as possible to avoid problems such as fouling or metal deterioration. Table 3 of the Steam Tables gives the properties of the superheated vapor, and it occupies 39 pages in the main table. The beginning of this table is for water vapor at low pressure, which can be treated as an ideal gas. For now, we will not be concerned with this section of Table 3. The main portion of the table extends to pressures of 1000 psia and 2400°F. In the SI tables, the values go to 60 MPa and 1300°C. For the superheated region, it is necessary to specify two variables, such as pressure and temperature or enthalpy and pressure, in order to specify the state of the vapor. Table 3 is organized using pressure and temperature as independent variables, and it lists values of specific volume, internal energy, enthalpy, and entropy corresponding to specified values of temperature and pressure. Referring to Figure 5.10a (Figure 5.10b gives SI units), which is an extract from Table 3, it will be noted that the topmost line lists the different pressures in psia and in parentheses displays the saturation temperature corresponding to the pressure. The second horizontal line down lists the column headings. All values are specific values, and the temperature is listed in °F. The third horizontal line shown lists saturation (Sat.) values corresponding to the pressure listed on the first line of the table. These values are for convenience so that it is not necessary to turn back to Tables 1 and 2 for saturation properties. The desired thermodynamic properties at a given temperature are read horizontally underneath the appropriate pressure heading. It will be noted that at the upper part of the table, values are given in italics for certain temperatures with a horizontal line separating the main portion of the table from the italicized values. The values in italics (above the horizontal dividing line) are for the vapor temperature below the saturation temperature corresponding to the pressure listed. These states are metastable states (they are not equilibrium states), and we will not deal with them at all in our study. They should be ignored at this time by the student. The SI tables are arranged in the same manner as the English tables. Pressures are in megapascals (MPa), temperatures are in degrees Celsius (°C), and the unit mass is the kilogram (kg). The energy unit is the kilojoule (kJ), and the volume unit is 103 × cubic meters/ kilogram (103 × m3/kg). Figure 5.10b is an extract from the superheat table.

v

1.3854 1.3360 1.3643 1.3917 1.4182 1.4441 1.4693 1.4940 1.5182 1.5419

v

1.4493 1.4110 1.4398 1.4677 1.4949 1.5213 1.5472 1.5726 1.5975 1.6219

h

1204.4 1194.4 1201.9 1209.2 1216.2 1223.1 1229.8 1236.3 1242.7 1249.0

1118.8 1108.3 1114.3 1120.1 1125.7 1131.1 1136.4 1141.5 1146.6 1151.5

u

1204.7 1191.2 1198.9 1206.4 1213.6 1220.7 1227.5 1234.2 1240.7 1247.1

h

335 (427.68)

1118.6 1110.8 1116.6 1122.2 1127.7 1133.0 1138.1 1143.2 1148.1 1152.9

u

320 (423.39) s

1.5017 1.4863 1.4952 1.5036 1.5117 1.5195 1.5270 1.5342 1.5412 1.5479

s

1.5058 1.4944 1.5030 1.5112 1.5191 1.5267 1.5340 1.5411 1.5479 1.5545

v

1.3653 1.3124 1.3406 1.3678 1.3941 1.4198 1.4448 1.4693 1.4933 1.5168

v

1.4274 1.3852 1.4139 1.4416 1.4686 1.4948 1.5205 1.5456 1.5702 1.5944

h 1204.5 1193.3 1200.9 1208.2 1215.4 1222.3 1229.0 1235.6 1242.0 1248.3

1118.9 1107.5 1113.6 1119.4 1125.0 1130.5 1135.8 1141.0 1146.0 1151.0

u 1204.8 1190.1 1197.9 1205.5 1212.8 1219.8 1226.7 1233.4 1240.0 1246.4

h

340 (429.07)

1118.6 1110.0 1115.9 1121.5 1127.0 1132.4 1137.6 1142.6 1147.6 1152.4

u

325 (424.84)

Vapor s

1.5004 1.4837 1.4926 1.5012 1.5093 1.5171 1.5247 1.5319 1.5389 1.5458

s

1.5044 1.4917 1.5004 1.5087 1.5166 1.5243 1.5316 1.5387 1.5456 1.5523

v

1.3457 1.2894 1.3175 1.3445 1.3707 1.3962 1.4210 1.4453 1.4691 1.4924

v

1.4061 1.3602 1.3887 1.4163 1.4430 1.4691 1.4945 1.5194 1.5438 1.5678 u 1118.9 1106.6 1112.8 1118.7 1124.4 1129.9 1135.2 1140.4 1145.5 1150.5

h

1204.9 1189.0 1196.9 1204.5 1211.9 1219.0 1226.0 1232.7 1239.3 1245.8

h

2204.6 1192.2 1199.9 1207.3 1214.5 1221.5 1228.2 1234.9 1241.4 1247.7 345 (430.45)

1118.7 1109.2 1118.1 1120.8 1126.4 1131.8 1137.0 1142.1 1147.1 1152.0

u

330 (426.27) s

1.4991 1.4810 1.4901 1.4987 1.5069 1.5148 1.5224 1.5297 1.5368 1.5436

s

1.5031 1.4890 1.4978 1.5061 1.5142 1.5219 1.5293 1.5364 1.5434 1.5501

FIGURE 5.10 (a) Extract from superheat table. More detailed values are found in Appendix 2. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

Sat. 410 420 430 440 450 460 470 480 490

t

p (t Sat.)

Sat. 410 420 430 440 450 460 470 480 490

t

p (t Sat.)

(a)

Properties of Liquids and Gases 203

h

2799.5 2761.1 2777.0 2792.3 2807.2 2821.7 2835.8 2849.6 2863.2 2876.5 2889.6

89.12 90.81 92.45 94.05 95.60 97.13 98.62 100.08 101.52

h

2766.0 2782.0 2797.6 2812.6 2827.3 2841.6 2855.6 2869.3 2882.7

2800.9

s

6.2419 6.2753 6.3073 6.3380 6.3676 6.3962 6.4238 6.4506 6.4767

6.3141

s

6.3409 6.2608 6.2941 6.3259 6.3566 6.3861 6.4147 6.4423 6.4691 6.4952 6.5205

10 v

10 v

86.71 88.38 90.01 91.58 93.12 94.63 96.10 97.54 98.96

90.73

3

97.25 92.52 94.29 96.01 97.69 99.32 100.92 102.48 104.02 105.52 107.01

3

h 28000.0 2757.3 2773.4 2788.9 2804.0 2818.7 2833.0 2847.0 2860.7 2874.1 2887.3

2571.5 2584.1 2596.3 2608.1 2619.5 2630.7 2641.6 2652.2 2662.7

2601.7

u

2762.2 2778.5 2794.3 2809.5 2824.4 2838.9 2853.0 2866.8 2880.4

2801.3

h

2.20 (217.29)

2600.7 2567.6 2580.1 2592.1 2603.7 2615.1 2626.1 2636.9 2647.5 2657.8 2668.0

u

2.05 (213.67)

Vapor s

6.2248 6.2587 6.2912 6.3223 6.3523 6.3812 6.4092 6.4362 6.4626

6.3056

s

6.3318 6.2427 6.2765 6.3089 6.3399 6.3699 6.3987 6.4267 6.4538 6.4801 6.5057 10 v

86.06 87.66 89.23 90.75 92.23 93.69 95.11 96.51

88.75

3

u

2581.3 2593.7 2605.7 2617.3 2628.6 2639.6 2650.4 2660.9

2602.0

h

2774.9 2790.9 2806.4 2821.5 2836.1 2850.4 2864.4 2878.1

2801.7

h

2769.7 2785.5 2800.8 2815.7 2830.2 2844.3 2858.2 2871.7 2885.0

2800.5

2.25 (218.45)

2577.2 2589.5 2601.3 2612.8 2623.9 2634.9 2645.5 2656.0 2666.2

91.65 93.35 95.01 96.62 98.20 99.74 101.25 102.74 104.20

u 2601.0

10 v

2.10 (214.90) 94.98

3

s

6.2423 6.2753 6.3068 6.3372 6.3664 6.3947 2.4220 6.4486

6.2972

s

6.2591 6.2920 6.3235 6.3538 6.3831 6.4113 6.4387 6.4653 6.4911

6.3229

FIGURE 5.10 (b) Extract from superheat table (51 units). (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. Sf Units Edition. 1978. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

2574.4 2586.8 2598.8 2610.4 2621.7 2632.8 2643.6 2654.1 2664.5

92.81

u

2601.4

10 v

Sat. 200 205 210 215 220 225 230 235 240 245

2.15 (216.10)

2600.3 2570.6 2582.8 2594.7 2606.2 2617.4 2628.3 2638.9 2649.4 2659.6 2669.7

u

2.00 (212.42)

t

3

99.63 95.27 97.06 98.80 100.50 102.15 103.77 105.36 106.91 108.45 109.95

p (t Sat.)

10 v

Sat. 200 205 210 215 220 225 230 235 240 245

3

t

p (t Sat.)

(b)

204 Thermodynamics and Heat Power

205

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.11 Determine the specific volume, internal energy, enthalpy, and entropy of superheated steam at 330 psia and 450°F. SOLUTION The values of temperature and pressure are listed in Table 3 (Figure 5.10a) and can be read directly.

v = 1.4691 ft.3/lbm



u = 1131.8 Btu/lbm



h = 1221.5 Btu/lbm



s = 1.5219 Btu/lbm·°R

ILLUSTRATIVE PROBLEM 5.12 Determine the specific volume, internal energy, enthalpy, and entropy of superheated steam at 2.0 MPa and 240°C. SOLUTION Reading directly from Figure 5.10b, we have

v = 108.45/103 = 0.10845 m3/kg



u = 2659.6 kJ/kg



h = 2876.5 kJ/kg



s = 6.4952 kJ/kg·K

206

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.13 Determine the specific volume, internal energy, enthalpy, and entropy of superheated steam at 330 psia and 455°F. SOLUTION Because the data in Figure 5.10a do not give the properties at this temperature, it is necessary to interpolate between 450°F and 460°F. Thus, at 330 psia, t 460 455 450

v 1.4945 1.4818 1.4691

v455 = 1.4691 + 1/2 (1.4945 – 1.4691) t 460 455 450

u 1137.0 1134.4 1131.8

u455 = 1131.8 + 1/2 (1137.0 – 1131.8) t 460 455 450

h 1228.2 1224.9 1221.5

h455 = 1221.5 + 1/2 (1228.2 – 1221.5) t 460 455 450

s 1.5293 1.5256 1.5219

s455 = 1.5219 + 1/2 (1.5293 – 1.5219)

Thus,

v = 1.4818 ft.3/lbm



u = 1134.4 Btu/lbm



h = 1224.9 Btu/lbm



s = 1.5256 Btu/lb·°R

207

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.14 Determine the specific volume and enthalpy of superheated steam at 465°F and 337 psia. SOLUTION It will be noted from Figure 5.10a that neither the temperature nor the pressure values of the problem are tabulated in Table 3. Thus, it becomes necessary to interpolate around both the listed temperature and pressure for the desired properties. We will first obtain the properties at 337 psia and 460°F and then at 337 psia and 470°F. Proceeding with the calculation, at 460°F, p 340 337 335

v 1.4448 1.4595 1.4693

v337 = 1.4693 − 2/5 (1.4693 – 1.4448) p 340 337 335

h 1226.7 1227.2 1227.5

h337 = 1227.5 − 2/5 (1227.5 – 1226.7)

and at 470°F, p 340 337 335

v 1.4693 1.4841 1.4940

v337 = 1.4940 − 2/5 (1.4940 – 1.4693) p 340 337 335

h 1233.4 1233.9 1234.2

h337 = 1234.2 − 2/5 (1234.2 – 1233.4)

208

Thermodynamics and Heat Power

Therefore, at 337 psia and 465°F, t

v

470 465 460

1.4841 1.4718 1.4595

v465 = 1.4595 + 1/2 (1.4841 – 1.4595) t

h

470 465 460

1233.9 1230.7 1227.5

h465 = 1227.5 + 1/2 (1233.9 – 1227.5)

The desired values of specific volume and enthalpy at 465°F and 337 psia are 1.4718 ft.3/lbm and 1230.7 Btu/lbm.

An extract from Table 4 of the Steam Tables entitled Liquid is shown in Figure 5.11a (Figure 5.11b gives SI units). The state of the liquid is the subcooled state, in which the pressure on the liquid exceeds the saturation pressure corresponding to the temperature of the liquid. In this region, the tabulated properties of specific volume, internal energy, enthalpy, and entropy are exhibited as functions of pressure and temperature similar to the format used for the superheated vapor. It will be noted from Figure 5.11a that italicized values are shown for certain values of pressure and temperature. Once again, these are metastable states, because they correspond to temperatures of the liquid above the saturation temperature. They are not to be used within the scope of this text. A useful first approximation is often made for the enthalpy of the subcooled liquid by assuming it to be essentially incompressible. Then

h − hf 

( p − p f )v f (5.5) J

where pf  and vf are the values of pressure and specific volume corresponding to the saturation condition at the temperature of the fluid. In other words, the change in enthalpy is approximately equal to vΔp, the work done on the fluid during a process carried out at nearly constant volume. In SI units,

h – hf ≃ (p –pf)vf (5.5a)

0.016022 0.016024 0.016130 0.016343 0.016635 0.017003 0.017453 0.018000 0.018668 0.019503 0.02060 0.02087 0.02116 0.02148 0.02182 0.02221 0.02265 0.02315

v

–0.01 18.06 68.05 117.95 168.05 218.52 269.61 321.59 374.85 429.96 488.1 500.3 512.7 525.5 538.6 552.1 566.1 580.8

u

0

–0.01 18.06 68.05 117.95 168.05 218.52 269.61 321.59 374.85 429.96 488.1 500.3 512.7 525.5 538.6 552.1 566.1 580.8

h 0.00003 0.0360 0.12963 0.21504 0.29402 0.36777 0.43732 0.50359 0.56740 0.62970 0.6919 0.7046 0.7173 0.7303 0.7434 0.7569 0.7707 0.7851

s

v 0.019748 0.015994 0.015998 0.016106 0.016318 0.016608 0.016972 0.017416 0.017954 0.018608 0.019420 0.02048 0.02073 0.02100 0.02130 0.02162 0.02198 0.02237 0.02281 0.02332 0.02392

447.70 0.00 18.02 67.87 117.66 167.65 217.99 268.92 320.71 373.68 428.40 485.9 497.9 510.1 522.6 535.3 548.4 562.0 576.0 590.8 606.4

u 449.53 1.49 19.50 69.36 119.17 169.19 219.56 270.53 322.37 375.40 430.19 487.8 499.8 512.0 524.5 357.3 550.5 564.0 578.1 592.9 608.6

h

500 (467.13)

Liquid s 0.64904 0.00000 0.03599 0.12932 0.21457 0.29341 0.36702 0.43641 0.50249 0.56604 0.62798 0.6896 0.7021 0.7146 0.7273 0.7402 0.7532 0.7666 0.7804 0.7946 0.8096

v 0.021591 0.015967 0.015972 0.016082 0.016293 0.016580 0.016941 0.017379 0.017909 0.018550 0.019340 0.02036 0.02060 0.02086 0.02114 0.02144 0.02177 0.02213 0.02253 0.02298 0.02349 0.02409 0.02482

538.39 0.03 17.99 67.70 117.38 167.26 217.47 268.24 319.83 372.55 426.89 483.8 495.6 507.6 519.9 532.4 545.1 558.3 571.8 585.9 600.6 616.2 632.9

u 542.38 2.99 20.94 70.68 120.40 170.32 220.61 271.46 323.15 375.98 430.47 487.5 499.4 511.5 523.8 536.3 549.2 562.4 576.0 590.1 604.9 620.6 637.5

h

1000 (544.75) s 0.74320 0.00005 0.03592 0.12901 0.21410 0.29281 0.36628 0.43552 0.50140 0.56472 0.62632 0.6874 0.6997 0.7121 0.7245 0.7372 0.7499 0.7630 0.7763 0.7899 0.8041 0.8189 0.8345

FIGURE 5.11 (a) Extract from subcooled table. More detailed values are found in Appendix 2. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

Sat. 32 50 100 150 200 250 300 350 400 450 500 510 520 530 540 550 560 570 580 590 600 610

t

p (t Sat.)

(a)

Properties of Liquids and Gases 209

1.0002 1.0018 1.0078 1.0172 1.1291 1.0436 1.0604 1.0800 1.1024 1.1283 1.1581 1.1749 1.1930 1.2129 1.2347 1.2590 1.2862 1.3173 1.3535 1.3971 1.4520

–0.03 83.95 167.56 251.12 334.87 418.96 503.57 588.89 675.19 762.72 851.8 897.1 943.0 989.6 1037.1 1085.6 1135.4 1186.8 1240.4 1297.0 1358.1

u

0

–0.03 83.95 167.56 251.12 334.87 418.96 503.57 588.89 675.19 762.72 851.8 897.1 943.0 989.6 1037.1 1085.6 1135.4 1186.8 1240.4 1297.0 1358.1

h –0.0001 0.2966 0.5725 0.8312 1.0753 1.3069 1.5278 1.7395 1.9434 2.1410 2.3334 2.4281 2.5221 2.6157 2.7091 2.8027 2.8970 2.9926 3.0904 3.1918 3.2992

s

10 v 1.1973 0.9990 1.0006 1.0067 1.0160 1.0280 1.0423 1.0590 1.0784 1.1006 1.1261 1.1555 1.1720 1.1898 1.2092 1.2305 1.2540 1.2804 1.3102 1.3447 1.3855 1.4357

3

959.1 –0.00 83.80 167.25 250.67 334.29 418.24 502.68 587.82 673.90 761.16 849.9 895.0 940.7 987.0 1034.2 1082.3 1131.6 1182.4 1235.1 1290.5 1349.6

u 962.1 2.50 86.30 169.77 253.21 336.86 420.85 505.33 590.52 676.65 763.97 852.8 898.0 943.7 990.1 1037.2 1085.4 1134.8 1185.7 1238.5 1294.0 1353.2

h

2.5 (223.99)

Liquid s 2.5546 –0.0000 0.2961 0.5715 0.8298 1.0737 1.3050 1.5255 1.7369 1.9404 2.1375 2.3294 2.4238 2.5174 2.6105 2.7034 2.7964 2.8898 2.9844 3.0808 3.1801 3.2843

10 v 1.2859 0.9977 0.9995 1.0056 1.0149 1.0268 1.0410 1.0576 1.0768 1.0988 1.1240 1.1530 1.1691 1.1866 1.2056 1.2264 1.2493 1.2749 1.3036 1.3365 1.3750 1.4214 1.4803

3

1147.8 0.04 83.65 166.95 250.23 333.72 417.52 501.80 586.76 672.62 759.63 848.1 893.0 938.4 984.5 1031.4 1079.1 1127.9 1178.2 1230.2 1284.4 1341.9 1404.1

u

h 1154.2 5.04 88.65 171.97 255.30 338.85 422.72 507.09 592.15 678.12 765.25 853.9 898.8 944.4 990.6 1037.5 1085.3 1134.3 1184.3 1236.8 1291.3 1349.0 1411.5

5.0 (263.99) s 2.9202 0.0001 0.2956 0.5705 0.8285 1.0720 1.3030 1.5233 1.7343 1.9375 2.1341 2.3255 2.4195 2.5128 2.6055 2.6979 2.7902 2.8830 2.9766 3.0717 3.1693 3.2708 3.3789

FIGURE 5.11 (b) Extract from subcooled table (SI units). (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. Sf Units Edition. 1978. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

10 v

Sat. 0 20 40 60 80 100 120 140 160 180 200 210 220 230 240 250 260 270 280 290 300 310

3

t

p (t Sat.) MPa

(b)

210 Thermodynamics and Heat Power

211

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.15 Determine the enthalpy specific volume, internal energy, and entropy of subcooled water at 300°F and 1000 psia. SOLUTION From Table 4 (Figure 5.11), we find that the values are directly tabulated. Therefore,

v = 0.017379 ft.3/lbm



u = 268.24 Btu/lbm



h = 271.46 Btu/lbm



s = 0.43552 Btu/lbm·°R

ILLUSTRATIVE PROBLEM 5.16 Determine the enthalpy of the subcooled water in Illustrative Problem 5.15 using the approximation of Equation 5.5, and compare the result obtained with the tabulated value. SOLUTION It is necessary to obtain the saturation values corresponding to 300°F. This is done by reading Table A.1 in Appendix 2, which gives us pf = 66.98 psia, vf = 0.017448 ft.3/lbm, and hf = 269.73 Btu/lbm. From Equation 5.5,

h = hf +

( p − p f )v f J

= 269.73 Btu/lbm +

(1000 − 66.98) lbf/in.2 (0.017448)ft.3/lbm × 144 in.2/ft.2 778 ft.⋅lbf/Btu

= 272.74 Btu/lbm



The difference between this value and the value found in Illustrative Problem 5.15 expressed as a percentage is

percent of error =

272.74 − 271.46 × 100 = 0.47% 271.46

For this pressure and temperature, the approximation expressed by Equation 5.5 is obviously within the accuracy required in most engineering calculations.

212

Thermodynamics and Heat Power

5.4 Computerized Properties It is obvious from Section 5.3 that a great deal of effort is involved in the interpolation in the Steam Tables and that the potential for errors is ever present. Values for the thermodynamic properties of steam are available in the form of computer programs that can provide the desired properties. Such a program has been utilized to provide steam tables and is available at the CRC Press website. Use the downloads/updates tab at http://www.crcpress​ .com/product/isbn/9781482238556. Any combination of two independent variables that define a state of steam may be entered, and the program will provide all of the other properties of that state. The user may select from temperature, pressure, specific volume, specific internal energy, specific enthalpy, specific entropy, and, if in saturation, quality. Note that temperature and pressure are not independent in the saturation range. Click on AUTO and follow the instructions. Select the desired fluid, steam, and press “Enter.” Use the cursor arrow up/down keys to select the system of units. Use “Page Down” to begin entering values. To quit the program, press “End.” Note that this program provides properties of fluids other than steam. Because the properties are computed from equations, they do not contain any interpolation errors.

ILLUSTRATIVE PROBLEM 5.17 Use the computer program to solve Illustrative Problem 5.1. SOLUTION The problem is to determine the enthalpy of saturated steam at 90°F. We select USCS units and enter 90°F and the quality, x, of 1.000. The program gives us the properties of the saturated liquid, the saturated vapor, and T, p, v, h, s, u, and x for the desired input. The agreement with Table 1 is very good.

Thermo Properties: T = 90.000 P = 0.6987 v = 467.65 h = 1039.9 s = 1100.3 u = 2.0078 x = 1.0000 Region: saturated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

213

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.18 Use the computer program to solve Illustrative Problem 5.3. SOLUTION This problem is similar to Illustrative Problem 5.17. The entries to the program are pressure (118 psia) and quality (x = 1.000). The results from the computer program are in excellent agreement with the interpolated values.

Thermo Properties: T = 340.06 P = 118.00 v = 3.789 h = 1108.0 s = 1190.7 u = 1.5899 x = 1.0000 Region: saturated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

ILLUSTRATIVE PROBLEM 5.19 Solve Illustrative Problem 5.7 using the computer program. SOLUTION The input to the program is USCS units; p = 120 psia, and x = 0.8. The results are in essentially exact agreement with the results of Illustrative Problem 5.7.

Thermo Properties: T = 341.32 P = 120.00 v = 2.987 h = 949.0 s = 1015.3 u = 1.3693 x = 0.8000 Region: saturated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

214

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.20 Use the computer program for steam to solve Illustrative Problem 5.8. SOLUTION The input to this problem is 1000 kPa (1 MPa) and x = 0.85. The printout agrees with the calculated values in Illustrative Problem 5.8.

Thermo Properties: T = 179.92 P = 1000.0 v = 0.16539 h = 2310.1 s = 2.475.5 u = 5.9189 x = 0.8500 Region: saturated

deg C kPa m3/kg kJ/kg kJ/kgK kJ/kg

ILLUSTRATIVE PROBLEM 5.21 Solve Illustrative Problem 5.9 using the computerized properties of steam. SOLUTION This problem has USCS inputs of 90°F and h = 900 Btu/lbm. The solution yields the quality and all of the other properties at this state.

Thermo Properties: T = 90.000 P = 0.69878 V = 377.77 h = 851.15 s = 900.00 u = 1.6433 x = 0.8078 Region: saturated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

215

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.22 Use the computer program to solve Illustrative Problem 5.12. SOLUTION The input for this problem is SI units of 240°C and 2000 kPa (2.0 MPa). The output of the program yields the desired properties.

Thermo Properties: T = 240.00 P = 2.0000 v = 0.10841 h = 2658.8 s = 2875.6 u = 6.4937 Region: superheated

deg C kPa m3/kg kJ/kg kJ/kgK kJ/kg

ILLUSTRATIVE PROBLEM 5.23 Solve Illustrative Problem 5.14 using the computerized properties. SOLUTION The inputs in USCS units are 465°F and 337 psia. The computer printout yields v, h, s, and u in an instant, while the calculated value in Illustrative Problem 5.14 requires six interpolations. Not only is the work less, but the potential for error in the interpolation is eliminated.

Thermo Properties: T = 465.00 P = 337.00 v = 1.4713 h = 1138.4 s = 1230.2 u = 1.5293 Region: superheated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

216

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.24 Use the computer program to solve Illustrative Problem 5.15. SOLUTION With USCS inputs of 300°F and 1000 psia, the program yields the following results. Thermo Properties: T = 300.00 P = 1000.0 v = 0.017379 h = 268.30 s = 271.51 u = 0.4356 Region: subcooled

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

The computer program for steam gives us the accuracy that is equivalent to that of the tables in Appendix 2 and should be used to avoid the tedious calculations entailed when using the tables. However, it is important to obtain an understanding and mastery of basics first and then to use the computerized tables as an invaluable tool.

5.5 Thermodynamic Diagrams Tables of thermodynamic properties provide accurate data for various substances. However, diagrams and charts based on the data of these tables are both useful and desirable. One most important fact must be borne in mind. Thermodynamic data such as those given by the Steam Tables are equilibrium data, and charts plotted from these data can represent only the equilibrium states. The path of a process that is not an equilibrium path cannot be drawn on these charts. Figure 5.12 is a T–s diagram for steam showing the liquid and vapor phases. In the wet region (below the saturation curve), lines of constant temperature and lines of constant pressure are horizontal lines. For convenience, lines of constant moisture (constant x) and lines of constant volume are also shown in the wet region. In the superheat region above the saturation curve, lines of constant pressure start at the saturation curve, rise steeply, and are almost vertical. Lines of constant enthalpy are nearly horizontal away from the saturation curve. Near the saturation curve, and especially near the critical point, there is a marked change in the curvature of the constant-enthalpy lines, which approach the vertical as the critical pressure is approached. On the large T–s diagram that is found in the Steam Tables, curves of constant superheat are also shown in the superheat region. A curve of constant superheat corresponds to a curve plotted parallel to the saturation curve and a fixed number of degrees above the saturation curve. Thus, the term 200 degrees of superheat means superheated steam whose temperature corresponds to saturation temperature plus

217

Properties of Liquids and Gases

Entropy (Btu/lb °F) 1.6 1.8 2.0 2.2

1000

Constant enthalpy

Te mp era tur e

(°F )

900

2

1

h

500

p2

stan

cu rve

100 0.4

600

0.6

400

h

Con h

0.2

700 p1

p1

200

0

800

h

x3 x 4

x2

on ati

Sa tur

300

1000 900

M

p2

t m oist ure ,x

600

400

1100

p1

800

700

500

e, p

1100

1200 pressur

p4

Consta nt

1200

p3 (crit ical)

1.4

N

300

h

E

200

Constant volume 0.8

1.0

1.2

100 1.4

1.6

1.8

2.0

2.2

0

Entropy (Btu/lb . °R) FIGURE 5.12 Outline of a temperature entropy diagram for steam. (From B. F. Dodge, Chemical Engineering Thermodynamics, New York: McGraw-Hill Book Co., 1944.)

200°F. While the T–s chart is useful in portraying processes, it is not as useful nor as widely used as the h–s diagram (or the Mollier chart as the h–s diagram is usually called). The Mollier chart is a plot on h–s coordinates of the thermodynamic properties of a substance. Figure 5.13 shows the outline of a portion of the Mollier chart for steam. Below the saturation line, lines of constant pressure (which are also lines of constant temperature) and lines of constant moisture are shown. Above the saturation line, curves of constant temperature, constant pressure, and constant superheat are shown. As noted for the T–s diagram, the curves of constant superheat correspond to curves plotted parallel to the saturation curve and a fixed number of degrees above the saturation curve. As we shall see, the Mollier chart is particularly suited to obtaining properties, describing flow, or describing constant-pressure processes. If a process is not reversible, then only its end states can be shown on a thermodynamic diagram such as the T–s diagram or the Mollier chart. A Mollier chart similar to the one in the Steam Tables is found in Appendix 2. Note that the specific volume property is not included in the Mollier chart.

218

Thermodynamics and Heat Power

1.1

1.2

1.3

1.4

Entropy (Btu/lb °F) 1.6 1.7

1.5

1.8

1.9 2.0 emperature, F t t n a t s n Co

2.1

2.2 1200

1600

2.3 100 1650 0 1100 900

1550

800

1500

900

700

1450

800

600

1400

700

500

1350

600

her e

400

tm F

100

istu

re %

200 100

1500

1450

1400

1350

1300

400

1250

300

1200

1150

0.2

line

1550

1100

5

1050

,p

sia

1100

mo

1.0

ant

Sat ura ted

0.5

eg

2.5

nst

200

5

550

Co

1150

500

300

da dar erh eat ,d

14 20 .69 6 10

50

100

200

400

sup

0

1200

ant

Sta n

nst

30

500

Co

0

300

Enthalpy (Btu/lbm)

1250

300

0 200 0 150 0 100 0

osp

1300

1000

1600

1050

ns

20

950

950

25

900

900

850

30

850

800

35

800

40

50

750 1.0

1000

Co

15

1000

ta

nt

pr

es

su

re

10

1.1

1.2

1.3

1.4

1.5

1.6 1.7 Entropy (Btu/lb°R)

1.8

1.9

2.0

FIGURE 5.13 Outline of h–s (Mollier) diagram for steam. (Courtesy of Babcock and Wilcox Corp.)

2.1

2.2

750 2.3

Enthalpy (Btu/lbm)

1.0 1650

219

Properties of Liquids and Gases

2.0

1.8

1.6

or

1.2

00 .

2

/in lb f

00

0

,00

10 80

00

00

30

/i lb f 00

00

10

50

n. 2

0

20

0.6

00

40

0 200

15

0.8

00

50

60

1.0

,0

Satura ted va p

15

cp (Btu/lbm°F)

1.4

0

0

0.4 200

400

600

800

1000

1200

1400

1600

t (°F) FIGURE 5.14 Specific heat of steam at constant pressure. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

In addition to the T–s and h–s charts, other diagrams of the thermodynamic properties also have utility. Figure 5.14 shows the specific heat of steam at constant pressure as a function of temperature and pressure. It can be proved by theoretical reasoning that the specific heats at the critical point are infinite, and it will be seen from Figure 5.14 that in the regions of the critical temperature, there is a sharp rise in specific-heat values.

220

Thermodynamics and Heat Power

The wide fluctuations in the region of the critical point are more evident from Figure 5.15, which also shows the specific heat at constant pressure for a saturated liquid. At the critical point, the saturated vapor and saturated liquid are indistinguishable, and both curves merge to infinity. The effect of pressure on the specific heat at constant pressure for a liquid (water) is shown in Figure 5.16. It should be noted that the specific heat at constant pressure and at given temperature decreases with increasing pressure. At a given pressure, it increases with temperature. It should be noted that Figure 5.12 through 5.16 exist in the (SI Units) Edition of the Steam Tables.

30

20 15

10 9

6

4 3

vap

or

5

Saturate

d liquid

7

Sat ura ted

cp (Btu/lbm°F)

8

50

2 1.5

25

20

00

1 600

650

700

30 00

750

00

35 ps i

00

800

40

00

45

00

00

850

700

0

ps i

60

00

900

t (°F) FIGURE 5.15 Specific heat at constant pressure near the critical point. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

221

Properties of Liquids and Gases

1.16 1.14 1.12

25 atur 50 00 ated liq 75 00 uid 00 lb f /i n. 2

1.08 1.06

S

cp (Btu/lb °F)

1.10

1.04

0 .2 ,00 /in 10 ,500 0 lb f 12 5,00 1

1.02 1.00 0.98 0.96 0.94

0

100

200

300

400

500

600

700

FIGURE 5.16 Specific heat of water at constant pressure. (J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore: Steam Tables. 1969. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

ILLUSTRATIVE PROBLEM 5.25 Determine the enthalpy of saturated steam at 90°F using the Mollier chart. Compare the result with Illustrative Problem 5.1. SOLUTION On the chart in Appendix 2, it is necessary to estimate the 90°F point on the saturation line. From the chart or the table in the upper left of the chart, we note that 90°F is between 1.4 and 1.5 in. of mercury. Estimating the intersection of this value with the saturation curve yields hg = 1100 Btu/lbm. This is in good agreement with Illustrative Problem 5.1.

ILLUSTRATIVE PROBLEM 5.26 Determine the enthalpy of a wet steam mixture at 120 psia having a quality of 80% by using the Mollier chart. Compare the results with Illustrative Problem 5.7. SOLUTION The Mollier chart has lines of constant moisture in the wet region that correspond to (1 – x). Therefore, we read at 20% moisture (80% quality) and 120 psia an enthalpy of 1015 Btu/lbm, which also agrees well with the calculated value in Illustrative Problem 5.7.

222

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.27 Using the Mollier chart, determine the quality of a wet steam mixture having an enthalpy of 900 Btu/lbm and a temperature of 90°F. Compare the result with Illustrative Problem 5.9. SOLUTION Entering the Mollier chart at 900 Btu/lbm and estimating 90°F (near the 1.5-in. Hg dashed line) yields a constant moisture percentage of 19.2%. The quality is therefore (1 – 0.192)(100) = 80.8%. We again show good agreement with the calculated value.

ILLUSTRATIVE PROBLEM 5.28 Determine the enthalpy of steam at 330 psia and 450°F using the Mollier chart. Compare the results with Illustrative Problem 5.11. SOLUTION From the chart, h = 1220 Btu/lbm, compared to 1221.5 Btu/lbm found in Illustrative Problem 5.11.

ILLUSTRATIVE PROBLEM 5.29 Determine the enthalpy and entropy of steam at 2.0 MPa and 240°C using the Mollier chart. SOLUTION We note that the steam is superheated. From the Mollier chart in SI units, h = 2880 kJ/kg and s = 6.5 kJ/kg K. These values compare with h = 2876.5 kJ/kg and s = 6.4952 kJ/kg K found in Illustrative Problem 5.12. For most purposes, this accuracy would be acceptable.

ILLUSTRATIVE PROBLEM 5.30 Determine the enthalpy of steam at 465°F and 337 psia using the Mollier chart. Compare the results with Illustrative Problem 5.14. SOLUTION Because neither pressure nor temperature is shown directly, it is necessary to estimate to obtain the desired value. Reading the chart in this manner, we obtain h = 1231 Btu/lbm. In Illustrative Problem 5.14, we obtained h = 1230.7 Btu/lbm. The agreement is good, and the savings in laborious interpolations is considerable.

223

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.31 Use the Mollier chart to solve Illustrative Problem 5.2. SOLUTION Reading the chart at 30°C and saturation gives us hg = 2556 kJ/kg, which is in excellent agreement with the tables.

ILLUSTRATIVE PROBLEM 5.32 Use the Mollier chart to solve Illustrative Problem 5.8. SOLUTION Reading the chart in the wet region at 1.0 MPa and x = 0.85 (moisture content of 15%) gives us

hx = 2476 kJ/kg sx = 5.92 kJ/kg·K

The chart does not give us ux or vx directly.

ILLUSTRATIVE PROBLEM 5.33 Solve Illustrative Problem 5.10 using the Mollier chart. SOLUTION Locate 30°C on the saturation line. Now follow a line of constant pressure, which is also a line of constant temperature in the wet region, until an enthalpy of 2000 kJ/kg is reached. At this point, we find the moisture content to be 23%, or x = 77%.

ILLUSTRATIVE PROBLEM 5.34 Solve Illustrative Problem 5.12 using the Mollier chart. SOLUTION We enter the chart in the superheat region at 2.0 MPa and 240°C to read the enthalpy and entropy. This procedure gives

h = 2877 kJ/kg



s = 6.495 kJ/kg·K

The other properties cannot be obtained directly from the chart.

224

Thermodynamics and Heat Power

Use of the Mollier chart does not permit us to obtain the specific volume or internal energy directly. Special charts are available that plot enthalpy as ordinate and specific volume as abscissa. These charts are particularly useful in steam turbine computations.

5.6 Processes Thus far, we have concerned ourselves with the properties of a substance in a given state. These properties are useful in actual processes to describe the path of the fluid or to establish the end states once the process has been specified. Some of the processes of interest are the throttling process (pipe flow and flow measurement), the constant-volume process (accumulator), reversible and irreversible compressions and expansions (pumps and turbines), and the constant-pressure process (heaters and boilers). For each of these processes, it is necessary to know the energy equation for the path and one of the end states. 5.6.1 Throttling The throttling process, as already noted in Chapter 2, is found to occur when an obstruction occurs in a pipe that locally disturbs the flow. This process is an irreversible adiabatic process whose path equation we have seen to be a constant-enthalpy path. Figure 5.17 shows this process on both Ts and hs coordinates. The end states, 1 and 2, are known. The path is shown as a dashed line on both diagrams, because it is an irreversible path. As will be noted from the diagram, steam that is initially wet will become drier, and depending on the initial and final states, it will become superheated after throttling. The final pressure is always less than the initial pressure. The superheating of initially wet steam in a throttling process provides the basis for a device known as a throttling calorimeter that is used to determine the quality of wet steam flowing in a pipe. Figure 5.18 is a diagram of the throttling calorimeter showing its installation in a vertical run of the pipe. The steam enters the sampling tube and is expanded in the orifice to the main body of the calorimeter. The initial pressure in the pipe is monitored by a pressure gauge, and the final temperature and pressure after expansion are monitored p1 T

p2

h 1

1

p1

p2

2

2

(a)

s

FIGURE 5.17 Throttling process. (a) T–s diagram. (b) h–s diagram.

(b)

s

225

Properties of Liquids and Gases

Pressure gauge for steam line

Thermometer

Steam line

Sampling tube

Orifice Close-off valve

Calorimeter

Steam out

Mercury manometer FIGURE 5.18 Schematic of a throttling calorimeter.

by a thermometer and manometer. To eliminate the velocity terms in the energy equation, the unit is sized so that the entry flow area and the flow area at the point of temperature measurement are made approximately equal. For reliable operation of the calorimeter, the final state should have a superheat of at least 10°F. The calculations for the throttling process are greatly simplified by use of the Mollier chart, as will be seen from Illustrative Problem 5.35.

ILLUSTRATIVE PROBLEM 5.35 Steam flows in a pipe at 150 psia. If a throttling calorimeter installed in the pipe has a thermometer reading of 250°F and the calorimeter is essentially 14.7 psia, determine the moisture in the steam flowing in the pipe. SOLUTION As already noted, h1 = h2 for this process. On the Mollier chart, h2 is found to be 1170 Btu/lbm at 14.7 psia and 250°F. Proceeding to the left on the chart, the constantenthalpy value of 1170 Btu/lbm to 150 psia yields a moisture of 3% or a quality of 97%.

226

Thermodynamics and Heat Power

If we use the tables to obtain the solution to this problem, we would first obtain h2 from the superheated vapor tables as 1168.8 Btu/lbm. Because hx = hf + xhfg, we obtain x as x= =

hx − h f h fg

where h f and h fg are values of 150 psiaa

1168.8 − 330.75 = 0.97 864.2



Very often, it is necessary to perform multiple interpolations if the tables are used, and the Mollier chart yields results within the required accuracy for most engineering problems and saves considerable time. We can also use the computerized properties to solve this problem. We first enter the 250°F and 14.7 psia to obtain h of 1168.7 Btu/lbm. We then continue by entering h of 1168.7 Btu/lbm and p of 150 psia. The printout gives us x of 0.9699 or 97%. Although the computer solution is quick and easy to use, you should still sketch out the problem on an h–s or T–s diagram to show the path of the process. Thermo Properties: T = 250.00 P = 14.700 v = 28.418 h = 1168.7 s = 1.7831 u = 1091.4 Region: superheated Thermo Properties: T = 358.49 P = 150.00 v = 2.925 h = 1168.7 s = 1.5384 u = 1087.5 x = 0.9699 Region: saturated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

5.6.2 Constant-Volume Process (Isometric Process) The constant-volume process is a nonflow process that we can consider to occur when a fluid is heated in a closed tank. Figure 5.19 shows a constant-volume process in which wet steam ① is heated at constant volume in a closed tank and goes to the superheated state at ②. The energy equation for this process has already been derived as q = u2 – u1. Because the Mollier chart does not have lines of constant internal energy, it is not suited for calculations of this process. The T–s chart does not have lines of constant internal energy, and it is not too useful in calculations involving the constant-volume process.

227

Properties of Liquids and Gases

h

T

2

Constant volume

volu

me

2

Con stan t

1

1

s

(a)

(b)

s

p

2

1 (c)

v

FIGURE 5.19 Constant-volume process. (a) h–s diagram. (b) T–s diagram. (c) p–v diagram.

ILLUSTRATIVE PROBLEM 5.36 A closed tank contains 1 lbm of saturated liquid at 150°F. If the tank is heated until it is filled with saturated steam, determine the final pressure of the steam and the heat added. The tank has a volume of 10 ft.3. SOLUTION Because the tank volume is 10 ft.3, the final specific volume of the steam is 10 ft.3/lbm. Interpolations in Table A.2 yield a final pressure of 42 psia. The heat added is simply the difference in internal energy between the two states.

q = u2 – u1 = (1093.0 – 117.95) = 975.05 Btu/lbm added

ILLUSTRATIVE PROBLEM 5.37 A closed tank has a volume of 60 ft.3. It contains 15 ft.3 of steam and 45 ft.3 of water at 14.7 psia. Heat is added until the pressure increases to 800 psia. Determine the heat added.

228

Thermodynamics and Heat Power

SOLUTION The mass in the tank is constant, and the heat added will be the change in internal energy of the contents of the tank between the two states. The initial mass in the tank is found as follows:



mf =

Vf 45 = = 2692.19 lbm v f 0.016715

mg =

Vg 15 = = 0.56 lbm v g 26.80

Total mass = 2692.75 lbm



The initial internal energy is the sum of the internal energy of the liquid plus the vapor:

Ug = mgug = 0.56 = 1077.6 = 603.5



Uf = mfuf = 2692.19 = 180.1 = 484 863.4



Total internal energy = 485 466.9 Btu

Because the mass in the tank is constant, the final specific volume must equal the initial specific volume, or

vx =

60 = 0.022282 ft 3/lbm 2692.75

But vx = vf + xvfg. Therefore, using Table A.2 at 800 psia,

x=

vx − v f 0.022282 − 0.02087 = = 0.0025756 v fg 0.5691 − 0.02087

The final amount of vapor is

0.0025756 = 2692.75 = 6.935 lbm

The final amount of liquid is

2692.75 – 6.935 = 2685.815 lbm

The final internal energy is found as before:

Ug = mgug = 6.935 = 1115.0 = 7732.5 U f = m f u f = 2685.15 × 506.6 =

The difference is

1360633.9 1368 366.4 Btu

229

Properties of Liquids and Gases



1 368 366.4 – 485 466.9 = 882 899.5 Btu

Per unit mass, the heat added is 882 899.5 = 327.88 Btu/lbm 2692.75



The small quantity of vapor mass necessitates the unusual accuracy needed to solve this problem.

5.6.3 Adiabatic Processes The adiabatic process is one of the most important processes that we shall consider, because most compressions and expansions can be idealized as adiabatic processes. Ideally, these processes would be carried out isentropically or approach isentropic conditions. Figure 5.20 shows the h–s diagram for two differing types of expansions and two differing types of compressions. The solid lines on this figure represent isentropic (reversible adiabatic) paths, while the dashed lines are used to represent irreversible processes. All the processes shown in Figure 5.20 are steady-flow processes. h

h

p2

p1

p2

p1

Compressor

Diffuser

s

s

(a) h

h p1

p1

p2

p2

Turbine

Nozzle

s

s (b)

FIGURE 5.20 Adiabatic processes. (a) Compression. (b) Expansion.

230

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.38 Steam is expanded isentropically without change in elevation and with negligible kinetic energy differences between the inlet and outlet sections of a turbine. If the initial pressure is 800 psia and the initial temperature is 600°F, determine the change in enthalpy if the end state pressure is 200 psia. SOLUTION As shown in Figure 5.20b, the process described in this problem is a vertical line on the Mollier chart. For 800 psia and 600°F, the Mollier chart yields h1 = 1270 Btu/lbm and s1 = 1.485. Proceeding vertically down the chart at constant s to 200 psia yields a final enthalpy h2 = 1148 Btu/lbm. The change in enthalpy for the process is 1270 – 1148 = 122 Btu/lbm. We may also solve this problem using the Steam Tables in Appendix 2. Thus, the enthalpy at 800 psia and 600°F is 1270.4 Btu/lbm, and its entropy is 1.4861 Btu/lbm °R. Because the process is isentropic, the final entropy at 200 psia must be 1.4861. From the saturation table, the entropy of saturated steam at 200 psia is 1.5464, which indicates that the final steam condition must be wet because the entropy of the final steam is less than the entropy of saturation. Using the wet steam relation yields sx = s f + xs fg 1.4861 = 0.5440 + x(1.0025)

x=

1.4861 − 0.544 = 0.95 1.0025

Therefore, the final enthalpy is

hx = hf + xhfg = 355.6 + 0.94(843.7) = 1148.7 Btu/lbm

The change in enthalpy is 1270.4 – 1148.7 = 121.7 Btu/lbm. Note the agreement with the Mollier chart solution. We can also use the computer program to solve this problem. For 600°F and 800 psia, h = 1270.0 Btu/lbm and s = 1.4857 Btu/lbm·°R. Now using P = 200 psia and s = 1.4857, we obtain h = 1148.1 Btu/lbm. The change in enthalpy is 1270.0 – 1148.1 = 121.9 Btu/lbm. Note the effort saved using either the Mollier chart or the computer program. Thermo Properties: T = 600.00 P = 800.00 v = 0.6774 h = 1270.0 s = 1.4857 u = 1169.7 Region: superheated T = 381.87 P = 200.00 v = 2.151 h = 1148.1 s = 1.4857 u = 1068.5 x = 0.9396 Region: saturated

deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

231

Properties of Liquids and Gases

ILLUSTRATIVE PROBLEM 5.39 If the process described in Illustrative Problem 5.38 is carried out adiabatically but not reversible between the same initial conditions and the same final pressure, determine the final state of the steam if only 80% of the isentropic enthalpy difference is realized. SOLUTION Again referring to Figure 5.20, it will be seen that the final temperature and enthalpy will both be higher than for the isentropic case. The change in enthalpy is 0.8 × 122 = 97.6 Btu/lbm. Therefore, the final enthalpy is 1270 – 97.6 = 1172.4 Btu/lbm, and the final pressure is 200 psia. The Mollier chart indicates the final state to be in the wet region, with a 3.1% moisture content and an entropy of 1.514 Btu/lbm·°R.

ILLUSTRATIVE PROBLEM 5.40 A turbine expands steam isentropically from an initial pressure of 1 MPa and an initial temperature of 250°C to a final pressure of 0.1 MPa. Neglecting kinetic and potential energy terms, determine the change in enthalpy of the steam. SOLUTION Using the Mollier chart, h1 = 2942 kJ/kg. Proceeding as shown in Figure 5.20b, that is, vertically at constant entropy to a pressure of 0.1 MPa, gives us a final enthalpy of 2512 kJ/kg. The change in enthalpy is 2942 – 2512 = 430 kJ/kg.

p

h

T

Constant pressure 2

1 (a)

v

(b)

T2

Con stan t pr essu re

2

1

2

s

FIGURE 5.21 Constant-pressure process. (a) p–v diagram. (b) T–s diagram. (c) h–s diagram.

1 (c)

s

232

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 5.41 Steam is expanded isentropically in a nozzle from an initial condition of 800 psia and 600°F to a final pressure of 200 psia. Determine the final velocity of the steam as it leaves the nozzle. SOLUTION The conditions given correspond to those in Illustrative Problem 5.38. Therefore, the isentropic change in enthalpy for this process is 122 Btu/lbm. We now recall from Chapter 3 that the change in velocity in a nozzle with negligible entering velocity as given from Illustrative Problem 3.22 is

V2 = 2 g c J ( h1 − h2 )



Substituting the value of 122 Btu/lbm for h1 – h2 yields

V2 = 2 × 32.17 lbm⋅ft./lb f ⋅s 2 × 778ft.⋅lb f /Btu × (122 Btu/lbm ) = 2471.2 ft./s



ILLUSTRATIVE PROBLEM 5.42 If the entering steam in Illustrative Problem 5.41 is expanded irreversibly in the nozzle to the same final pressure and to saturated vapor, determine the final velocity as the steam leaves the nozzle. SOLUTION Because the process is irreversible, we cannot show it on the Mollier diagram. However, the analysis of Illustrative Problem 3.22 for the nozzle is still valid, and all that is needed is the enthalpy at the beginning and the end of the expansion. From Illustrative Problem 5.38, h1 is 1270 Btu/lbm. For h2, we locate the state point on the Mollier diagram as being saturated vapor at 200 psia. This gives us 1199 Btu/lbm. Using the results of Illustrative Problem 3.22 yields V2 = 2 g c J ( h1 − h2 )

= 2 × 32.17 lbm⋅ft./lb f ⋅s 2 × 778ft.⋅lb f /Btu × (1270 − 1199)Btu/lbm = 1885.2 ft./s



As would be expected, the final velocity in the irreversible process is less than the final velocity that we obtained for the isentropic expansion. It is left as an exercise for the student to use the computer program to solve this problem.

233

Properties of Liquids and Gases

5.6.4 Constant-Pressure Process (Isobaric Process) The constant-pressure process is an idealization that can be used to describe the addition of heat to the working fluid in a boiler or the combustion process in a gas turbine. Figure 5.21 shows the p–v, T–s, and h–s diagrams for a vapor undergoing an irreversible, constantpressure process. The paths are shown as dashed lines to denote that the process is irreversible. Both the heat-addition portion and the heat-rejection portion of the gas turbine cycle are considered as constant-pressure flow processes. Because the exhaust temperature of a gas turbine is relatively high, the exhaust gases can also be used as a heat source such as to generate steam for a steam turbine generator. Supplemental oil or gas firing keeps steam pressure and temperature at the required level. Because a substantial number of Btu’s are recovered from the gas-turbine exhaust, this unit operates at relatively high efficiency. This combination of gas turbine and heatrecovery steam generator is responsible for much of the current interest in on-site generating systems for commercial buildings and small industrial plants. ILLUSTRATIVE PROBLEM 5.43 Steam that is initially saturated is superheated in a boiler at constant pressure. Determine the final state if the initial pressure is 500 psia and the final temperature is 800°F. How much heat per pound of steam was added? SOLUTION From the saturation table, 500 psia corresponds to a temperature of 467.13°F, and the saturated vapor has an enthalpy of 1205.3 Btu/lbm. At 500 psia and 800°F, the superheated vapor has an enthalpy of 1412.1 Btu/lbm. Because this process is a steady-flow process at constant pressure, the energy equation becomes q = h2 – h1 assuming that differences in the kinetic energy and potential energy terms are negligible. Therefore, q = 1412.1 – 1205.3 = 206.8 Btu/lbm added. 5.6.5 Constant-Temperature Process (Isothermal Process) At the exhaust of a steam turbine, the steam is usually wet. This steam is subsequently condensed in a unit appropriately known as a condenser. Because the steam is initially wet, this process is carried out essentially at constant temperature (isothermally). This process is also one of constant pressure in the wet region. Figure 5.22 shows the isothermal T

h 2

2

1

1 (a)

s

FIGURE 5.22 Isothermal process. (a) T–s diagram. (b) h–s diagram.

(b)

s

234

Thermodynamics and Heat Power

Steam

Water

Condensate

Water

FIGURE 5.23 Shell-and-tube condenser.

process on various diagrams, and Figure 5.23 shows a schematic of a shell-and-tube condenser, indicating the steam flow and cooling water paths. ILLUSTRATIVE PROBLEM 5.44 Steam is initially wet, having a moisture content of 3% at 1 psia. If it is condensed to saturated liquid, how much heat is removed? SOLUTION From the saturation table at 1 psia, hf = 69.74 Btu/lbm, hfg = 1036.0 Btu/lbm, and hg = 1105.8 Btu/lbm. Because the condensation process is carried out at constant pressure, the energy equation is q = Δh. The initial enthalpy is

hx = hf + xhfg = 69.74 + (0.97) (1036.0) = 1074.66 Btu/lbm

The final enthalpy is hf = 69.74. The enthalpy difference (Δh) is 1074.66 – 69.74 = 1004.92 Btu/lbm removed during the condensation process. The computer solution is given below where Δh = 1074.3 – 69.72 = 1004.6 Btu/lbm. Saturation Properties T = 101.71 P = 1.0000 v (ft3/lbm) h (BTU/lbm) s (BTU/lbmF) u (BTU/lbm) Thermo Properties T = 101.71 P = 1.0000 v = 323.55 h = 1074.3 s = 1.9221 u = 1014.4 x = 0.9700 Region: saturated

deg F psia f 0.016137 69.72 0.1326 69.72

g 333.56 1105.4 1.9774 1043.6 deg F psia ft3/lbm BTU/lbm BTU/lbmF BTU/lbm

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p1 Isentropic expansion

p2

Irreversible adiabatic expansion

Constant temperature process in the superheat region Throttling process 1

2 Saturation line

h p1 p2

Constant pressure process (Also constant temperature process in the wet region)

s FIGURE 5.24 Processes on a Mollier diagram.

A summary of all the foregoing processes on the Mollier diagram is shown in Figure 5.24. The dashed paths are used to indicate that these are not equilibrium paths, and as such, they cannot really be drawn on an equilibrium diagram. For the irreversible expansion between the same pressure limits, the final enthalpy (and temperature) is higher than for the same process performed reversibly. The constantpressure process is also one of constant temperature in the wet region. Finally, throttling is the irreversible, constant-enthalpy process shown in Figure 5.24.

5.7 Review Although this chapter is entitled “Properties of Liquids and Gases,” it has been devoted primarily to the properties of water because the most detailed and complete information is known about water. This information exists in the Steam Tables in extensive tabulations and charts. A great deal of time was spent in exercises to become familiar with the nomenclature and the format of the tables and charts. Once familiar with this resource, we were able to apply the tables and charts to solve various problems. Unfortunately, there are great amounts of arithmetic computation associated with the application of the data in the Steam Tables. The equations for the properties of steam have been programmed and are available in the disk included with the text. In addition, it was shown that these computer programs will yield the desired properties with relative ease. Whether the Steam Tables or a computer program is used, it is important to write the energy equation for the process and to sketch out the process on an appropriate T–s or h–s diagram. This procedure will lead to a better understanding of the problem and eliminate a great deal of unnecessary numerical calculations.

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Key Terms Terms used for the first time in this chapter are as follows: critical point: A limiting state of a fluid in which the density of saturated liquid equals the density of saturated vapor. Also, the latent heat of vaporization is zero at this state. At the critical point, the saturated liquid and saturated vapor states are identical. critical pressure: The pressure at the critical point. critical temperature: The temperature at the critical point. gas: A vapor that is either at very low pressure or far removed from the saturated state. Mollier chart: A chart having enthalpy–entropy coordinates. percent moisture: The percent by weight of moisture in a wet mixture; equal to where quality is expressed as a percentage. phase: That part of a pure substance that consists of a single-homogeneous aggregate of matter; for our purposes, these may be characterized as solid, liquid, and gas. quality: (x) fraction by weight of vapor in a mixture. saturation: The state of a liquid or vapor in which the vapor and liquid coexist in equilibrium in any proportion. Saturation temperature and saturation pressure refer, respectively, to the properties in the saturation state. Steam Tables: J. H. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore, Steam Tables— Thermodynamic Properties of Water Including Vapor, Liquid, and Solid Phases (New York: John Wiley & Sons, Inc., 1969, 1978). subcooled: That liquid state in which the pressure exceeds the saturation pressure corresponding to the temperature of the liquid. subscripts: f for saturated liquid, g for saturated vapor, and fg for a property change due to vaporization. superheated vapor: A vapor whose temperature is greater than the saturation temperature corresponding to the pressure. throttling calorimeter: A device that uses the throttling process to determine the quality of steam. USCS: United States conventional system of units. vapor: The gaseous phase that is in contact with saturated liquid or is not far from the saturated state. wet: A mixture of vapor plus liquid.

Equations Developed in This Chapter Saturation properties

hg = h f + h fg v g = v f + v fg sg = s f + s fg ug = u f + u fg

(5.1)

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Definition of enthalpy Definition of enthalpy (SI) Wet mixture property Wet mixture property Wet mixture property Wet mixture property Approximation for the enthalpy of subcooled liquid

h = u+

pv J

h = u + pv hx = hf + xhfg sx = sf + xsfg ux = uf + xvfg vx = vf + xvfg h − hf 

( p − p f )v f J

(5.2) (5.2a) (5.4a) (5.4b) (5.4c) (5.4d) (5.5)

QUESTIONS 5.1 Define the word phase, and list the three common phases of matter. 5.2 State the difference between a gas and a vapor. 5.3 As the saturation pressure is increased, does the saturation temperature (a) increase, (b) decrease, or (c) remain the same? 5.4 What is meant by the critical point? 5.5 Define the subscripts f, g, and fg. To what states do these subscripts refer? 5.6 Define the term wet. How is this term related to percent moisture? 5.7 How many properties are required to determine (a) the saturation state, (b) the superheat state, and (c) the wet state? 5.8 What are the principal coordinates of the Mollier diagram? 5.9 How is an isentropic process shown on a Mollier diagram? 5.10 How do you show a constant-temperature line in the wet region on the Mollier diagram? 5.11 Can the path of an irreversible process be shown on a T–s or a Mollier diagram? 5.12 What is known about the path of a throttling process on the Mollier diagram? 5.13 What is the ideal way that a compressor or an expander should be operated? 5.14  Using a sketch of the Mollier diagram show constant-pressure, constanttemperature, isentropic expansion, irreversible expansion, and throttling processes. PROBLEMS Wherever appropriate, sketch processes on a T–s or h–s diagram. Also, use the tables and Mollier charts in Appendix 2 for all problems. Problems Involving the Use of the Tables and Charts 5.1 Determine the enthalpy, entropy, specific volume, and internal energy of saturated steam at 100 and 1000 psia. 5.2 Determine the enthalpy, entropy, specific volume, and internal energy of saturated steam at 1.0 and 1.1 MPa.

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5.3 Determine the enthalpy, entropy, specific volume, and internal energy of saturated water at 1.0 and 1.1 MPa. 5.4 Determine the pressure, specific volume, and enthalpy of saturated water at 350°F and 500°F. 5.5 Determine the internal energy of steam at 10 MPa and 500°C. 5.6 Determine hfg at 400°F. 5.7 Determine sfg at 150°F. 5.8 Determine ufg at 212°F knowing hfg and vfg. Check your answer against the tabulated value. 5.9 Determine the pressure, specific volume, and entropy of saturated water at 35°C. 5.10 Determine the enthalpy, entropy, specific volume, and internal energy of wet steam at 100 psia if it has 5% moisture. 5.11 Determine the enthalpy, specific volume, entropy, and internal energy of wet steam at 1.12 MPa if the quality is 90%. 5.12 Steam at 200 psia has an enthalpy of 1050 Btu/lbm. Determine its quality. 5.13 If the enthalpy of steam at 1.0 MPa is 1400 kJ/kg, what is its quality? 5.14 Steam at 150 psia has a quality of 97%. What is the specific volume of this wet mixture? 5.15 The internal energy of wet steam is 2000 kJ/kg. If the pressure is 1.18 MPa, what is the quality of the mixture? 5.16 Determine the internal energy for a steam–water mixture for t = 400°F and x = 0.6 in Btu/lbm. 5.17 Determine the specific volume of wet steam at 200°C if the quality is 60%. 5.18 Calculate the specific volume of wet steam at 250°F if the mixture has a quality of 80%. 5.19 A steam–water mixture has a specific volume of 0.19 m3/kg. If the pressure of the mixture is 44 kPa, determine the quality and temperature of the mixture. 5.20 The temperature of a steam–water mixture is 270°F. If the specific volume of the mixture is 4.0 ft.3/lbm, determine the quality and pressure of the mixture. 5.21 A tank contains 2 kg of water and 0.2 kg of vapor at 220°C. Determine the quality, the volume of the tank, the volume of the water, and the pressure in the tank. 5.22 Saturated steam has an enthalpy of 2782.0 kJ/kg. What is its pressure? 5.23 If the enthalpy of saturated water is 100 Btu/lbm, determine its pressure, temperature, and specific volume. 5.24 Steam at 500 psia has a specific volume of 0.800 ft.3/lbm. Determine its enthalpy and temperature. 5.25 Steam at 2.0 MPa has a specific volume of 0.08 m3/kg. Determine its temperature and enthalpy. 5.26 Steam at 300 psia is at 600°F. Determine its specific volume. 5.27 Steam at 600 psia has a specific volume of 1.500 ft.3/lbm. Determine its enthalpy. 5.28 Steam at 900°F has an enthalpy of 1465 Btu/lbm. Determine its pressure. 5.29 Steam at 1000 psia has an enthalpy of 1250 Btu/lbm. Determine its specific volume.

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239

5.30 Steam at 1.00 MPa is at 400°C. Determine its specific volume. 5.31 Steam is at 2.0 MPa and 225°C. Determine its enthalpy. 5.32 Steam at 200 psia is at 610°F. Determine its enthalpy. 5.33 Steam is at 2.5 MPa and 227°C. Determine its enthalpy. 5.34 Determine the internal energy of steam at 190 psia and 910°F. 5.35 Calculate the internal energy of a mixture of steam and water for t = 200°C and x = 0.8, in kJ/kg. 5.36 Determine the specific volume, enthalpy, and internal energy of steam having a pressure of 5 psia and a quality of 90%. 5.37 What is the internal energy of steam at 2.17 MPa and 225°C? 5.38 Determine the enthalpy, specific volume, internal energy, and entropy of subcooled water at 500°F and 4000 psia. 5.39 Determine the enthalpy of subcooled water at 500°F and 4000 psia using Equation 5.5. Compare your result with Problem 5.38. 5.40 Steam at 245°C has a specific volume of 0.10 m3/kg. Determine its pressure. *5.41 Steam at 500 psia has a specific volume of 1.7500 ft.3/lbm. Determine its temperature and enthalpy. Problems Involving the Use of the Computerized Tables 5.42–5.82 Solve assigned problems 5.1–5.41 using the computerized tables on the CRC Press website. Problems Involving Processes Use the Steam Tables and Mollier chart as applicable to solve the following problems. 5.83 A tank contains 200 lbm of water and 20 lbm of steam at 400 psia. Determine the volume of the tank and the quality of the mixture. 5.84 A tank contains a steam–water mixture. The tank volume is 1.5 m3 and the pressure is 700 kPa. Calculate the mass of the mixture in the tank if the quality is 0.85. 5.85 A tank having a volume of 30 ft.3 is half filled with water, and the remainder is filled with water vapor at 100 psia. Calculate the quality of the mixture and the enthalpy of the mixture in Btu/lbm. 5.86 A 20 ft.3 drum contains saturated steam at 400°F. What is the pressure in the drum, and what is the mass of vapor in the drum? 5.87 Solve Problem 5.86 if the drum contains saturated water. 5.88 A 5 m3 drum contains saturated steam at 300°C. Determine the pressure in the drum and the mass of steam in the drum. 5.89 A 3 m3 drum contains saturated water at 150°C. Determine the pressure in the drum and the mass of water in the drum. 5.90 A steam drum has a volume of 70 ft.3. If 70% of the volume is occupied by the vapor and the contents of the drum are at 500 psia, determine the weight of liquid and vapor in the drum. 5.91 Ten pounds of steam–water mixture occupies a steam drum. If the quality of the mixture is 65%, what is the volume of the drum? The pressure is 100 psia.

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5.92 A steam drum has a volume of 7 m3. If the quality is 80% and the drum is at 1.1 MPa, determine the weight of liquid and vapor in the drum. 5.93 A rigid, closed vessel contains a mixture of liquid and vapor at 400°F. If there is 45% liquid and 55% vapor by volume in the tank, determine the quality and pressure in the vessel. 5.94 A mixture of steam and water at 230°F has a volume of 150 ft.3. If there is 12 lbm in the mixture, determine its quality. 5.95 Dry saturated steam at 350°C is cooled to 300°C in a tank. Determine the final quality. 5.96 Dry saturated steam at 350°F is cooled in a tank until the temperature is 300°F. Determine the final quality. 5.97 Dry saturated steam at 200°C expands to a specific volume of 1.1 m3/kg at constant temperature. Determine the final pressure. *5.98 How much heat must be added to 1 lbm of dry saturated steam at 500 psia in a closed tank to convert it to superheated steam at 900 psia and 1000°F? *5.99 Dry saturated steam fills a 100 ft.3 container at 100 psia. If the container is cooled until the contents are at 50 psia, what is the quality of the final mixture? 5.100 A closed, rigid vessel contains vapor and liquid at 400°F. If there is initially 45% liquid and 55% vapor by volume in the tank, determine the final percent by volume if the tank is cooled to 300°F. 5.101 One pound of superheated steam is initially at 100 psia and 400°F. If it is cooled at constant volume, determine the pressure at which it becomes saturated. 5.102 A rigid (constant volume) tank has a volume of 2.0 ft.3 and contains saturated water at 50 psia. Heat is transferred from the tank until the pressure is 20 psia. Calculate the heat transfer from the tank. 5.103 A closed container has 20 lbm of liquid and 20 lbm of vapor in it at 400°F. Determine the heat that must be added to raise the temperature to 425°F. 5.104 A boiler drum contains a steam–water mixture at 100 psia. At this time, there is 10,000 lbm of water in the drum and 5 lbm of vapor. If the contents of the drum are now heated until the pressure is 200 psia, how much heat was added? 5.105 Steam at 50 psia undergoes a process in which its temperature goes from 500°F to 700°F. What is the change in enthalpy for this process? 5.106 One pound of saturated water at 200°F is converted to saturated steam at 100 psia. Determine the enthalpy difference between these two states. 5.107 If saturated steam at 500 psia is superheated to a temperature of 1000°F, determine the change in enthalpy between these two states. Assume the final pressure of the steam to be 500 psia. 5.108 If the final pressure of the steam in Problem 5.107 is 450 psia, determine the difference in enthalpy between the two states given. 5.109 A steam line contains wet steam at 200 psia. A sample of this steam leaves a throttling calorimeter at 4 psia and 200°F. Determine the percent moisture in the steam line. 5.110 Steam flowing in a pipe is throttled by a partly open valve. The initial steam conditions are 600 psia and 800°F. Determine the final temperature if the final pressure of the steam is 100 psia.

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241

5.111 Wet steam at a pressure of 200 psia and a quality of 90% is throttled to a final pressure of 80 psia. What is the temperature and quality of the final condition? Use the Steam Tables to obtain your solution. 5.112 Solve Problem 5.111 using the Mollier chart. 5.113 After throttling, it is found that the pressure and temperature of steam are 30 psia and 300°F, respectively. If the pressure before throttling is 400 psia, what is the quality of the initial mixture? Use the Steam Tables. 5.114 Solve Problem 5.113 using the Mollier chart. 5.115 Superheated steam is expanded isentropically from 900 psia and 700°F to saturated vapor. Determine the difference in specific enthalpy for this expansion. Use the Steam Tables. 5.116 Solve Problem 5.115 using the Mollier chart. 5.117 One pound mass of steam is expanded isentropically from 500 psia and 800°F to 10 psia. Use the Mollier chart to determine the final enthalpy. 5.118 Solve Problem 5.117 using the Steam Tables. 5.119 Steam expands isentropically from 300 psia and 620°F to saturation. Determine the final enthalpy using the Mollier chart. 5.120 Solve Problem 5.119 using the Steam Tables. 5.121 Steam is used for heating a room. Assuming that the required heating load is 10,000 Btu/h and the steam enters at 20 psia and 250°F and is condensed, how many pounds of steam per hour are required? Assume that pressure losses are negligible and that the liquid is just saturated. 5.122 Calculate the “average” specific heat at constant pressure for superheated steam between 400°F and 1000°F if the pressure is 200 psia. The definition of average for this case is Δh/ΔT. 5.123 Steam expands isentropically in a turbine from 500 psia and 1000°F to 14.7 psia. Determine the difference in enthalpy between the initial and final conditions. 5.124 If the expansion in Problem 5.123 is not carried out isentropically but is expanded irreversibly to the same final pressure and has 40°F of superheat, determine the difference in enthalpy between the initial and final conditions. Use the Mollier chart. 5.125 One pound of superheated steam at 200 psia and 800°F expands irreversibly and adiabatically to 14.7 psia and 250°F. Determine the change in enthalpy between the initial and final states. 5.126  Wet steam leaves the exhaust of a turbine and is subsequently condensed. Assuming the wet steam to be at 0.5 psia with 15% moisture, determine the heat extracted in the condenser if the condensation process takes the mixture to saturated liquid. 5.127 Heat is added to steam in a closed cylinder. If a movable piston is placed on one end of the cylinder, it is possible (in principle) to carry out the process at constant pressure. If the initial steam is at 250°F and is saturated, how much heat is added if the final temperature is 500°F? 5.128 Two kilograms of saturated water at 1.0 MPa are heated to saturated vapor at constant pressure. Determine the heat transfer for this process.

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5.129 Two lbm of saturated water at 200 psia is vaporized to saturated steam at constant pressure. Determine the change in volume for this change. 5.130 Steam having a quality of 0.80 is contained in a rigid vessel at a pressure of 300 psia. Heat is added until the temperature reaches 500°F. Determine the final pressure. 5.131 Steam at 340 kPa and 600°C undergoes a constant pressure process to 900°C. Calculate the work done per kilogram of steam. 5.132 Determine the change in internal energy of water vapor per lbm as it undergoes a constant pressure process from 30 psia and 500°F to 700°F. 5.133 A kilogram of saturated water at 200°C expands isothermally until it changes into a saturated vapor. Determine the work done. 5.134 Dry saturated steam at 350°F is heated at constant pressure until it reaches a temperature of 600°F. Determine the work for this process in Btu/lbm. 5.135 In a constant pressure piston-cylinder process, steam is compressed from 1 MPa and 500°C to a saturated vapor. Calculate the work done to compress the steam and the heat transfer per kilogram. 5.136 Saturated steam at 500°F expands isothermally to 100 psia. Determine the change in enthalpy between the initial and final states. *5.137 Saturated water enters a boiler at 500 psia. It is vaporized and superheated to a final condition of 500 psia and 1000°F. From this state, it enters a turbine where it is expanded isentropically to 1 in. Hg. What fraction of the energy required to produce the steam is obtained from the turbine if the turbine is 100% efficient? 5.138 Steam is expanded isentropically in an ideal nozzle from a state of 1000 psia and 1000°F to a final state of 20 psia. Determine the final velocity of the steam from the nozzle if the initial velocity is negligible. Use the Mollier chart. 5.139 Solve Problem 5.138 if the initial velocity in the nozzle is 950 ft./s. 5.140 Steam is expanded isentropically in a nozzle from 1 MPa and 500°C to saturated vapor. If the initial velocity is negligible, determine the final velocity from the nozzle. Use the Mollier chart. 5.141 Steam expands irreversibly in a nozzle. If the initial state is 900 psia and 600°F and the steam is expanded to 50 psia and a moisture content of 12%, determine the final velocity. Assume that the initial velocity is negligible. Use the Mollier chart. 5.142 Steam expands irreversibly in a nozzle. This initial state is 1 MPa and 500°C. The final state is 20 kPa and a moisture content of 2%. If the initial velocity can be neglected, determine the final velocity from the nozzle. Use the Mollier chart. Use the Computerized Properties to Solve Any of the Following Problems 5.143–5.202 Solve assigned problems 5.83–5.142 using the computerized properties.

6 The Ideal Gas

L E A R N I NG G OA L S

After reading and studying the material in this chapter, you should be able to

1. Understand the terms ideal and perfect as applied to gases 2. Express the units of the gas constant in both SI and English systems, and use the molecular weight (MW) to determine the gas constant for a given gas 3. Calculate the average specific heat of a gas for a gas over a temperature range 4. Use the Gas Tables to solve gas processes 5. Write the general expression for the entropy change of an ideal gas from which the equation of path for an isentropic process is obtained 6. Derive relations for constant-volume, constant-pressure, constant-temperature, isentropic, and polytropic processes, for both open and closed systems 7. Understand the difference between real and ideal gases 8. Apply the equation of state for real gases 9. Understand how the paddle-work problem relates to frictional effects

6.1 Introduction In Chapter 1, we derived a simple equation for the pressure–volume relation of a gas based on elementary considerations. Because many oversimplifications were involved in this derivation, it could not be reasonably expected that the result obtained in this manner would even closely approach the behavior of a real gas. Surprisingly, it has been found that the equation can be used to represent the behavior of a large class of actual gases with accuracy usually sufficient for engineering applications. In any case, this equation can be used to predict qualitatively the behavior of most gases, and the results so obtained can be employed as a guide for design or performance purposes. The expressions ideal gas and perfect gas appear in many textbooks on thermodynamics, and unfortunately, some confusion has developed regarding the exact definition of these terms. For clarity and consistency, these terms will be given identical meanings and defined as gases having equations of state that correspond to Equation 6.7 or 6.8.

243

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6.2 Basic Considerations The first observations concerning the equation of state of a gas were made by Robert Boyle (1629–1691), an English chemist, in the year 1662. He observed experimentally that the volume of a given quantity of gas varies inversely with absolute pressure if the temperature of the gas is held constant. We can write Boyle’s law as

p1 V2 = p2 V1



or p1V1 = p2V2 = constant (6.1)

Because T = constant, we can also write Equation 6.1 as pV = C

(6.1a)

where C represents a constant for a given temperature. A family of curves for different temperatures is shown in Figure 6.1. Each of these curves is an equilateral hyperbola, because they are of the form xy = C.

p

p1

1

2

p2 0

FIGURE 6.1 Boyle’s law.

V1

V2

Ta = constant Tb = constant Tc = constant

V

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The Ideal Gas

ILLUSTRATIVE PROBLEM 6.1 A gas occupies a volume of 100 ft.3 and is at a pressure of 100 psia. If the pressure is reduced to 30 psia, what volume will the gas occupy? Assume that the gas temperature is kept constant. SOLUTION For a constant temperature process, Boyle’s law is p1V1 = p2V2 Therefore,

V2 =

p1 V1 p2

and

V2 =

100 (100 ft.3 ) = 333 ft.3 30

ILLUSTRATIVE PROBLEM 6.2 A gas occupies a volume of 2 m3 at a pressure of 1 MPa. If the pressure is increased to 8 MPa, what volume will the gas occupy if the gas temperature is kept constant? SOLUTION For the constant-temperature process, we again have from Boyle’s law p1V1 = p2V2 and



V2 =

p1 106 (2 m 3 ) = 0.25 m 3 V1 = p2 8 × 106

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In 1787, approximately 100 years after Boyle’s law was formulated, the French physicist Jacques Charles (1747–1832) investigated and published his experiments that showed that the volume of a gas was directly proportional to its absolute temperature if the pressure was held constant. He also demonstrated that the pressure of a gas was directly proportional to the absolute temperature if the volume was held constant. Mathematically, Charles’ laws can be written as

V = constant (pressure constant) (6.2) T



P = constant (volume constant) (6.3) T

ILLUSTRATIVE PROBLEM 6.3 A given mass of gas occupies 150 ft.3 at 32°F. If heat is added while the gas pressure is kept constant, determine the volume if its temperature is 100°F. SOLUTION For the conditions given, T1 = 32 + 460 = 492°R and T2 = 100 + 460 = 560°R. Thus, for a constant-pressure process,

V1 T1 = V2 T2

or V2 = V1

T2 (150 ft.3 )(560) = = 170.7 ft.3 T1 492

ILLUSTRATIVE PROBLEM 6.4 If after the process performed in Illustrative Problem 6.3 the gas is contained at constant volume and its absolute temperature is increased by 25%, what percent increase in its solute pressure will occur? SOLUTION If for this process T2 = 1.25T1,

T2 = 1.25 T1

Therefore,

p1 T1 = p2 T2

or

p2 T2 = p1 T1

Thus, p2/p1 = T2/Tl = 1.25, and the absolute gas pressure increases by 25%.

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ILLUSTRATIVE PROBLEM 6.5 A gas is cooled at constant pressure from 100°C to 0°C. If the initial volume is 4 m3, what will its final volume be? SOLUTION

V2 = V1

T2 0 + 273 = (4 m3 ) = 2.93 m 3 T1 100 + 273

By combining Boyle’s law and Charles’ laws into a single relation, we can obtain a general gas law. We can do this by considering a gas that goes from one state, state ①, to a second state, state ②. To go from state ① to state ②, we shall first assume that the pressure is increased from state ① to the pressure of state ② by heating at constant volume. The gas is then cooled at constant pressure (the pressure at ②) until its volume reaches the volume of state ②. These events are portrayed in Figure 6.2. From this figure, we can write for the constant-volume path 1 – a, pa Ta = (6.4) p1 T1



and for path a – 2, the constant-pressure path, Ta Va = (6.5) T2 V2



Solving for Ta from Equation 6.4 and substituting into Equation 6.5 yields paT1 T2Va = (6.6) p1 V2



p

2

a

1

V FIGURE 6.2 Ideal gas law derivation.

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but pa = p2 and Va = V1. Using this and rearranging gives us p1V1 p2Va = T1 T2



(6.7)

Because we selected points ① and ② arbitrarily, it follows that the term pV/T must be a constant for a given gas. For convenience, it is easier to express this constant on the basis of a unit mass of gas. Denoting the gas constant per unit mass by the symbol R, we have

pV = pmv = mRT (6.8)

It will be recalled from Chapter 1 that we identified the velocity term in the equation derived on the basis of elementary kinetic theory as being proportional to the temperature of the gas (the random motion of the gas molecules). Using this, we can also obtain the equation of state of a gas as Equation 6.8. In English engineering units, p is the pressure in pounds force per square foot absolute, V is the total volume of the gas in cubic feet, T is the absolute temperature in degrees Rankine, m is the mass of gas in pounds mass, and R is a constant of proportionality in ft. lbf/lbm·°R. If m is eliminated in Equation 6.8, it becomes

pv = RT (6.9)

in which p, R, and T correspond to the terms in Equation 6.8, and v represents the specific volume. In SI units, p is in kilopascals, T is in degrees Kelvin, m is in kilograms when R is in kJ/kg·K, and v is in cubic meters per kilogram. R for actual gases is not a constant and varies from gas to gas. However, it has been found experimentally that most gases at very low pressure or with high degrees of superheat exhibit nearly constant values of R. As further indicated in Table 6.1, the product of molecular weight (MW) and R for most gases is nearly constant and, in usual English engineering units, equals 1545.3 ft. lbf/lbm mol·°R. For any other combination of pressure, volume, and temperature units, it is a relatively straightforward calculation to derive R. Some values of this constant in other systems are listed in Table 6.2. For the purposes of this book, a value of MW × R of 1545 ft. lbf/lbm mol·°R is used. In SI units, the value of this product is 8.314 kJ/kg mol·K. These values are often called the universal gas constant in their respective unit systems with the notation Ro.

TABLE 6.1 Gas Constant Data Gas Air Ammonia (NH3) Carbon dioxide (CO2) Carbon monoxide (CO) Hydrogen (H2) Nitrogen (N2) Oxygen (O2)

Gas MW

Product MW × R (rounded)

28.97 17.02 44.01 28.01 2.02 28.02 32.00

1545 ft. lbf/lbm·mol·oR 1520 1532 1545 1535 1537 1543

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TABLE 6.2 Universal Gas Constant Values Molecular Weight × R 1545.3 ft. lbf/lbm mol·°R 0.082 L·atm/g mol·K 8.3143 × 107 erg/g mol·K 8.314 J/g mol·K 1.986 Btu/lbm mol °R 1.986 cal/g mol·K

The pound mole, or more briefly, the mole, is the amount of a substance whose mass is equal to its MW in pounds mass. Similarly, the kilogram mole is the amount of a substance whose mass is its MW in kilograms. Thus, the mole is essentially a unit of volume, but the pound mole and the kilogram mole occupy different volumes. The number of moles of a gas (n) equals the mass of the gas divided by its MW. Thus, 28 lbm of nitrogen is 1 lb.-mole of nitrogen. Two moles of nitrogen would have a mass of 2 × 28, or 56 lbm. MWs and gas constant values for many gases can be found in Appendix 2, Table A.13. The idea gas equation can now be written in two ways:

pV = mRT (6.9a)

or

pV = nRoT (6.9b)

where n equals the number of moles.

ILLUSTRATIVE PROBLEM 6.6 Nitrogen at 200 psig is used to fill a container of 120 in.3. The filling process is very slow, and the contents of the tank attain the room temperature of 73°F. How much gas is there in the container? SOLUTION Let us first put each of the given variables into a consistent set of units: p = (200 + 14.7 )(144) psfa (lbf /ft.2 ) T = ( 460 + 73)°R

120 3 ft. 1728 1545 R= ft. lbf /lbm⋅°R (because the molecular weight of nitrogen is 28) 28

V=

250

Thermodynamics and Heat Power

Applying Equation 6.9, pv = RT, v = RT/p, and

v=



(1545/28)( 460 + 73) (200 + 14.7 )(144)

bm = 0.951 ft.3 /lb

The mass of gas is the total volume divided by the specific volume. Thus, (120/1728) ft.3 = 0.073 lbm 0.951 ft.3 /lbm



The same result is obtained by direct use of Equation 6.8: pV = mRT, m = pV/RT, and



m=

(200 + 14.7 )(144)(120/1728) = 0.073 lbm (1545/28)( 460 + 73)

ILLUSTRATIVE PROBLEM 6.7 If the gas in Illustrative Problem 6.6 is now heated until the temperature is 200°F, what is the pressure? SOLUTION Apply Equation 6.8 and note that the volume is constant.



p1V1 p2V2 T = and p2 = p1 2 because V1 = V2 T1 T2 T1

Therefore,



p2 = (200 + 14.7 )

460 + 200 = 266 psia 460 + 73

251

The Ideal Gas

ILLUSTRATIVE PROBLEM 6.8 Carbon dioxide (MW = 44) occupies a tank at 100°C. If the volume of the tank of 0.5 m3 and the pressure is 500 kPa, determine the mass of gas in the tank. SOLUTION For CO2,



R=

8.314 kJ/kg⋅mol⋅K = 0.1890 kJ/kg⋅K 44 kg/kg⋅mol

Applying Equation 6.8, pV = mRT, and



m=

pV (500)(0.5) = = 3.546 kg RT 0.1890(273 + 100)

It is sometimes convenient to express the volume of a gas in terms of the volume that 1 mol of gas will occupy at a given temperature and pressure. We can readily obtain this value by considering Equation 6.9. Let us multiply both sides of this equation by MW, the molecular weight of a given gas. Thus, (MW)pv = (MW)RT

(6.10)

Because R = 1545/MW, pv(MW) = 1545T (6.11) Because v(MW) equals V(MW)/m and m/(MW) is the number of moles, n, 1 mol of a gas would have a volume, called Vmolar, of

Vmolar =

1545T p

or

8.314T p

in SI units (6.12)

It is apparent from Equation 6.12 that for a given pressure and temperature, a mole of any gas will occupy the same volume. Quite often, the term standard state appears in the engineering and scientific literature, and some confusion exists as to its specific meaning. This is due to the lack of general agreement on the definition of temperature and pressure at this state. The most common standard state in use is 32°F and 14.7 psia. For this state, it will be found that 1 lbm mol occupies 358 ft.3 or 22.4 L/g mol. The use of the term standard state should be avoided unless the conditions of this state are specified.

252

Thermodynamics and Heat Power

6.3 Specific Heat In the general case of a fluid involved in a thermodynamic process, both heat and work energy interchanges are involved, and concurrently, there is a temperature change of the working fluid. The term specific heat has been defined in Chapter 3 as the ratio of the heat transferred per unit mass by the working fluid in a process to the corresponding change in temperature of the fluid. Mathematically,

c=

q ∆T

(6.13)

Several features of Equation 6.13 have already been noted in Chapter 3 and are repeated here for emphasis. Heat is transferred energy and, by convention, is positive if added to a system and negative if extracted from a system. Also, the addition or removal of energy as work does not enter into the definition of specific heat. These concepts lead us to the conclusion that the specific heat of a process can be zero, positive, negative, or even infinite. Two processes proved themselves to be of particular interest: the constant-pressure process and the constant-volume process. For these processes, the respective specific heats are

cp =

cv =

q ∆T q ∆T

(flow or nonflow) p constant

(6.14)

v constant

Throughout this chapter, it will be necessary to invoke both the first and second laws to specify the path and state conditions as a gas undergoes a change of state. In Chapter 3, the first law was applied to the steady-flow and nonflow, constant-pressure processes, and the energy relation q = Δh resulted in both processes. Although a complete discussion of the temperature and pressure dependence of the specific heat of a real gas is beyond the scope of this book, it may be noted that a gas whose equation of state is given by Equation 6.9 has both its internal energy and enthalpy independent of pressure and that these properties depend solely on temperature. Therefore, for the ideal gas for any process, flow or nonflow,

cp =

∆h ∆T

cv =

∆u (6.15b) ∆T

(6.15a)

and

Note that these equations are valid for any ideal gas in any process. Thus, Δh always equals cpΔT even for a constant-volume process and Δu always equals cvΔT even for a constant-pressure process.

253

The Ideal Gas

CALCULUS ENRICHMENT Because temperature and specific volume are independent, measurable properties, they can be used to establish the thermodynamic state of a substance. Therefore, we can state that the internal energy, u, is given as a function of T and v. Mathematically, u = u(T,v) (a) The total differential of u is given in terms of the partial derivatives as

du =

δu δT

dT + v

δu δv

dv (b) T

The first partial derivative in Equation a is the change in internal energy per degree of temperature change for a constant volume process, and it is called the specific heat at constant volume. Thus, cv ≡



δu δT

(c) v

In a series of famous experiments, Sir James Prescott Joule (1818–1889), an English physicist, determined that the internal energy of a gas depended only on its temperature. Joule performed his experiments on an apparatus such as the one shown schematically in the figure below. Basically, it consisted of two tanks connected by a valve that were placed in a tank of water. The temperature of the water was monitored with a thermometer. One tank was evacuated while a gas was sealed in the other tank. The valve was slowly opened, and after equilibrium was attained, the temperature of the water was found to be unchanged. There was no heat transfer to or from the system, and no work was performed on or by the system. From the first law for a closed system, we conclude that there was no change in the internal energy of the system, even though both the pressure and specific volume of the gas changed. Joule concluded that the internal energy of the gas was a function only of temperature, making Equation a

u = u(T) (d)

Thermometer

Evacuated tank

Valve

Water

Pressurized gas

254

Thermodynamics and Heat Power

Equation d can also be derived mathematically for a gas whose equation of state corresponds to Equation 6.9. Equation c can be changed as it is applied to an ideal gas as

cv =

du dT

(ideal gas) (e)

We can consider the change in enthalpy of an ideal gas in the same manner as we considered the internal energy. Thus, h = h(T,p) (f) where the independent variables chosen are pressure and temperature. The change in enthalpy is



dh =

δh δT

dT + p

δh δp

dp (g) T

The first partial derivative in Equation g is the change in enthalpy per degree of temperature change for a constant pressure process, and it is called the specific heat at constant pressure. Thus,



cp ≡

δh δT

(h) p

Because the definition of enthalpy is h ≡ u + pv (i) we can write for the ideal gas that h = u + RT (j) Therefore, because R is a constant and u is only a function of temperature, it follows that for the ideal gas, the enthalpy is a function only of temperature. The specific heat at constant pressure for the ideal gas is

cp =

dh (k) dT

255

The Ideal Gas

When internal energy or enthalpy data are available (e.g., in the work of Keenan and Kaye [1948]), an “average” value of cp and cv can readily be obtained.

cp =

h2 − h1 T2 − T1

(6.16)



cv =

u2 − u1 T2 − T1

(6.17)

For cases in which internal energy or enthalpy data are not available, equations have been developed from either empirical or spectroscopic data expressing the dependence of the specific heat on temperature. These equations are commonly of the following forms, with A, B, and D as constants:

c = A + BT + DT2

(6.18a)



c=A +

B D + T T2

(6.18b)

The mean or average specific heat of a substance can be defined as that value, when multiplied by the temperature interval, that will give the energy as heat interchanged during a process. Thus, if the specific heat varies as shown in Figure 6.3, the mean value occurs when areas abcd and aefd are equal. For gases whose specific heats are of the form given by Equation 6.18, mean specific heats are, respectively,

c = A+



B D 2 (T2 + T1 ) + T2 + T2T1 + T12 2 3

(6.19a)

B ln(T2 /T1 ) D + T2 − T1 T2T1

(6.19b)

(

c=A +

c

)

Area A = area B Area abcd = area aefd c

c

B

e

f

A b a T1

FIGURE 6.3 Mean specific heat.

d T2

T

256

Thermodynamics and Heat Power

An alternative interpretation of the average specific heat can be illustrated graphically if reference is again made to Figure 6.3. The c and T scales are plotted linearly, and c expresses the condition that the equal positive and negative areas cancel each other. In other words, area A equals area B. Note that the mean specific heat does not necessarily occur at the arithmetic mean temperature unless c is constant or a linear function of T.

CALCULUS ENRICHMENT The mathematical definition of the average value of a function can be written as



y=

∫

x2

x1

y dx (a)



x2 − x1

Using Equation 6.18a,

∫ c=

T2

T1



( A + BT + DT 2 ) dT (b)



(T2 − T1 )

Integrating,



c=

A(T2 − T1 ) +

(

)

(

)

B T22 − T12 D T23 − T13 + 2 3 (c) (T2 − T1 )

Factoring and dividing by T2 – T1,

c = A+

B D 2 (T2 + T1 ) + T2 + T2T1 + T12 (6.19a) 2 3

(

)

Using Equation 6.18b,

∫ c=

T2

T1



B D + dT T T2 (d) (T2 − T1 )

A +

Integrating, T2 − T2−1 − T1−1 T1 (e) T2 − T1

A (T2 − T1 ) + B ln

c=

(

)

257

The Ideal Gas

and 1 1 − T T1 B ln(T2 /T1 ) − 2 c=A + T2 − T1 T2 − T1



(f)

Rearranging the last term in Equation f, c=A +



1 B ln(T2 /T1 ) − T2 − T1 T2T1

(6.19b)

ILLUSTRATIVE PROBLEM 6.9 For nitrogen between 540°R and 9000°R, an equation for the instantaneous specific heat at constant pressure is

cp = 0.338 −

1.24 × 102 4.15 × 10 4 + Btu/lbm⋅°R T T2

Determine the mean specific heat at constant pressure between 80°F and 500°F. SOLUTION This equation has the form of Equation 6.18b, with A′ = 0.338, B′ = –1.24 × 102, and D′ = 4.15 × 104. Therefore, from Equation 6.19b, with temperatures in degrees Rankine,



cp = 0.338 −

1.24 × 102 ln (960/540) 4.15 × 10 4 + (540)(960) 960 − 540

= 0.248 Btu/lbm⋅°R

ILLUSTRATIVE PROBLEM 6.10 Using the data from the properties of some gases at low pressure in Appendix 2, solve Illustrative Problem 6.9. SOLUTION The table in Appendix 2 does not give us the enthalpy data at 960°R and 540°R that we need. Interpolating yields T 3

537 540 600

63

h

T

h

3729.5 3750.4 4167.9

900 960 1000

6268.1 6694.0 6977.9

60

100

258

Thermodynamics and Heat Power

3 ( 4167.9 − 3729.5) 63 60 = 6268.1 + (6977.9 − 6268.1) 100

h540 = 3729.5 +

h960

Note that h is given for a mass of 1 lb. mol. To obtain the enthalpy per pound, it is necessary to divide the values of h by the MW, 28.

c=

h2 − h1 6694.0 − 3750.4 /lbm⋅°R = = 0.250 Btu/ 28(960 − 540) T2 − T1

With the more extensive Gas Tables, these interpolations are avoided. The Gas Tables provide a relatively easy and accurate method of obtaining average specific heats. Also, these tables have been computerized for ease of application.

ILLUSTRATIVE PROBLEM 6.11 The specific heat of air between 500°R and 2700°R is given by cp = 0.219 + 3.42 × 10 –5 T – 2.93 × 10 –9 T2 Btu/lbm·°R Determine the mean specific heat at constant pressure for air between 80°F and 500°F. SOLUTION The equation for the instantaneous specific heat is of the form of Equation 6.18a, with A = 0.219, B = 3.42 × 10 –5, and D = –2.93 × 10 –9. Using these values and Equation 6.19a yields 3.42 × 10−5 (960 + 540) 2 2.93 × 10−9 − (9602 + 960 × 540 + 5402 ) 3 = 0.243 Btu/lbm⋅°R

cp = 0.219 +

For the ideal gas, certain unique and simple relations relating the specific heat at constant pressure to the specific heat at constant volume can be derived. Let us first recall the general definition of the term enthalpy,

h = u+

pv (6.20) J

259

The Ideal Gas

The change in enthalpy between any two states therefore is

h2 − h1 = (u2 − u1 ) +

p2 v2 p1 v1 − (6.21) J J

But

h2 – h1 = cp(T2 – T1);  u2– u1 = cv(T2 – T1)

and

pv = RT (6.22)

Substituting Equation 6.22 into Equation 6.21 gives

c p (T2 − T1 ) = cv (T2 − T1 ) +

R (T2 − T1 ) (6.23) J

Rearranging and simplifying Equation 6.23 yields the desired result:

c p − cv =

R (6.24) J

In SI units, the conversion factor J is not included. Therefore,

cp − cv = R  SI units

(6.24a)

At this point, it is often found convenient to express the results of Equation 6.24 in terms of the ratio of the specific heats. By defining



k=

cp cv



(6.25)

and dividing Equation 6.24 by cv, we obtain



cp cv

−

cv R = c v Jcv

(6.26)

Using the definition of k given by Equation 6.25, we have



k−1=

R Jcv

(6.27)

260

Thermodynamics and Heat Power

Rearranging yields



cv =

R J ( k − 1)

(6.28)

R k−1

(6.28a)

In SI units,



cv =

Because cp = kcv,

cp =



R k (6.29) J k−1

In SI units,

cp = R



k (6.29a) k−1

ILLUSTRATIVE PROBLEM 6.12 Oxygen has a cp of 0.24 Btu/lbm·°R at a given temperature. Determine cv if its MW is 32. SOLUTION The MW of oxygen is 32. Therefore, R is 1545/32 = 48.28. Because cp – cv = R/J,

cv = c p −

R J

= 0.24 −

48.28 = 0.178 Btu/lbm⋅°R 778

261

The Ideal Gas

ILLUSTRATIVE PROBLEM 6.13 If k of oxygen is 1.4, determine cp and cv in SI units. SOLUTION From Equation 6.28a,

cv =

kJ R 8.314/32 = = 0.6495 kg⋅K k−1 1.4 − 1

Because cp = kcv,

c p = (1.4)(0.6495) = 0.9093

kJ kg⋅K

ILLUSTRATIVE PROBLEM 6.14 A gas having an R = 60 ft. lbf/lbm·°R undergoes a process in which Δh = 500 Btu/lbm and Δu = 350 Btu/lbm. Determine k, cp, and cv, for this gas. SOLUTION Because Δh = cpΔT and Δu = cvΔT, ∆h c p ∆T c p = = =k ∆u c v ∆T cv

Therefore,

k=

500 = 1.429 300

From Equation 6.28,



cv =

R 60 = J ( k − 1) (778)(1.429 − 1)

= 0.180 Btu/lbm⋅°R

and

cp = kcv

yielding cp = (1.429)(0.180) = 0.257 Btu/lbm·°R

262

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 6.15 A closed, rigid container with a volume of 60 in.3 contains 0.0116 lbm of a certain gas of 90 psia and 40°F (Figure 6.4). The gas is heated to 140°F and 108 psia, and the heat input is found to be 0.33 Btu. Assuming this to be a perfect gas, find the specific heat at constant pressure cp. SOLUTION When solving this type of problem, it is necessary to note carefully the information given and to write the correct energy equation for the process. Because the process is carried out at constant volume, the heat added equals the change in internal energy. Because the change in internal energy per pound for the ideal gas is cv(T2 – T1), the total change in internal energy for m pounds must equal the heat added. Thus, Q = m(u2 – u1) = mcv(T2 – T1)



Using the data of the problem, 0.33 = 0.0116cv(600 – 500) and cv = 0.284 Btu/lbm·°R To obtain cp, it is first necessary to obtain R. Enough information was given in the initial conditions of the problem to apply Equation 6.8 for R, pV = mRT, 60 = 0.0116(R) ( 460 + 40) 1728

(90)(144)

and

R = 77.6 ft. lbf/lbm·°R

Because c p − cv =

R J

c p = cv +



R J

c p = 0.284 +

77.6 = 0.384 Btu/lbm⋅°R 778

Initial conditions V m p T FIGURE 6.4 Illustrative Problem 6.15.

Final conditions

3

60 in 0.0116 lbs 90 psia (460 40)

Heat

V m p T

60 in3 0.0116 lbs 108 psia (460 140)

263

The Ideal Gas

6.4 Entropy Changes of Ideal Gas In the rest of this chapter, various nonflow processes of the ideal gas will be studied. It must be remembered that the energy quantities called work and heat depend on the path that the gas undergoes, whereas enthalpy, entropy, and internal energy are determined by the final and initial states of the fluid because they are properties. Consider a gas that undergoes a change in state from A to B, as shown in Figure 6.5a, on pressure–volume coordinates. In this process (path A, B), the pressure, volume, and temperature change to the final values so that p2, v2, and T2 are greater than p1, v1, and T1. To go from state A to state B, let us select the two separate reversible paths A, C and C, B. Path A, C is carried out at constant volume, and path C, B is carried out at constant pressure. These paths are shown in Figure 6.5a as dashed lines and are similarly shown on T–s coordinates in Figure 6.5b. It is important to note that the properties at the initial and final states will determine the changes in enthalpy, entropy, and internal energy, but that the path selected between these states will determine the energy interchange as both heat and work. The change in entropy for a gas undergoing the reversible paths A, C and C, B can readily be determined. For the constant-volume path, q = Δu = cvΔT, and for the constantpressure path, q = Δh = cpΔT. Therefore, from the definition of the property entropy, ∆s =



q c ∆T = v T T

c p ∆T

+

T

v

(6.30) p

p p2 , v1 , Tc

B

C

p2 , v2 , T2

A p1 , v1 , T1 (a)

v

T B C

A (b) FIGURE 6.5 General gas process. (a) p–v diagram. (b) T–s diagram.

s

264

Thermodynamics and Heat Power

where the subscripts v and p refer to the constant-volume and constant-pressure processes, respectively. To obtain the total change in entropy for a finite process between the temperature limits of T2 and T1, it is necessary to sum all the terms of Equation 6.30 over the entire temperature range. Let us first assume that the specific heats are independent of temperature. It is necessary only to sum the ΔT/T values. This process has already been illustrated, but it is worth repeating at this point. Figure 6.6 shows a plot of 1/T as a function of T. By selecting a value of ΔT, as shown, the shaded area is ΔT/T. Thus, the sum of the ΔT/T values is the area under the curve between the desired temperature limits. By the methods of the calculus, it can be shown that this area is ln T2/T1. By performing the summation required by Equation 6.30 and again noting that the specific heats are constant,

∆s = c v ln



Tc T1

+ c p ln v

T2 Tc

(6.31)

p

Equation 6.31 can be put into a more useful form by noting that for the constant-volume process, Equation 6.9 yields Tc/T1 = p2/p1, and for the constant-pressure process, T2/Tc = v2/ v1. Thus,



∆s = cv ln

p2 v + c p ln 2 p1 v1

(6.32)

By dividing both sides of Equation 6.32 by cv and noting that k = cp/cv, we obtain p ∆s v = k ln 2 + ln 2 (6.33) cv v1 p1



1 T

T 1 Area = T × = T T T T1 FIGURE 6.6 Evaluation of ΔT/T.

T2

T

265

The Ideal Gas

Another form of Equation 6.32 can be derived by using Equations 6.24 and 6.33:

∆s = c p ln

T2 R p2 − ln T1 J p1

(6.34)

Equation 6.34 can also be derived in the following alternative way, from Chapter 4:

v∆p J

T∆s = ∆h −

Dividing through by T and noting that Δh = cpΔT and v/T = R/p,

∆s = c p

∆T R ∆p − T J p

Summing each term on the right-hand side of this equation gives us Equation 6.34. The utility of these considerations and equations will become apparent as the individual gas processes are studied. Students should note that Equations 6.31 through 6.34 are valid for any process of an ideal gas when the specific heats are constant. Note that in SI units, the J in the preceding equations is not necessary. CALCULUS ENRICHMENT In Chapter 4, we wrote the first of the Gibbs or T ds equations as T  ds = du + p dv (a) Assuming that we are dealing with an ideal gas, du = cvdT (b) and

pv = RT (c)

Inserting Equations b and c into Equation a and solving for ds,

∫

s2

s1

ds =

∫

p dv du + = T T

∫

∫

T2

T1

cv

dT + T

∫

v2

v1

R

dv (d) v

For constant specific heats, Equation d is integrated to yield

s2 − s1 = ∆s = c v ln

T2 v + R ln 2 (e) T1 v1

266

Thermodynamics and Heat Power

Equation e can be rearranged to yield Equation 6.32 using cp – cv = R. Thus,

∆s = cv ln

T2 v + (c p − cv ) ln 2 (f) T1 v1

and

∆s = cv ln

Combining the cv terms and using



T2 v v + c p ln 2 − c v ln 2 (g) T1 v1 v1

p1 v1 p2 v2 = yields T1 T2

∆s = cv ln

p2 v + c p ln 2 (h) p1 v1

which is Equation 6.32.

ILLUSTRATIVE PROBLEM 6.16 One pound of air (MW = 29) expands from 100 psia and 100°F to 15 psia and 0°F. Determine the change in entropy. Assume that cp of air is 0.24 Btu/lbm·°R and is constant. SOLUTION On the basis of the data given, we can use Equation 6.34 to solve this problem. Thus,

∆s = 0.24 ln

460 R 15 − ln 460 + 100 J 100

We can make these logarithms positive quantities by noting that log x = –log 1/x. Therefore, − ∆s = 0.24 ln

460 + 100 R 100 − ln 460 J 15

= 0.24 ln

560 1545/29 100 − ln 460 778 15



and

− ∆s = 0.04721 − 0.1299 = 0.0827 or ∆s = 0.0827 Btu/lbm⋅°R

267

The Ideal Gas

ILLUSTRATIVE PROBLEM 6.17 Solve Illustrative Problem 6.16 using Equation 6.32. SOLUTION Because cp and R are given, let us first solve for cv.

cp =

0.24 =

Rk J ( k − 1) (1545/29)( k ) 778( k − 1)

Solving for k yields



k = 1.399 and c v =

cp k

=

0.24 = 0.1716 Btu/lbm⋅°R 1.399

Using Equation 6.32 gives us



∆s = cv ln

p2 v + c p ln 2 p1 v1

But



v2 T p1 460 + 0 = 2 = v1 T1 p2 460 + 100

100 = 5.476 15

Thus,



15 + 0.24 ln 5.476 100 = −0.3255 + 0.4081 = 0.0826 Btu/lbm⋅°R

∆s = 0.1716 ln

The agreement is very good.

268

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 6.18 Two kilograms of oxygen expand from 500 kPa and 100°C to 150 kPa and 0°C. Determine the change in entropy if cp = 0.9093 kJ/kg·K and remains constant. SOLUTION Using Equation 6.34 and dropping J gives us

∆s = 0.9093 ln

8.314 150 273  −  ln = 0.029 kJJ/kgK 273 + 100 32 500

For 2 kg, ΔS = 2(0.02901) = 0.05802 kJ/K

ILLUSTRATIVE PROBLEM 6.19 An ideal gas with constant specific heats undergoes a change during which its specific volume is halved and its entropy increases by an amount equal to one quarter of its specific heat at constant volume. Assuming that k is 1.4, what was the increase in pressure for this process? SOLUTION From Equation 6.33 and the data given, p ∆s v = k ln 2 + ln 2 cv v1 p1



p 1/4cv 1/2 = 1.4 ln + ln 2 cv p1 1

or p 1 1 − 1.4 ln = ln 2 4 2 p1

1 2

But –1.4 ln = –1.4(ln 1 – ln 2) = –1.4(0 – 0.693) = 1.4(0.693). Thus,



p 1 + 1.4(0.693) = ln 2 4 p1 ln

p2 = 1.22 p1

and by taking antilogarithms,

p2 = 3.4 or p2 = 3.4 p1 p1

269

The Ideal Gas

6.5 Nonflow Gas Processes In the following portions of this section, five nonflow gas processes are analyzed in detail. These processes are constant-volume, constant-pressure, isothermal, isentropic, and polytropic. The derivations in each case proceed from a consideration of the equation of state and the equation of the path. Paths shown as dashed lines indicate nonequilibrium paths. 6.5.1 Constant-Volume Process (Isometric Process) The constant-volume process is best exemplified by a closed tank from which heat is either added or removed. In Figure 6.7, the indicated path is one in which heat is being added. From Equation 6.9, the equation of the path can readily be written as p1 p2 = T1 T2



(6.35)

The applications of the first law yield the relationship between the heat added and the final state condition. Because there is no volume change, no work is done. Thus, q = u2 – u1 = cv(T2 – T1) (6.36)

Also,

w = 0

(6.37)

because there is no change in volume. The change in entropy for this process is given directly by the defining equation for entropy or as the volume part of Equation 6.31. In either case,

∆s = cv ln

T2 T1

(6.38)

Two further considerations complete all the necessary relations for the constant-volume process. The first of these states that the specific heat for this process is by definition cv p

T

2

2 v = constant

1 (a)

1 v

FIGURE 6.7 Constant-volume process. (a) p–v diagram. (b) T–s diagram.

(b)

s

270

Thermodynamics and Heat Power

and that we have assumed it to be constant. The second consideration (whose utility will appear later) determines the exponent in the equation pvn = constant that will make this equation fit the constant-volume process. Rearranging this equation gives us p1 p2



v1 v2

n

= 1 or

p v1 = 2 v2 p1

1/n

(6.39)

Because v1/v2 = 1, it becomes necessary for 1/n to be zero or n → ∞

(6.40)

ILLUSTRATIVE PROBLEM 6.20 If 1/2 lb. of gas is heated at constant volume from 70°F to 270°F, determine the change in entropy for this process. Assume that cv = 0.17 Btu/lbm·°R. SOLUTION For this process, T1 = 530°R and T2 = 730°R. Therefore, ∆s = c v ln

T2 730 = 0.17 ln T1 530

∆s = 0.0544 Btu/lbm⋅°R ∆S =

1 (0.0544) = 0.0270 Btu/°R 2

ILLUSTRATIVE PROBLEM 6.21 If 0.2 kg of air is heated at constant volume from 20°C to 100°C, determine the change in entropy for the process. Assume that cv is constant and equal to 0.7186 kJ/kg·K. SOLUTION T2 100 + 273 = 0.7186 ln T1 20 + 273 kJ = 0.1735 kg ⋅ K

∆s = c v ln

For 0.2 kg,

∆S = (0.2)(0.1735) = 0.03470

kJ K

271

The Ideal Gas

ILLUSTRATIVE PROBLEM 6.22 The entropy of 1 lb. of gas changes by 0.0743 Btu/lbm·°R when heated from 100°F to some higher temperature at constant volume. If cv = 0.219 Btu/lbm·°R, determine the higher temperature for this process. SOLUTION

∆s = cv ln

T2 T1

0.0743 = 0.219 ln

T2 100 + 460

or

ln

T2 = 0.3393 560

Taking antilogarithms gives us



T2 = e 0.3393 560 = 1.404 T2 = 786.2°R

ILLUSTRATIVE PROBLEM 6.23 If 1.5 kg of a gas is heated at constant volume to a final temperature of 425°C and the entropy increase is found to be 0.4386 kJ/K, determine the initial temperature of the process. Use cv = 0.8216 kJ/kg·K. SOLUTION As before, ∆S = mcv ln

T2 T1

0.4386 = 1.5 × 0.8216 ln

273 + 425 T1

272

Thermodynamics and Heat Power

or ln

698 = 0.35589 T1 698 = e 0.35589 = 1.4275 T1

and

T1 =

698 = 489 K = 216°C 1.4275

6.5.2 Constant-Pressure Process (Isobaric Process) The constant-pressure process is a good approximation to many of the common physical processes with which we are familiar. The combustion of fuel in a boiler or a gas turbine engine, the flow of fluids, the flow of air in ducts, and other processes can be used to illustrate constant pressure. Both the nonflow and flow processes yield to the following analysis: For an ideal gas, Equation 6.9 once again gives us the equation of the path for this process.

v1 T1 = v2 T2

(6.41)

From the first law, the constant-pressure process has as its energy equation (neglecting kinetic and potential energy terms)

q = h2 – h1

(6.42)

and consequently,

q = cp(T2 – T1) (6.43)

where cp is the specific heat of the process. During the constant-pressure process shown in Figure 6.8, work is removed as heat is added. The amount of work is the area under the pv curve, which is

p(v2 – v1) = p2v2 – p1v1 (6.44)

Application of Equation 6.9 and reduction of the mechanical units of Equation 6.44 to thermal units yields

p2 v2 − p1 v1 =

R (T2 − T1 ) J

(6.45)

273

The Ideal Gas

T

p 1

2

2

p = constant

1 v1

v2 v

s

(a)

(b)

FIGURE 6.8 Constant-pressure process. (a) p–v diagram. (b) T–s diagram.

The exponent of pvn that is applicable to this process is found as follows: p2 p1



v2 v1

n

= 1 but

p2 =1 p1

Therefore, n = 0 for a constant-pressure process. Finally, the change in entropy for this process is

∆s = c p ln

T2 (6.46) T1

ILLUSTRATIVE PROBLEM 6.24 In a gas turbine cycle, heat is added to the working fluid (air) at constant pressure. Determine the heat transferred, the increase in entropy, and the flow work change per pound of air if the initial pressure is 100 psia and the temperature goes from 70°F to 400°F. The specific heat cp for this process is constant and equals 0.24 Btu/lbm·°F. SOLUTION This process is shown graphically in Figure 6.11. From the energy equation for the constant-pressure process, the heat transferred is Δh. Therefore, q = ∆h = c p (T2 − T1 ) = (0.24)(860 − 530) o the system) = 79.2 Btu/lb (into

860 T ∆s = c p ln 2 = 0.24 ln 530 T1 = 0.116 Btu/lbm⋅°R

274

Thermodynamics and Heat Power

The flow work change is

p2 v2 p1v1 R − = (T2 − T1 ) J J J (1545/29)(860 − 530) 778 = 22.6 Btu/lbm =



In addition to each of the assumptions made in all the processes being considered, it has further been tacitly assumed that these processes are carried out quasi-statically and without friction.

ILLUSTRATIVE PROBLEM 6.25 Heat is added to a turbofan engine at constant pressure. If the air temperature is raised from 20°C to 500°C in the combustion chamber, which is operated at 1 MPa, determine the heat transferred and the increase in entropy per kilogram of air. Use cp = 1.0062 kJ/kg·K. SOLUTION We proceed as in Illustrative Problem 6.24. q = Δh = cp(T2 – T1) = (1.0062)(500 – 20) = 483.0 kJ/kg and



∆s = c p ln

T2 500 + 273 = 1.0062 ln T1 20 + 273

= 0.9761kJ/kg ⋅ K

6.5.3 Constant-Temperature Process (Isothermal Process) The expansion process shown in Figure 6.9 could conceivably be one in which a gas expands in a hot cylinder. Heat would be transferred from the hot cylinder walls to maintain the gas temperature constant. The path equation is p1v1 = P2v2 = constant (6.47)

275

The Ideal Gas

p

T

1

1

2

pV = constant 2 (a)

v

(b)

s

FIGURE 6.9 Isothermal process. (a) p–v diagram. (b) T–s diagram.

and from the first law, it can be deduced that both the changes in enthalpy and internal energy for this process are zero because the temperature is constant. Therefore, the work of the isothermal process must exactly equal the heat transferred. Thus,



q=

w J

(6.48)

or

q = w  in SI units

(6.49)

Let us evaluate the change in entropy for the isothermal nonflow process from Equation 6.32 as follows:

∆s = c p ln

v2 p + c v ln 2 v1 p1

(6.50)

Because p1v1 = p2v2, v1 p2 = v2 p1





∆s = c p ln

v2 v + c v ln 1 v1 v2

(6.51)

(6.52)

However,



ln

v1 v = − ln 2 v2 v1

(6.53)

276

Thermodynamics and Heat Power

Therefore,

∆s = c p ln

v1 v − cv ln 2 v2 v1

(6.54)

∆s = ln

v2 (c p − c v ) v1

(6.55)

R v2 ln J v1

(6.56)

∆s =

pv v2 R v2 ln = ln TJ v1 J v1

(6.57)

∆s =

pv v2 v ln =R ln 2 T v1 v1

(6.57a)

Factoring yields But cp – cv = R/J. Therefore, ∆s =

Equation 6.56 can also be written as In SI units, Equation 6.57 is

We can now determine the energy interchange as heat and also the work by noting that

∆s =

q or q = T∆s T

(6.58)

But from Equation 6.48, q = w/J. This gives us

w RT v2 p1v1 v2 p2 v2 v2 ln = q = T∆s = ln = ln = J J v1 J v1 J v1

(6.59)

In SI units,

w = p2 v2 ln

v2 v1

(6.59a)

Because there is no change in temperature for this process and a finite quantity of energy as heat has crossed the system boundaries, the definition of specific heat requires that the specific heat of the isothermal process be infinite. Also, in order for both pv and pvn to be the equation of the path, n must be unity.

277

The Ideal Gas

ILLUSTRATIVE PROBLEM 6.26 If 0.1 lb. of nitrogen is kept at a constant temperature of 200°F while its volume is increased to twice its initial volume, determine the heat added and work out of the system. SOLUTION From Equation 6.59, we have

q=

RT v2 ln J v1

(1545/28)( 460 + 200) 2 ln 778 1 = 32.4 Btu/llbm =

For 0.1 lb., Q = 0.1 × 32.4 = 3.24 Btu (added to system). The work out of the system is equal to the heat added; thus,



W = 3.24 Btu (out of system) J

ILLUSTRATIVE PROBLEM 6.27 If 1 kg of oxygen has its volume halved at a constant temperature of 50°C, determine the heat added and the work out of the system. SOLUTION q = RT ln

v2 8.314 1 = (273 + 50)ln v1 32 2

= −58.17

kJ kg

( heat out of system)

Therefore,

w = q = −58.17

kJ (into system) kg

278

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 6.28 Determine the change in entropy in Illustrative Problem 6.27. SOLUTION For constant temperature,

q T

∆s =

Therefore,

∆s =

−58.17 kJ/kg = −0.1801 kJ/kg ⋅ K (50 + 273)K

6.5.4 Constant-Entropy Process (Isentropic Process) The turbofan engine and the gas turbine engine produce useful work by the expansion of hot combustion gases in turbines. These processes are ideally isentropic. It will be recalled that the isentropic process is a reversible, adiabatic process. An alternative definition is a process carried out with no change in entropy. Equation 6.33 serves to define this path:

p ∆s v = k ln 2 + ln 2 = 0 cv v1 p1

(6.33)

or

v ln 2 v1

k

= ln

p2 (6.60) p1

Taking antilogarithms and rearranging yields

p1 v1k = p2 v2k (6.61)

Equation 6.61 is the path equation for this process, and by using the equation of state (Equation 6.9), it is possible to rewrite Equation 6.61 in terms of pressures and temperatures as



p v2 = 1 v1 p2

1/k

(6.62)

279

The Ideal Gas

and p1v1/T1 = p2v2/T2 from Equation 6.9. Therefore, p1 T2 p = 1 p2 T1 p2



1/k

Rearranging gives us p T1 = 1 T2 p2



( k − 1)/k

(6.63)

Similarly, we obtain the p, v relation from Equation 6.61 as p1 v = 2 P2 v1



k

or p1 v1k = p2 v2k (6.64)

From Equation 6.9, we have p1/p2 = (v2/v1)(T1/T2). Substitution into Equation 6.64 yields

T1 v = 2 T2 v1

k −1

(6.65)

Equations 6.61, 6.63, and 6.65 define both the state and path of an ideal gas undergoing an isentropic change. Because the energy interchange as heat is zero and there is a finite change in temperature, the specific heat for this process must be zero. Note that the process specific heat is defined by the path and differs from the specific heat at constant pressure or the specific heat at constant volume. These other specific heats serve to define the enthalpy and internal energy of the gas at the state conditions at the endpoints of the path. By the identification of pvk with pvn, the exponent n must equal the isentropic exponent k for the isentropic process. The work of the nonflow process shown in Figure 6.10 can be evaluated by noticing that the work done in a nonflow process in the absence of heat transfer equals the change in internal energy. Therefore, work = u1 − u2

work = c v (T1 − T2 ) cv =

R J ( k − 1)

Therefore,



w R(T1 − T2 ) or J J ( k − 1)

R(T2 − T1 ) Btu/lbm (6.66) J (1 − k )

Again, note that in SI units, the conversion factor J is not included.

280

Thermodynamics and Heat Power

p

T

1

1 The isentropic process is reversible. All path lines are solid.

pvk = constant

2

2 s

v (a)

(b)

FIGURE 6.10 Isentropic process. (a) p–v diagram. (b) T–s diagram.

CALCULUS ENRICHMENT The work of the nonflow, isentropic process can be obtained by integration of the area under the p–v curve as shown in the figure below. Therefore,

∫

w=

2

1

p d v (a)

1

pv k = const p 2

p

dv

v

The path of the isentropic process is given by pvk = constant. Inserting this into Equation a,

w=

∫

2

1

c d v (b) vk

Integrating,



v − k +1 w=c −k + 1

2

= 1

c v2− k + 1 − v1− k + 1 (c) −k + 1

281

The Ideal Gas

Because c = pv k = p1 v1k = p2 v k2 , Equation c becomes

w=

p2 v2 − p1 v1 (d) −k + 1

w=

R(T2 − T1 ) (e) 1− k

but pv = RT;

Equation e is the same as Equation 6.66 in appropriate units.

ILLUSTRATIVE PROBLEM 6.29 One pound of air expands isentropically from 5 atm absolute to 1 atm absolute. If the initial temperature is 1000°R, determine the final state and the work done by the air if k is 1.4 over this range of temperature. SOLUTION From Equation 6.63,

T2 = T1

p2 p1

( k − 1)/k

1 = 1000 5

( 1.4−1/1.4 )

= 631°R

From Equation 6.66,



work =

R(T2 − T1 ) (1545)(631 − 1000) = (29)(778)(1 − 1.4) J (1 − k )

= 63 Btu/lbm (out )

282

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 6.30 If the initial temperature in Illustrative Problem 6.29 is 500°C, determine the final state and the work done. Assume a mass of 1 kg. SOLUTION p2 p1

T2 = T1

( k − 1)/k

= (500 + 273)

1 5

( 1.4 − 1)/1.4

= 488.06 K = 215.06°C work =

R(T2 − T1 ) 8.314 215.06 − 500 = 1− k 29 1 − 1.4

= 204.2

kJ (out) kg

ILLUSTRATIVE PROBLEM 6.31 A gas expands isentropically from 5 to 1 MPa. If the initial temperature is 800°C and the final temperature is 500°C, determine k for this gas. SOLUTION Because



p T2 = 2 T1 p1 273 + 500 1 = 273 + 800 5

( k − 1)/k

( k − 1)/k

Taking the logarithms of both sides of this equation yields



ln

k−1 1 273 + 500 = ln k 5 273 + 800

283

The Ideal Gas

or k−1 = k



ln

273 + 500 273 + 800 = 0.2038 1 ln 5

Solving, k = 1.256

6.5.5 Polytropic Process Each of the processes discussed in this section can have its path equation written in terms of

pvn = constant

(6.67)

which is known as the polytropic equation and is used, in general, to characterize any mechanically reversible process. It is also used as an approximation for real processes. A diagram is shown in Figure 6.11. To recapitulate those processes already considered, see Table 6.3. If each of these processes is plotted on pv and TS coordinates (basically, the superposition of Figures 6.7 through 6.10), it is possible to show the entire spectrum of n values. Observe in Figure 6.12 that going from an initial state of pressure and volume, represented by the point where n = ∞ and n = 0 axes meet, to a second state, the exponent n determines the slope of the p–v path. At greater values of n, the slope is steeper. Since work is the area under the p–v curve, one should strive for the isothermal process in compression (to minimize work) or in expansion (to maximize work). Figure 6.13 shows these relationships on a T–s diagram.

p

T 1

1 pvn = constant 2

2 v (a) FIGURE 6.11 Polytropic process. (a) p–v diagram. (b) T–s diagram.

s (b)

284

Thermodynamics and Heat Power

TABLE 6.3 Values of n for Polytropic Processes n

Process Constant volume Constant pressure Isothermal Isentropic Polytropic

p

n=1

n=

Compression

n=k

∞ 0 1 k –∞ to + ∞

Isometric (constant volume)

Isothermal Isentropic n=0

n = 0 Constant pressure (isobaric)

n=1

n=

Isothermal (constant temperature) n=k Isometric

Isentropic (constant entropy) Expansion v

FIGURE 6.12 Polytropic processes. T n=k Isometric n=

Isobaric n=0

n=1

Isothermal

Constant temperature

Constant pressure Constant volume

n=k

n=1

Isentropic s

FIGURE 6.13 Polytropic processes.

285

The Ideal Gas

The pressure, temperature, and volume relations for the polytropic process corresponding to Equations 6.62, 6.63, and 6.65 can be written as follows:









1/n

p v2 = 1 v1 p2

p1 v = 2 p2 v1

(6.68)

n

or p1 v1n = p2 v2n

p T1 = 1 T2 p2

(6.69)

( n− 1)/n

T1 v = 2 T2 v1



(6.70)

n− 1



(6.71)

The work of the polytropic process can be determined by the same method used to obtain the work of the isentropic process. The result is



work =

p2 v2 − p1 v1 1− n

work =

R(T2 − T1 ) (6.73) J (1 − n)

(6.72)

and in terms of thermal units



To determine the specific heat of the polytropic process, we shall use the energy equation for the nonflow process:



q = (u2 − u1 ) +

w J

(6.74)

It is convenient to define the heat transferred by cn(T2 – T1) = q (6.75)

286

Thermodynamics and Heat Power

where cn is the polytropic specific heat. Substitution of Equations 6.73 and 6.75 into Equation 6.74 yields



R(T2 − T1 ) (6.76) J (1 − n)

cn (T2 − T1 ) = cv (T2 − T1 ) +



cn = c v +

R (6.77) J (1 − n)

and

cn =

Jcc − nJc v + R (6.78) J (1 − n)

Using Equation 6.29, we have

cn =

c p − nc v (1 − n)

(6.79)

or

cn = c v

k−n (6.80) 1− n

Note that cn can be positive or negative depending on the values of n and k. Substitution of cn into Equation 6.75 gives the heat transferred in the polytropic process:



q = cv

k−n (T2 − T1 ) 1− n

(6.81)

The change in entropy for the polytropic process can be arrived at by using Equation 6.30 and assuming that cn is independent of temperature:

∆s =

q cn ∆T (6.82) = T T

Evaluating Equation 6.82 as done previously by summing the ΔT/T terms yields

∆s = cn ln

T2 T1

(6.83)

287

The Ideal Gas

ILLUSTRATIVE PROBLEM 6.32 For an internal combustion engine, the expansion process can be characterized by pv1.3 = constant. If the ratio of specific heats for this gas is 1.4 and the specific heat at constant pressure is 0.24 Btu/lbm·°R, determine the heat transferred as the gas expands from 1500°R. Also evaluate the work done and the change in entropy for the process. R equals 53.3 for this gas. SOLUTION From

cp cv



=k

cv =

0.24 = 0.171 1.4



Therefore,



cn = c v

k−1 = 0.171 1− n

1.4 − 1.3 = −0.0570Btu/lbm⋅°R 1 − 1.3

The negative sign of cn indicates that either the heat transfer for the process comes from the system or there is a negative temperature change while heat is transferred to the system. The heat transferred is cn(T2 – T1). Therefore, q = −0.0570(600 − 1500)

= 51.3 Btu/lbm (to the system)



The work done can be found using Equation 6.73, giving us



work =

R(T2 − T1 ) 53.3 600 − 1500 = 778 1 − 1.3 J (1 − n)

= 205.5 Btu/lbm (from the system)



The change in entropy Δs is given by 600 1500 1500 = −0.0570 − ln = 0.0522 Btu/lbm⋅°R 600

∆s = −0.0570 ln

288

Thermodynamics and Heat Power

ILLUSTRATIVE PROBLEM 6.33 Determine the ratio of the inlet to the outlet pressure in Illustrative Problem 6.32. SOLUTION From Equation 6.70, p T1 = 1 T2 p2



( n− 1)/n



For this problem,



p 1500 = 1 600 p2 2.5 =

p1 p2

( 1.3 − 1)/1.3

0.3/1.3

p1 p2

=

0.2308



Taking the logarithms of both sides of this equation yields

ln 2.5 = 0.2308 ln

p1 p2

p 0.9162 = ln 1 = 3.97 p2 0.2308



and

p1 = 52.99 p2



Keep in mind that when deriving the equations in this chapter, the specific heats were assumed to be constants, independent of temperature. The same assumption was made for k. When the variation of these quantities does not permit us to assume an essentially constant average value, the methods of the calculus must be employed. For these techniques, students are referred to the references. Table 6.4 summarizes the results of the derivations made for nonflow processes. In this table, the enthalpy and internal energies have also been tabulated, and it will be noted that these quantities depend only on the end states of the specified process and are independent of the path. This table has been included as a convenient reference. Students are cautioned against memorizing the table or using it without fully understanding the restrictions involved in each of the processes discussed.

289

The Ideal Gas

TABLE 6.4 Ideal Gas Relations (per Unit Mass of Gas, Closed System)a

Process → → p,v,T

Constant Volume V = Constant (Isometric)

Constant Pressure p = Constant (Isobaric or Isopiestic)

T1 p1 = T2 p2

T1 v1 = T2 v2

Isothermal T = Constant p1v1 = p2v2

Isentropic s = Constant p1v1k = p2 v2k T1 v = 2 T2 v1 p T1 = 1 T2 p2

w u2 – u1 q n c

h2 – h1 s2 – s1

a

0

p(v2 – v1)

cv(T2 – T1) cv(T2 – T1)

cv(T2 – T1) cp(T2 – T1)

∞ cv

0 cp

cp(T2 – T1)

cp(T2 – T1)

T c v ln 2 T1

T c p ln 2 T1

Polytropic pvn = Constant p1v1n = p2 v2n

k −1

T1 v = 2 T2 v1

( k − 1)/k

p T1 = 1 T2 p2

n− 1

( n − 1)/n

p2 v2 − p1v1 1− k

p2 v2 − p1v1 1− n

cv(T2 – T1) 0

cv(T2 – T1) cn(T2 – T1)

1 ∞

k 0

–∞ to +∞

0

cp(T2 – T1) 0

p1v1 ln

v2 v1

0 v p1v1 ln 2 v1

v R ln 2 v1

cn = c v

k−n 1− n

cp(T2 – T1) cn ln

T2 T1

The conversion factor J has been omitted from all equations. Care should be taken when using this table with English units.

The change in enthalpy and the change in internal energy for the ideal gas are useful quantities, and we can obtain these readily from the previous considerations in this chapter. Thus, for enthalpy, we can write h2 – h1 = cp(T2 – T1) (6.84) From Equation 6.9, we have T = pv/R, and from Equation 6.29, we have cp = R/J(k – 1). Substitution of these quantities in Equation 6.84 gives us



h2 − h1 =

R k J k−1

p2 v2 p1 v1 − (6.85) R R

Simplifying yields

h2 − h1 =

k ( p2 v2 − p1 v1 ) J ( k − 1)

(6.86)

290

Thermodynamics and Heat Power

or



h2 − h1 =

k ( p2 v2 − p1 v1 ) SI units (6.86a) k−1

Similarly, for internal energy, u2 – u1 = cv(T2 – T1) and

u2 − u1 =

k ( p2 v2 − p1 v1 ) (6.87) J ( k − 1)

or

u2 − u1 =

1 ( p2 v2 − p1 v1 ) SI units (6.87a) k−1

As a check on Equations 6.86 and 6.87, note that the ratio of h2 – h1 to u2 – u1 is the ratio of cp to cv, which it should be.

6.6 The Gas Tables The Gas Tables provide a convenient and most useful set of tables for the computation of gas processes. By designating Equation 6.9 as the equation of state, it has been possible to express the various thermodynamic properties of these gases in terms of their temperatures. For air at 32°F, the error in using this equation of state is of the order of 1% at 300 psia and only 0.1% at atmospheric pressure. In addition to using the equation of state of an ideal gas, the specific heats listed in these tables were based on spectroscopic data at zero pressure. The zero of entropy and enthalpy were chosen to be zero at zero degrees absolute. Use of the specific heats at zero pressure is equivalent to the assumption that the specific heat is a function of temperature only. The outline of the Gas Tables can be easily developed by considering that the specific heats are temperature functions. The enthalpy values are listed as functions of the absolute temperature, and the change in enthalpy for a process is just the difference for the values tabulated at the final and initial temperatures. Because ideal gas relations are used,

u2 − u1 = ( h2 − h1 ) −

R (T2 − T1 ) J

(6.88)

291

The Ideal Gas

The general expression for the change in entropy of an ideal gas with a variable specific heat can be obtained, and the change in entropy per unit mass between states 1 and 2 is then

s2 − s1 = φ2 − φ1 −

R p2 ln J p1

(6.89)

where ϕ is a function of the temperature given in the tables for each gas at each temperature. For an isentropic change,

ln

p2 J = (φ2 − φ1 ) p1 R

(6.90)

CALCULUS ENRICHMENT When the specific heat of an ideal gas is not constant, we need to return to the second Gibbs or T ds equation, namely, T  ds = dh – v dp (a) Using dh = cp dT and pv = RT for the ideal gas yields

ds = c p

dT R − dp (b) T p

It is possible to remove the constant R from the integral of Equation b. However, with cp = cp(T), that is, a function of temperature, cp cannot be removed from the integral. Therefore, we write

∫

s2

s1

ds =

∫

T2

c p dT

T1

T

− R ln

p2 (c) p1

The integral in Equation c is a function only of temperature. In the Gas Tables, the tabulated function is



∫

T2

T1

c p dT T

= φ2 − φ1 (d)

The change in entropy for an ideal gas with variable specific heats therefore is

∆s = s2 − s1 = φ2 − φ1 − R ln

p2 (e) p1

292

Thermodynamics and Heat Power

In English units,

s2 − s1 = φ2 − φ1 −

R p2 ln (f) J p1

where Equation f is the same as Equation 6.89. If we now use the first Gibbs or T ds equation, T  ds = du + p dv (g) Dividing by T and using du = cvdT,

∫

s2

s1

ds =

∫

T2

T1

cv dT v + R ln 2 (h) T v1

or

s2 − s1 =

∫

T2

T1

c v dT v + R ln 2 (i) T v1

For an isentropic process,

v2 + v1

− R ln

∫

If we now define the relative volume, vr = ln



vr =

1 R

∫

T2

T1

T2

T1

c v dT (j) T

v2 , v1 c v dT (k) T

The Gas Tables tabulate two other useful properties: the relative pressure pr and the relative volume vr. If we define the relative pressure pr as



ln pr =

φ (6.90a) R

then Equation 6.90 becomes



ln

pr 2 = (φ2 − φ1 ) (6.90b) pr 1

293

The Ideal Gas

Equating Equations 6.90 and 6.90b,

ln

pr 2 p = ln 2 (6.90c) pr 1 p1

or p2 pr 2 = for an isentropic process (6.90d) p1 pr 1



If we now use the definition of the relative volume vr as

vr = ln

v2 (6.90e) v1

we can show that vr 2 v2 = for an isentropic process (6.90f) vr 1 v1



The Gas Tables also have adopted the definition that vr =



RT pr

(6.91)

with the units of R selected so that vr is the specific volume in cubic feet per pound when the pressure is in psia for those tables based on a unit mass. When the mass is the poundmole, vr is the molal specific volume in cubic feet per pound-mole when the pressure is psia. The following problems will serve to illustrate the use of the abridged air table, which is given in Appendix 2, Table A.20. ILLUSTRATIVE PROBLEM 6.34 Determine the change in enthalpy, internal energy, and entropy when air is heated at constant pressure from 500°R to 1000°R. SOLUTION From the Table at 1000°R h = 240.98 Btu/lbm u = 172.43 Btu/lbm ϕ = 0.75042 Btu/lbm·°R

From the Table at 500°R h = 119.48 Btu/lbm u = 85.20 Btu/lbm ϕ = 0.58233 Btu/lbm·°R

294

Thermodynamics and Heat Power

The change in enthalpy is h2 – h1 = 240.98 – 119.48 = 121.5 Btu/lbm. The change in internal energy is u2 – u1 = 172.43 – 85.20 = 87.23 Btu/lbm. Because in the constant-pressure process – R ln(p2/p1) is zero, Δs = ϕ2 – ϕ1 = 0.75042 – 0.58233 = 0.16809 Btu/lbm·°R

ILLUSTRATIVE PROBLEM 6.35 Solve Illustrative Problem 6.29 using the Gas Tables. SOLUTION In this problem, the air expands from 5 atm absolute to 1 atm absolute from an initial temperature of 1000°R. At 1000°R, pr = 12.298 and h = 240.98 Btu/lbm. The value of the final pr = 12.298/5 = 2.4596. Interpolation in the air table yields the following: T



620 +

pr

620

2.249

640

2.4596 2.514

2.4596 − 2.249 × 20 = 635.9 or 636°R 2.514 − 2.249

The work done in an isentropic nonflow expansion is work = u1 – u2 = 172.43 – 108.51 = 63.92 Btu/lbm where the value of u2 is obtained by interpolation at 636°R, and the value of u1 is read from the air table at 1000°R.

The fact that the results found by using the Gas Tables agree well with those found from the ideal gas relations is not a coincidence. In all these problems, the pressures were low and the temperatures relatively high. Under these conditions, it would be expected that these gases would behave much like ideal gases. The principal differences are caused by the fact that the specific heats vary with temperature. The Gas Tables take this variation into account and reduce the work of computations considerably.

The Ideal Gas

295

A computerized table of properties of air is available at the CRC Press website. Use the Downloads/Updates tab at http://www.crcpress.com/product/isbn/9781482238556. Properties of other common gases (carbon dioxide, carbon monoxide, hydrogen, nitrogen, oxygen, and water vapor) are available as well.

6.7 Steady Flow Gas Processes In a manner similar to that for nonflow gas processes, the steady flow of an ideal gas can be analyzed. The steady-flow energy equation, the ideal gas law, and the definitions of specific heat and entropy are utilized. These are applied to a control volume such as that shown in Figure 3.8. In most ideal gas flow processes, the K.E. and P.E. terms are negligible. Thus, as shown in the calculus enrichment of Section 3.4.2, the differential reversible work per unit mass flowing is dw = −v dp (6.92) From this equation, we see that reversible work is a function of specific volume, the inverse of fluid density. Thus, for turbomachinery such as a compressor, which consumes work, the greater the density of the fluid, the less the work required for a given pressure differential. Conversely, for devices that produce work such as a turbine, the least density fluid is desired. Thus, the steam turbine cycle described in Chapter 8 expands a gas (steam) to produce work and compresses a liquid (water) when input work is required. Equation 6.92 may be integrated to obtain relationships for flow work for the same various processes that were analyzed in Section 6.5. The ideal gas relationships for pressure, temperature, specific volume, specific heats, and entropy apply to flow as well as nonflow processes. To solve steady-flow problems, note that the mass flow rate is assumed to be constant; the volume flow rates may vary from the inlet to the outlet of the device. The power developed or consumed by the device is found by multiplying the specific work w by the mass flow rate. For conservation, all the energy entering the system must equal that leaving the system. For most steady-flow gas problems, the potential and kinetic energy changes are insignificant relative to the enthalpy changes. Thus, the energy equation becomes dq = dh – dw = dh − v dp (6.93) This equation is solved by integration. For constant specific heat, the integral of dh is h2 – h1 = cp(T2 – T1) The integral of the work term depends on the process, which will now be discussed. Note that after finding the work per unit mass, w, the power is found by multiplying w by the  Heat transfer can then be found from Equation 6.93. appropriate mass flow rate, m.

296

Thermodynamics and Heat Power

6.7.1 Constant-Specific Volume Process When the specific volume of the fluid remains constant, this is equivalent to an incompressible flow problem. Even when a gas is compressed just slightly, the assumption of incompressibility is valid. Integration of Equation 6.92 shows the work to be

w = −v(p2 − p1) (6.94)

Here, subscripts 1 and 2 refer to the entrance and exit conditions, respectively. Utilizing the ideal gas law, this is equivalent to a process that depends only on the temperature difference between the inlet and the outlet, as, in SI units:

w = −R(T2 − T1) (6.95)

In solving problems involving a constant specific volume of an ideal gas, the ideal gas law yields the relationship p1 T1 =  . (6.96) p2 T2



ILLUSTRATED PROBLEM 6.36 A small compressor receives 0.70 m3/s of air at 70°C and 101 kPa. It discharges the air at 100°C and 110 kPa. If the air is considered incompressible, find the compressor power required. SOLUTION Assuming air as an ideal gas, the first law for a steady-flow system can be written as q = cp(T2 – T1) + w  = mw  . We find m  since W  from the equation of state To find power, we must find m  pV = mRT

Thus,

 = (101 kPa)(0.70 m 3/s)/(0.287 kJ/kgK )(343 K ) = 0.718 kg/s m

Solving for w yields w = −R(T2 − T1) = −0.287 kJ/kgK × (373 K – 343 K) = –8.61 kJ/kg

 = mw  = 0.718 kg/s × (−8.61 kJ/kg) = −6.18 kW W



A negative answer is expected since a compressor takes in power.

297

The Ideal Gas

6.7.2 Constant-Pressure Process It can be seen from Equation 6.93 that in the absence of kinetic and potential energy effects, no work is done in a constant pressure open system. The first law then yields

 p (T2 − T1 ) (6.97) Q = mc

Open systems that typify the constant pressure types are heat exchangers where a cold fluid is used to cool a hotter fluid flowing through it. Both fluids flow at constant pressure, with the hotter one losing heat from its entrance at point 1 to its exit at point 2. The coolant gains heat going from its entrance at point 3 to its exit at point 4. Most heat exchangers are well insulated and may be considered adiabatic. Thus,

 ph (T2 − T1 ) = − mc  pc (T4 − T3 ) mc

where cph is the specific heat of the hot fluid and cpc is the specific heat of the cold fluid. Note that the negative sign is needed because the heat transfers are going in opposite directions. Heat exchangers are discussed in more detail in Chapter 11. 6.7.3 Constant-Temperature Process Next, the isothermal steady-flow process for the ideal gas is considered. Here, the relationship pv = constant is substituted into Equation 6.92, which is then integrated to yield

w = p1 v1 ln

p1 (6.98) p2

Using the ideal gas law, this relationship can also be written as

w = RT ln

p1 (6.99) p2

Since the temperature is constant, there is no change in enthalpy for such processes. In practice, reversible constant temperature processes are never realized but are a goal to shoot for as they represent the minimum work input for compression and the maximum work output for expansion (see Section 6.5.5). This is also what makes the Carnot cycle with its two constant temperature processes exist only in the ideal state. Note that even though the temperature may be constant, there can still be heat transfer equal to the work being done. 6.7.4 Isentropic Process Next, the isentropic steady-flow ideal gas process is considered. The general path equation is given in Equation 6.67, which may be substituted into Equation 6.92 with n = k. The integration of this equation yields

w=

k( p2 v2 − p1 v1 ) (6.100) 1− k

298

Thermodynamics and Heat Power

The ideal gas law may be used to find alternate expressions for Equation 6.98 that are more useful for the values given in a particular problem. The following is a useful relationship between pressures and temperatures for a process from state 1 to state 2: p T2 =  2 T1 p1



k −1 k

(6.101)



If only temperatures are known, the following expression may be used to find work per unit mass flowing:

w = 

kR(T2 − T1 ) (6.102) 1− k

In many cases, only the initial temperature and pressure ratio of a process are known. In such cases, the manipulation of the work expression yields kRT1 w12 =   1− k



P2 P1

k −1 k

− 1 (6.103)

These equations are used to solve reversible adiabatic processes, which frequently apply to compressor and turbine problems, which often provide only initial conditions and pressure or compression ratios. ILLUSTRATIVE PROBLEM 6.37 The input to a compressor is air at 101 kPa and 30°C. The pressure ratio is 5. If the flow rate of the air is 100 kg/min, find (a) exit air temperature and (b) power consumed. SOLUTION Using Equation 6.101, the exit temperature is

T2 =  T1



p2 p1

k −1 k

=   303(5)0.2857   = 479.9 K or 2006.9°C

The work is found using Equation 6.103:



kRT1 w12 =   1− k

P2 P1

k −1 k

−1 =

1.4   ×   0.287   ×   303 [(5)0.2857 − 1] =   −177.7   kJ/kg −0.4

The power consumed is

 = mw  = 100 × (−177.7 )/ 60 = −296.16 kW W



299

The Ideal Gas

6.7.5 Polytropic Process Finally, the polytropic process may be analyzed as Section 6.7.4 with the exponent n instead of k. The integration of Equation 6.92 yields, for this case,

w=

n( p2 v2 − p1 v1 ) (6.104) 1− n

Note that in the equations for polytropic processes, they may be stated in terms of temperatures only by invoking the ideal gas law pv = RT as in Equation 6.100 with n instead of k. For problems involving turbomachinery, the most commonly used equation for work is Equation 6.103 with n instead of k: nRT1 w =  1− n



P2 P1

n− 1 n

− 1 (6.105)

Also note that in polytropic processes, there is usually heat transferred into or out of the control system. For steady-flow processes, the relationships for specific heat, internal energy change, enthalpy change, and entropy change are the same as for the nonflow processes. It is suggested that students utilize these results to construct a chart similar to that of Table 6.4 for steady-flow processes. It should be remembered that these results are for work per unit mass and are given in SI units. To find the power or the heat transfer rate, multiply the  equations given above by the mass flow rate m. Heat transfer in a polytropic process is found from the first law, Equation 6.93, finding work and the change in enthalpy as a function of the temperature change. There is a shortcut found by creating an artificial specific heat, cn, defined as follows: cn =   c v



k−n (6.106) 1− n

which allows heat transfer to be calculated directly as

q = cn(T2 – T1) (6.107) ILLUSTRATIVE PROBLEM 6.38 A turbine receives 120 lbm/min of air at 60 psia and 2000°R and expands it polytropically (n = 1.5) to 14.7 psia. Find the power generated and the heat transfer rate. SOLUTION The exit temperature is found from Equation 6.101:



T2 =  T1

p2 p1

k −1 k

14.7 = 2000 60

0.5 1.5

  = 1251.47°R

300

Thermodynamics and Heat Power

The work is found from Equation 6.105:



nRT1 w =  1− n

P2 P1

n− 1 n

1.5   ×   53.34   ×   2000 −1 0.5   ×   778

14.7 60

0.5 1.5

− 1 = 153.97 Btu/ min

Power is found by multiplying work by the mass flow rate:

 = mw  = 120 × 153.97 = 18, 476.76 Btu/min or 453.3 hp W



The heat transfer rate is found from the integration of Equation 6.93, with each term multiplied by the mass flow rate:

 = 120 × 0.24 = (1251.47 − 2000) − 18, 4766.76 = −3080 Btu/ min  p (T2 − T1 ) − W Q = mc



The negative sign for the heat rate means that the turbine loses heat to its surroundings. Equation 6.107 may be used to verify this result.

6.8 Real Gases Many equations have been proposed to describe the pressure, volume, and temperature behavior of real gases where the simple equation of state for the ideal gas is inadequate. The earliest equation of state, based on elementary kinetic theory, was proposed by van der Waals. This equation is

p+

a ( v − b) = RT (6.108) v2

where v is the volume occupied by 1 lb. mol of gas, R is the universal gas constant (1545), and a and b are constants for each gas. In the limit, as a and b go to zero, the van der Waals equation reduces to the ideal gas relation. This equation of state is most accurate when applied to gases that are removed from the saturated vapor state. It is possible to evaluate a and b in terms of the conditions at the critical state (the c state). When this is done, it will be found that the van der Waals equation of state can be rewritten in terms of the reduced properties p/pc, T/Tc, and v/vc. These ratios are known, respectively, as the reduced pressure, the reduced temperature, and the reduced specific volume and are indicated by the symbols pr, Tr, and vr. The values with subscript c correspond to properties at the critical state of the gas, when its velocity is the speed of sound. Using this notation, we can show from the van der Waals equation that all gases have the same p, v, T relation when their reduced properties are the same. This is essentially the law of corresponding states. This law is not universally correct, and it has been modified to make it more generally applicable. The utility of the law of corresponding states lies in the fact that a single curve (called a generalized compressibility chart) can be used to evaluate the p, v, T data for all gases. Most charts (made for various classes of gases) based on this principle use Z as the ordinate, where Z = pv/RT. A generalized compressibility chart is shown in Figure 6.14.

301

The Ideal Gas

1.2

2.5(Boyle isotherm) 5.0

1

A

20

0.8

1.4 B

1.2

Z

0.6 Sat. vap 0.4

Tr = 1.0

Sat. liq

0.2 0

Tr = 0.9 0

1

2

3

4

5 PR

6

7

8

9

10

FIGURE 6.14 Compressibility factor Z versus reduced pressure PR. (From Annamalai, K. et al., Advanced Thermodynamics Engineering, 2nd edition, CRC Press, Boca Raton, Florida, 2011.)

ILLUSTRATIVE PROBLEM 6.39 Methane (CH4, MW = 16) has a critical temperature of 343°R and a critical pressure of 674 psia. Determine the specific volume of methane at 50°F and 500 psia using both the ideal gas relation and Figure 6.14. SOLUTION



pr =

p 500 = = 0.742 pc 674

Tr =

T 460 + 50 = = 1.487 Tc 343



Reading Figure 6.14 at these values gives Z equal to 0.93. Therefore,



Z = 0.93 =

pv RT

v = 0.93

RT p



302

Thermodynamics and Heat Power

and

v=

0.93(1545/16)(510) = 0.635 ft.3/ lbm 500 × 144

For the ideal gas,

v=

RT 1545 × 510 = = 0.683 ft.3/ lbm p 16 × 500 × 144



To obtain the other thermodynamic properties of the real gas, similar procedures based on the law of corresponding states have been developed. The interested reader is referred to the references for this information. In general, the ideal gas relations yield more nearly correct results when the gas under consideration is at a pressure that is small compared to the critical pressure and when its temperature is much greater than the critical temperature. In other words, when Tr >> 1 and pr Fe >

1 s 1 1 + −1 ε1 ε 2 a

1 1 A1 1 + −1 ε1 A2 ε 2 ε1ε2

dA See special cases 7, 8, 9b

dA

See Figure 11.20

ε1ε2

dA

Sum of FA’s determined for each rectangle as in case 7 Formula belowc

ε1ε2

A1 or A2

Figure 11.21, curves 1 and 2

ε1ε2

A1 or A2

Figure 11.21, curve 3

ε1ε2

dA

A1 or A2

1/2

(F F ) nd A A

ε1ε2

ε1ε2 or

Figure 11.22

1 1 1 + −1 ε1 ε 2

A1 or A2

Figure 11.23

ε1ε2

A1 or A2

Figure 11.24

ε1ε2 (continued)

559

Heat Transfer

TABLE 11.4 (Continued) Radiation between Solids: Factors for Use in Equation 11.31 Source: A. I. Brown and S. M. Marco, Introduction to Heat Transfer, 3rd ed., New York: McGraw-Hill Book Co., 1958. With permission. a This form results from assumption of completely diffuse reflection. If reflection is completely specular (mirrorlike), then Fe = 1/[(1/ε1 + 1/ε2) − 1]. b A complete treatment of this subject, including formulas for special complicated cases and the description of a mechanical device for solving problems in radiation, is given by H. C. Hottel, Mech. Eng., 52(7), 699, July 1930. c Case 9, R = radius of disk + distance between planes; x = distance from dA to normal through center of disk + distance between planes. 1 x2 + 1 − R2 FA = 1− 2 2 x + 2(1 − R 2 )x 2 + (1 + R 2 )2 FA = FA for squares equivalent to the short side of the rectangle (Figure 11.21, curve 2). FA = FA for squares equivalent to the short side of the rectangle (Figure 11.21, curve 2). Fe = ε1ε2 if the areas are small compared with L. Fe = 1/[(l/ε1 + l/ε1) – 1] if the areas are large compared with L. d

D/L2, Dimension ratio

3.5

L1 and L2 are 3.0 sides of rectangle; D is distance from 2.5 dA to rectangle

L1

F

A

L2 D dA

2.0 1.5 1.0 0.5 0

0. 0.14 1 0. 6

0. 18 0. 20 0.2 22 4

0.0 12 0.10 8

0.

0.5 1.0 1.5 2.0

0.0

.02

0.0

3

0.0

4

0.0

6

=0

5

2.5 3.0 3.5 4.0 4.5 5.0 5.5

D/L1, Dimension ratio FIGURE 11.20 Radiation between a surface element and a rectangle above and parallel to the surface element. 1.0

Factor, FA

0.8 3

0.6

2

1. Disks 2. Squares 3. Total radiation between squares or disks connected by nonconducting but reradiating walls

1

0.4 0.2 0

1

2 Ratio

3

4

5

6

7

Side or diameter Distance between planes

FIGURE 11.21 Direct radiation between equal disks or squares in parallel planes directly opposed.

8

560

Thermodynamics and Heat Power

0.9 R1= L/D = 20.0

0.8 D

0.7

L 0.6

10.0

2

6.0 4.0

1 W

3.0

Factor, FA

2.0 0.5

1.5

0.4

1.0 0.8

0.3

0.6 0.2

0.4 0.2

0.1

0.1 0

0

1.0

2.0

3.0 R2 = W/D

4.0

5.0

6.0

FIGURE 11.22 Radiation shape factor for parallel, directly opposed rectangles.

In many situations where both radiation and convection occur simultaneously from a body, it is desirable to evaluate a combined heat-transfer coefficient for the process. To arrive at a heat-transfer coefficient for radiation, we will equate Equations 11.16 and 11.31 as follows:

(

)

Q r = hr (T1 − T2 )A = σFe FA A T 41 − T 42 (11.32)

and



hr =

(

)

σFe FA T 41 − T 42 (11.33) T1 − T2

561

Heat Transfer

z y

A

A = Area on which heat transfer equation is based Y = y/x Z = z/x

x

0.50 Y = 0.1

Factor, FA

Dimension ratio, Y = 0.1

0.2

0.40

0.3 0.4 0.6

0.30

0.8 1.0

0.20

1.5 2.0

0.10

3.0 4.0 6.0 8.0

0

1.0

Asymptotes

Scale changes here 2.0

3.0

4.0

6

8

10

Dimension ratio, Z FIGURE 11.23 Radiation between adjacent rectangles in perpendicular planes.

which can be rewritten as



hr = Fe FA

(

σ T 41 − T 42 T1 − T2

)

= Fe FA hr (11.34)

For small temperature differences, the term in brackets, hr , has been evaluated and plotted in terms of the upper temperature t1 in degrees Fahrenheit and the temperature difference Δ in degrees Fahrenheit between the two bodies in Figure 11.25.

562

Thermodynamics and Heat Power

Nonconducting refractory

Radiating plane Ordinate is fraction of heat radiated from the plane to an infinite number of rows of tubes or to a plane replacing the tubes

Factor of comparison with two parallel planes

1.0 Tot al to both T row whe otal t s n on o on ly o e row ne p rese Tota nt l to 1 st ro w

0.8 0.6 0.4

Total to 2nd row

0.2 0

1

2 Ratio

3

4

5

6

7

Center-to-center distance Tube diameter

FIGURE 11.24 Radiation from a plane to one or two rows of tubes above and parallel to the plane.

ILLUSTRATIVE PROBLEM 11.22 Determine the radiation heat-transfer coefficient for the pipe of Illustrative Problem 11.21. SOLUTION The upper temperature is given as 120°F and the temperature difference Δ is 120 − 70  = 50°F. Using Figure 11.25, hr = 1.18 and hr = Fe FA hr = 1 × 0.79 × 1.18 = 0.93. As a check, using the results of Illustrative Problem 11.19,



hr =

214.5 Q = A∆t [π(3.5/12)] × 5(120 − 70) = 0.94 Btu/h·ft.2 ·°F



563

Heat Transfer

ILLUSTRATIVE PROBLEM 11.23 Solve Illustrative Problem 11.16 taking into account both convection and radiation.

1 10 20 30 50

6.0

100

Factor for radiation coefficient, h´r

Btu h ft2 °F

5.0

Temperature difference,

, °F

SOLUTION Because the conditions of Illustrative Problem 11.16 are the same as for Illustrative Problems 11.21 and 11.22, we can solve this problem in two ways to obtain a check. Thus, adding the results of these problems yields Q total = 206.2 + 214.5 = 420.7 Btu/h . We can also approach this solution by obtaining a combined radiation and convection heat-transfer coefficient. Thus, hcombined = 0.9 + 0.94 = 1.84. Q total = 184(π × 3.5/12)5 × (120 − 70) = 421.5 Btu/h. This procedure of obtaining combined or overall heat transfer coefficients is discussed further in Sections 11.5 and 11.6.

4.0

3.0

2.0

1.0

0

100

200 300 Upper temperature, t1, °F

400

500

FIGURE 11.25 Factor for radiation coefficient. (From I. Granet, “Coefficient of radiation heat transfer,” Design News, September 1970.)

564

Thermodynamics and Heat Power

In solving radiation heat-transfer problems involving the fourth power of the absolute temperatures, the numbers can become excessively large. Because the radiation heattransfer equation involves the Stefan–Boltzmann constant with its factor of 10−8, a useful device is to express the absolute temperature as a number times 102 (e.g., 1400 is 14 × 102). When this temperature is taken to the fourth power, a number times 108 results. This factor is conveniently cancelled by the 10−8 of the Stefan–Boltzmann constant, leaving students with more manageable numbers. Before proceeding, let us look at a general approach to obtaining Fe for two gray bodies­ interchanging radiation. This method is called the network method and can be adapted to determining Fe for systems in which more than two bodies are interchanging radiation. When radiant energy is intercepted by a nonblackbody, that is, a gray body, some of the energy may be absorbed, some may be reflected, and some may be transmitted through the body, as in the case of glass. The fraction of the total incident radiation absorbed by the body is denoted by α, the absorptivity of the surface; the fraction of the incident radiation that is reflected is denoted by ρ, the reflectivity of the surface; and finally, the fraction of the incident radiation that is transmitted is denoted by τ, the transmissivity of the body. Based on these definitions, we can write

α + ρ + τ = 1

(11.35)

When a body is opaque, it does not transmit any radiation, giving us τ = 0, which yields the following equation for an opaque body:

α + ρ = 1

(11.35a)

We now denote the total incident energy per unit area to be the irradiation, Q i, having English units of Btu/h·ft.2, and the total energy leaving the body as the radiosity Q r, in consistent units. We further denote Q b to be the amount of energy that a blackbody would emit at the same  temperature as the gray surface being considered. Using these definitions, we can write

Q i = ρQ i + εQ b (11.36)

Simplifying Equation 11.36,

Q i (1 − ρ) = εQ b (11.36a)

The net heat transferred to the body, Q net, is

(

)

Q net = A Q r − Q i (11.37)

565

Heat Transfer

Combining Equation 11.36a with Equation 11.37 yields Q − Q r Q net = b (11.38) (1 − ε) εA



We can compare Equation 11.38 to Ohm’s law, giving us Q b − Q r as representing a poten­ tial, (1 − ε)/εA representing a resistance, and Q net representing a current flow. Thus, we can represent a system of two surfaces that see each other and nothing else by the circuit diagram of Figure 11.26. Each gray surface has a resistance of (1 – ε)/εA, and these resistances are connected by a resistance that is due to the geometry of the system, namely, 1/A1F1–2. In Figure 11.26, we have three resistances in series across an overall potential difference equal to Q b ,1 − Q b , 2 = σ T 41 − T 42 . Therefore,

(



)

Q net =

(

)

σ T 41 − T 42 (1 − ε1 ) 1 (1 − ε 2 ) (11.39) + + ε1 A ε2 A A

If we factor the A in the denominator and rearrange terms, we obtain

(

)

σ T 41 − T 42 A Q net = (11.40) 1 1 + −1 ε1 ε 2



Comparing Equation 11.40 with Equation 11.31 gives us the value of Fe for this case as

Fe =

1 1 + − 1 (11.41) ε1 ε 2

which is the same as case 1 in Table 11.4.

Qb, 1 – Qb, 2 = σ (T 41 – T 42 ) Qb, 1 – Qr, 1 1 – ε1 ε1 A

Qr, 1 – Qr, 2 1 A1 F 1

= 2

Qr, 2– Qb, 2 1 – ε2

1 A2 F 2

1

ε2 A

FIGURE 11.26 Electrical analogy for two gray bodies interchanging radiation; two infinite radiating planes that see each other and nothing else.

566

Thermodynamics and Heat Power

The electric analogy can be applied to many situations that would be difficult to solve in any other manner. In many cases, the complex interactions lead to a group of simulta­ neous equations that can be written in condensed matrix form. A solution is then obtained by the process of inverting the matrix. The interested reader should consult the references for these procedures.

11.5 Heat Exchangers When heat is transferred from one fluid to another in an industrial process without mixing, the fluids are separated and the heat transfer takes place in an apparatus known as a heat exchanger. A heat exchanger can be of varied shape and size and is usually designed to perform a specific function. The steam-generation plant uses heat exchangers as condensers, economizers, air heaters, feedwater heaters, reheaters, and so on. It is common to designate heat exchangers by their geometric shape and the relative directions of flow of the heat-transfer fluids. For example, Figure 11.27a shows a concentric-tube (or doublepipe) unit in which the fluids would be said to be flowing parallel to each other, and the unit would be called a parallel-flow, double-pipe unit. Other common types are shown in the remainder of Figure 11.27. The problem of calculating the heat transfer in these units differs from our previous discussion in that the temperature of one or both of the fluids varies continuously as the fluids proceed through the heat exchanger. This can be seen in Figure 11.28, where the fluid temperatures have been plotted as a function of the heat-transfer surface for the most common cases of parallel flow, counterflow, and for one fluid at constant temperature. The subscript h is used to denote the hot fluid, and the subscript c denotes the cold fluid. The sub-subscript 1 is used to denote the temperature at the entry of a fluid of the heat exchanger, and 2 denotes the temperature of the fluid at the exit of the heat exchanger. The direction of flow of each fluid through the exchanger is shown by the arrowheads on the temperature curves. The largest temperature difference between the fluids in the unit (at either inlet or outlet) is designated as θA, and the least temperature difference between the fluids (at either inlet or outlet) is designated as θB. Newton’s law of cooling (Equation 11.16) can be written for the heat exchangers as

Q = UA(∆t)m (11.42)

where U is the overall conductance or overall heat-transfer coefficient having the same physical units as the convection coefficient h, Btu/(h·ft.2·°F) or W/m2 °C; A is the heat transfer surface in square feet; and (Δt)m is an appropriate mean temperature difference. The overall heat-transfer coefficient, U, in Equation 11.42 is not usually constant for all locations in the heat exchanger, and its local value is a function of the local fluid temperatures. However, it is usual practice to evaluate the individual heat-transfer coefficients based on the arithmetic average fluid temperatures. By analogy to convection, we have 1/UA = resistance. The concept of the overall heat-transfer coefficient is best illustrated by Illustrative Problems 11.24 and 11.25.

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Heat Transfer

(b)

(a)

(c)

Wh

Wc

(d)

(e)

(f )

Wh Wc

(g)

Wh

Wc

FIGURE 11.27 Representative types of heat exchangers. (a) Concentric tubes counter flow. (b) Shell and tube counter flow heat exchanger. (c) Shell and tube exchanger, segmented baffles, two tube passes, one shell pass. (d) Disk and doughnut baffle. (e) Segmented baffle. (f) Crossflow tubular exchanger. (g) Plate-fin exchanger. (From W. M. Rohsenow and H. Y. Choi, Heat, Mass and Momentum Transfer, Englewood Cliffs, N.J.: Prentice Hall, Inc., 1961. With permission.)

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Thermodynamics and Heat Power

th1

(b)

Temperature

th A

0

Temperature

(a)

th2

tc

tc2

B

th1 tc2

B

th

th2

tc

A

tc1

tc1

100

Percent surface (c)

0

Percent surface

100

Temperature

th1 th

A

th2

tc

0

B

Percent surface

100

FIGURE 11.28 Fluid temperatures in heat exchangers. (a) Parallel flow. (b) Counter flow. (c) Constant temperature.

ILLUSTRATIVE PROBLEM 11.24 Determine the overall heat-transfer coefficient for the composite wall of Illustrative Problem 11.4 if h on the hot side is 0.9 Btu/(h·ft.2·°F) and h on the cold side is 1.5 Btu/ (h·ft.2·°F). The temperatures given are to be the respective air temperatures (see Figure 11.7).

1 2

in. k = 0.3

6 in. 30°F

k = 0.4 k = 0.8

Plaster

Brick Concrete FIGURE 11.7 (Repeated) Illustrative Problem 11.24.

Q

70°F

Brick

Concrete Plaster

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Heat Transfer

SOLUTION For a plane wall, the areas are all the same, and if we use 1 ft.2 of the wall surface as the reference area, brick resistance =

∆x 6/12 = = 1.25 kA 0.4 × 1

1 / 12 ∆x concrete resistance = = 2 = 0.052 kA 0.8 × 1

1 ∆x 2 / 12 plaster resistance = = = 0.139 kA 0.3 × 1 “ hot film” resistance =

1 1 = = 1.11 hA 0.9 × 1

“cold film” resistance =

1 1 = = 0.67 hA 1.5 × 1

total resistance =

3.22

The overall conductance (or overall heat-transfer coefficient) U = 1/(overall resistance) = 1/3.22 = 0.31 Btu/h·ft.2. In Illustrative Problem 11.24, the solution is straightforward, because the heat-transfer area is constant for all series resistances.

ILLUSTRATIVE PROBLEM 11.25 A steel pipe, k = 26 Btu/(h·ft.·°F), having an outside diameter of 3.5 in. and an inside diameter of 3.00 in., and 5 ft. long, is covered with 1 in. of mineral wool, k = 0.026 Btu/ (h·ft.·°F). If the film coefficient on the inside of the pipe is 45 Btu/(h·ft.2·°F) and on the outside is 0.9 Btu/(h·ft.2·°F), determine the overall heat transfer coefficient. (See Figure 11.29 and Illustrative Problems 11.10 and 11.12.) SOLUTION Because the same amount of heat traverses each of the paths, we can write Q = Q i = Ai hi (ti − t1 ) = 2 πr1Lhi (ti − t1 ) =

2 πk1L (t1 − t2 ) ln(r2/r1 )

=

2 πk2 L (t2 − t3 ) ln(r3/r2 )



= Ao ho (t3 − to ) = 2 πr3 Lho (t3 − to )



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Thermodynamics and Heat Power

1 h iA i

r ln r2 1 2 k1L

r3

1 h oA o r ln r3 2 2 k2L

ti

hi ti k1

r2 t1 t3

to

to , ho

r1 t2

k2

Ai = Inside pipe area Ao = Outside pipe area FIGURE 11.29 Illustrative Problem 11.25.

Solving for the temperature differences and adding them yields

Q =

ti − to (a) 1 ln(r2/r1 ) ln(r3/r2 ) 1 + + + 2 πr1Lhi 2 πk1L 2 πk2 L 2 πr3 Lho

Although this equation looks formidable, we can simplify it and interpret it in terms of j items discussed previously in this chapter. Thus,

Q =

(ti − to )2 πL (b) 1 ln(r2/r1 ) ln(r3/r2 ) 1 + + + k2 ho r3 hi r1 k1

Let us now define Uo as the overall heat-transfer coefficient based on the outside pipe surface Ao as Q = U o Ao (ti − to ) (c)



If we multiply the numerator and the denominator of Equation b by r3, we obtain

Q =

(ti − to )2 πLr3 (d) r r3 r3 r r r + ln 2 + 3 ln 3 + 3 r2 ho r3 hi r1 k1 r1 k2

Comparison of Equations c and d yields

Uo =

1 (e) 1 1 r3 r2 r r + ln + 3 ln 3 + ho hi (r1/r3 ) k1 r1 k2 r2

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Heat Transfer

Note that Uo is the overall heat-transfer coefficient based on the outside tube surface. If we had multiplied Equation b by r1/r1 we would obtain the overall heat-transfer coefficient Ui based on the inside surface as

Ui =

1 r1 r + ln 2 hi k1 r1

1 (f) 1 r r + 1 ln 3 + k2 r2 ho (r3/r1 )

In effect, we have required that UoAo = Ui Ai. When discussing an overall heat-transfer coefficient, the reference area must be given. Proceeding with the numerical problems yields 1 1 = = 0.02222 hi 45 3.50 r1 r 3.00 = 0.00074 ln 2 = (26 × 12) ln 3.00 k1 r1 2

r1 r 3.00 5.50 ln 3 = (0.026 × 12) ln = 2.1730 k2 r2 2 3.50 1 1 = 0.6061 = ho (r3/r1 ) 0.9(5.50/3.00) ∑ = 2.8021



Therefore,

Ui =

1 Btu = 0.357 (of inside area) 2.8021 h·ft.2 ·°F

Because UoAo = UiAi, Uo = 0.357 × Ai/Ao = 0.357 D1/D3 = (0.357) (3.00/5.50) = 0.195 Btu/ (h·ft.2·°F) (of the outside area).

The true mean temperature difference of two fluids exchanging heat in a heat exchanger cannot be determined by simply subtracting temperatures. Let us make the following assumptions in order to obtain the true temperature difference:

1. U is constant over the entire heat exchanger. 2. Both fluid flows are steady, that is, constant with time. 3. The specific heat of each fluid is constant over the entire heat exchanger. 4. Heat losses are negligible.

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Thermodynamics and Heat Power

TABLE 11.5 Approximate Overall Coefficients for Preliminary Estimates Overall Coefficient, U Duty

(Btu/(h·ft.2·°F))a

Steam to water Instantaneous heater Storage-tank heater Steam to oil Heavy fuel Light fuel Steam to aqueous solutions Steam condenser Steam to gases Water to compressed air Water to water, jacket water coolers Water to lubricating oil Water to condensing oil vapors Water to condensing alcohol Water to condensing Freon-12 Water to condensing ammonia Water to organic solvents, alcohol Water to boiling Freon-12 Water to gasoline a

(W/m2 °C)

400–600 160–212

2270–3400 900–1200

10–70 30–70 100–600 170–1050 5–50 10–30 150–300 20–60 40–100 45–120 50–180 140–250 40–120 50–180 50–180

50–400 170–400 570–3400 1000–6000 28–280 57–170 850–1700 100–350 220–570 255–680 300–1000 800–1400 250–700 300–1000 300–1000

1 Btu/(h ft.2 °F) = 5.6786 W/m2 °C.

Then (Δt)m in Equation 11.42 is given for parallel flow, counterflow, and constant-temperature­ exchangers as

(∆t)m =

θ A − θB (11.43) ln(θ A/θB )

where θA is the greatest temperature difference between the fluids (at either inlet or outlet) and θB is the least temperature difference between the fluids (at either inlet or outlet; see Figure 11.28). Thus, (Δt)m is known as the logarithmic mean temperature difference. Because heat losses are assumed to be negligible, the heat transferred from the hot fluid must equal that received by the cold fluid. Therefore,

(

)

(

 c (c p )c tc2 − tc1 = m  h (c p )h th1 − th2 m

) (11.44)

Some typical values of overall heat-transfer coefficients are given in Table 11.5 and are useful in making preliminary design calculations. CALCULUS ENRICHMENT Let us consider the counterflow heat exchanger shown in the figure below. In this figure, the “hot” fluid, h, enters at the left and exits at the right, while the “cold” fluid,

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Heat Transfer

c, enters at the right and exits at the left. A small section of the heat exchanger having a heat transfer area dA is isolated as shown, with the temperature differences being dth and dtc, respectively. Based on making the same assumptions noted earlier, a heat balance for each fluid yields  h c ph dth (a) dQ = UdA(th − tc ) = m



th1 dth

Temperature

a

Hot fluid tc2

t

dtc

th2

b

Cold fluid

tc1

Percent surface

and

 c c pc dtc (b) dQ = UdA(th − tc ) = m

For the entire heat exchanger, Q = UA(∆t)m (c)



where (Δt)m is the appropriate mean temperature difference. Also,

(

)

(

 h c ph th2 − th1 = m  c c pc tc1 − tc2 Q = m

) (d)

Equating the right-hand sides of Equations a and b and integrating,

1 1 d(th − tc ) + = (e)   mh c ph mc c pc U dA(th − tc )

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Thermodynamics and Heat Power

and from Equation d,

(

) (

)

) (

) (g)

th − th2 − tc2 − tc1 1 1 + = 1  h c ph m  c c pc m UA(∆t)m

(f)

Combining Equations e and f,

(

th − th2 − tc2 − tc1 d(th − tc ) = 1 UdA(th − tc ) UA(∆t)m

Denoting (th − tc) as θ and rearranging terms yields

∫



θb

θa

dθ θ a − θb (h) = θ (∆t)m

Integrating Equation h,

ln

θ a θ a − θb (i) = θb (∆t)m

and (∆t)m =



θ a − θb (j) θ ln a θb

where (Δt)m is the log mean temperature difference. Our derivation was for a counterflow heat exchanger. Using the same procedure, it can also be shown that Equation j is also applicable for parallel flow and for heat exchangers in which there is a change of phase in one of the fluids.

ILLUSTRATIVE PROBLEM 11.26 A counterflow heat exchanger is used to cool a flow of 400 lb./min of lubricating oil. Hot oil enters at 215°F and leaves at 125°F. The specific heat of the oil is 0.85 Btu/lb.·°F, and the overall coefficient of heat transfer of the unit is 40 Btu/(h·ft.2·°F) (of the outside tube surface). Water enters the unit at 60°F and leaves at 90°F. Determine the outside tube surface required. SOLUTION From Figure 11.30, θA = 215 − 90 = 125°F, and θB = 125 − 60 = 65°F. Therefore,

(∆t)m =

θ A − θB 125 − 65 = = 92°F ln(θ A/θB ) ln(125/65)

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Heat Transfer

Temperature

215

Oil 90

125

Water 0

Percent surface

60 100

FIGURE 11.30 Illustrative Problem 11.26.

 p  Δt = 400 × 60 × 0.85(215 – 125) = 1 836 000 From the oil data, the heat transfer Q = mc Btu/h, and from the heat transfer equations, Q = UA(∆t)m = 1836 000 = 40 × A × 92. Therefore, A = 499 ft.2 of the outside surface is required.

ILLUSTRATIVE PROBLEM 11.27 If the best exchanger in Illustrative Problem 11.26 is operated in parallel flow, determine the outside tube surface required. SOLUTION From Figure 11.31, θA = 215 – 60 = 155°F, and θB = 125 – 90 = 35°F. Therefore,

(∆t)m =

θ A − θB 155 − 35 = = 80.6°F ln(θ A/θB ) ln(155/35)

Because all other conditions are the same, Q = 1836 000 Btu/h.

1 836 000 = 40 × A × 80.6

Therefore, A = 569 ft.2 of the outside surface is required.

Temperature

215 Oil Water 60 0

100 Percent surface

FIGURE 11.31 Illustrative Problem 11.27.

125 90

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Thermodynamics and Heat Power

TABLE 11.6 Typical Fouling Factors Fouling Resistance Types of Fluid Seawater below 50°C (122°F) Seawater above 50°C (122°F) Treated boiler feedwater River water Fuel oil Vapor refrigerants Alcohol vapors Steam, non-oil-bearing Industrial air Refrigerating liquid a

(h·°F·ft.2/Btu)a

(m2·°C/W)

0.0005 0.001 0.001 0.001–0.006 0.005 0.002 0.0005 0.0005 0.002 0.001

0.0001 0.0002 0.0002 0.0002–0.001 0.0009 0.0004 0.0001 0.0001 0.0004 0.0002

Dividing the values by 5.6786 will yield m2·°C/W.

From the results of Illustrative Problems 11.26 and 11.27, we note that operation of a heat exchanger in parallel flow requires more surface for the same terminal temperatures than for a unit operated in counterflow. This conclusion is general because (Δt)m between the same terminal temperature limits is always greater for counterflow than for parallel flow. Thus, where a choice exists, it is preferable to operate a unit in counterflow, because this type of operation will give the minimum surface requirements. Another advantage of counterflow is that it is possible to raise the exit temperature of the cooling fluid closer to the inlet temperature of the hot fluid. After a period of operation, it is found that heat exchangers cannot transfer as much heat as when they are first started and were clean. This is due to a buildup of scale, dirt, or oxide films and is known as fouling. This effect is taken into account in heat-exchanger design by introducing series resistances known as fouling factors in the design calculations. Table 11.6 gives typical values of fouling factors for various fluids.

ILLUSTRATIVE PROBLEM 11.28 Using Table 11.6 for the appropriate fouling factors, calculate the surface required for Illustrative Problem 11.27. SOLUTION For the oil side, a resistance (fouling factor) of 0.005 h·°F·ft.2/Btu can be used, and for the water side, a fouling factor of 0.001 h·°F·ft.2/Btu can be used. Because of the approximate nature of these resistances, we shall not correct them for inside or outside reference areas, and we will assume that they can be used directly with the value of U of 40 Btu/(h·ft.2·°F). The overall resistance and the overall heat transfer coefficient are obtained as

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Heat Transfer

oil, R =

0.005

water, R =

0.001

clean unit, R = 1/40 0.025



0.031

Roverall = U overall =

1 Btu = 32.3 0.0031 h·ft.2 ·ºF

Because all other parameters are the same, the surface required will vary inversely as U. Therefore, A = 569 × 40/32.3 = 705 ft.2 or an increase in surface required of approximately 24% due to fouling. This obviously represents an important consideration in the design of industrial equipment.

In many heat exchangers, the flow paths of the fluids are not simply parallel or counterflow. In Figure 11.27c, we have an illustration of a shell-and-tube heat exchanger, which is said to have one shell pass and two tube passes. In addition, the shell-side fluid passes over segmented baffles in a sinuous path. For this type of a heat exchanger as well as others, correction factors have been developed to account for the deviation from parallel or counterflow. The correction factor is applied to the log mean temperature difference to obtain the true temperature difference. Thus,

true mean temperature difference = F × log mean temperature difference (11.45)

Figures 11.32 and 11.33 show the correction factor for two arrangements of flow paths. To obtain the true mean temperature difference for any of these arrangements, the log mean temperature difference for counterflow is multiplied by the appropriate correction factor. 1.0

T1 t2 t1

0.8

0.2

0.5

0.4

0.4

0.6

0

0.8

0.5

R=

1.0

0.6

1.5

0.7

T2 2.0

3.0 R = 4.0

Correction factor, F

0.9

T1 – T2 t2 – t1 0.1

0.2

0.3

P=

0.6

0.7

0.8

0.9

1.0

t2 – t1 T1 – t1

FIGURE 11.32 Correction factor for heat exchangers with 1 shell pass and 2, 4, or any multiple of 2 tube passes.

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Thermodynamics and Heat Power

T1

0.4

0.8

0.9

0. 2

0 .6

0.5

0 .8

0.4

1 .0

t1 1 .5

0.8

2.0

t2

3.0

0.9

R = 4.0

Correction factor, F

1.0

T2

0.7 0.6 0.5

R= 0

T1 – T2 t2 – t1

0.1

0.2

0.3

P=

0.6

0.7

1.0

t2 – t1 T1 – t1

FIGURE 11.33 Correction factor for heat exchangers with 2 shell passes, and 4, 8, or any multiple of 4 tube passes.

Note that t1 and t2 refer to the fluid temperatures entering and leaving, respectively, on the tube side, and T1 and T2 refer to the fluid temperatures entering and leaving, respectively, on the shell side.

ILLUSTRATIVE PROBLEM 11.29 A heat exchanger has one shell pass and two tube passes similar to Figure 11.27c. Oil flows in the tube side and is cooled from 280°F to 140°F. On the shell side, water is heated from 85°F to 115°F. Determine the true mean temperature difference. SOLUTION In order to use Figure 11.32, which is applicable to this problem, we need to calculate P and R. From the figure, P=

t2 − t1 140 − 280 = = 0.72 85 − 280 T1 − t1

R=

85 − 115 T1 − T2 = 0.21 = t2 − t1 140 − 280



From Figure 11.32, F = 0.91. Thus, true mean temperature difference = 0.91 × LMTD counterflow = 0.91 = 91°F

(280 − 115) − (140 − 85) (280 − 115) ln (140 − 85)

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Heat Transfer

In selecting a heat exchanger for a particular task, one typically starts with the rate of the heat transfer needed. This depends on the fluid of interest, its specific heat, its flow rate, and the desired temperature change. The other fluid is chosen based on its properties and its compatibility with heat exchanger materials. Its flow rate is chosen based on weighing effectiveness against pressure drop and the subsequent need for pumping power. The most common choice is the shell-and-tube exchanger with the more viscous fluid usually selected for the shell side, which offers a larger cross-sectional area to minimize the pressure drop. Other factors involved in the selection are costs, size and weight, and pumping power required. Note that the value of U is usually not constant for a particular heat exchanger and so it is often overdesigned.

11.6 Combined Modes of Heat Transfer Heat-transfer situations often exhibit combined heat-transfer effects of conduction, convection, and radiation. For example, an insulated steel pipe could be used to carry flowing hot water in a large room of still air. The path taken by the heat as it flows from the hot water through the pipe wall and into the room would be as follows:

1. Forced convection from the hot water to the inside wall of the pipe 2. Conduction through the pipe wall and its insulation 3. Natural convection from the outer surface of the insulation to the room air in parallel with radiation to the room

An equivalent resistance circuit is shown in Figure 11.34. An overall heat-transfer coefficient, U, would then be U=



1 1 r1 1 r3 r r r + ln 2 + 1 ln 3 + hi k1 r1 k2 r2 ho + hr r1

(11.46)

Units of U are typically in Btu/(h·ft.2·°F). Note that free convection and radiation occur simultaneously from the surface of the pipe’s insulation. The total heat-transfer rate is thus the sum of the rates of convection and radiation. 1 ho Ao

1 hi Ai

( )

r ln r2 1 2 k1L

ln

(r ) r3 2

2 k2L

1 hr Ao

Heat transfer coefficients hi forced convection k1 , k2 conduction ho natural convection hr radiation

FIGURE 11.34 Electrical analogy for combined heat transfer from a hot fluid flowing in a pipe to still air in a large room.

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Thermodynamics and Heat Power

11.7 Cooling Electronic Equipment The principles described in this chapter can be applied to a critical requirement of modern manufacturing: keeping electronic equipment sufficiently cool. Most electronic components have a maximum allowable operating temperature. They generate power in confined spaces, and it is important for designers to devise an adequate path for the removal of the heat developed by the dissipation of this power. Heating of parts also has the potential for enhancing corrosion and producing thermal stresses that can fracture bonds between different materials that expand at different rates with increased temperature. It is not the purpose of this text to provide an exhaustive review of the problem of cooling electronic systems; rather a brief summary of the approach will be given. For more detailed information on this application, the reader is advised to consult the references, in particular, that of Steinberg (1991) and Cengel (1998). The International Electronic Research Corporation, a manufacturer of heat sinks, also publishes a very useful “Thermal Management Guide” (International Electronic Research Corporation 1990). Electronic equipment that generates heat during operation includes printed circuit boards (PCBs) with a variety of mounted components, power transistors, and transformers. Components are typically mounted and enclosed in a chassis, with cooling available by conduction through contact with solid heat sinks; by convection to the surrounding air, either free or forced by a small fan; and by radiation to the air and the surrounding walls. The first level of temperature control usually begins at the silicon wafer-based chip. The chip generates heat at its location that is called the junction. For typical semiconductor chips, the maximum allowable junction temperature is 125°C, but lower temperatures are desirable for long-term reliability. Manufacturers of encased chips provide a junction-to-case resistance, usually referred to as θjc in units of °C/W or °F/Btu per hour. This is where the heat transfer path begins and can include all three mechanisms of heat transfer. From the case, some heat can travel by conduction through the PCB on which the case is mounted. The PCB is often attached to a heat sink made of a highly conductive material with fins that increase the surface area. The fins transfer the heat to the surrounding air principally by convection with some radiation heat transfer in parallel. An electronics chassis often contains PCBs stacked vertically, each generating heat. Thus, the surroundings of these boards are of similar high temperatures, reducing the capability for heat removal within the chassis. Only the boards adjacent to the cooler chassis walls can lose a reasonable amount of heat by radiation. Thus, a good design mandates placing those boards with the highest power output nearest the chassis walls. To improve heat transfer, forced convection is often employed by placing a fan in the chassis or attaching a cold plate heat exchanger to the circuit board rack. The latter is similar in principle to an automobile’s radiator: two plates with multiple thin fins in the thin space between the plates are attached to the heat-generating components. Air or another fluid is passed through the fins to provide a low-resistance heat flow path from the chassis. The additional thermal path(s) from the component case to the surrounding air is summed and identified as thermal resistance θca. Thus, the junction temperature can be determined from the temperature difference between the junction and the air when the air temperature is known. The equation is

 ∆T = QR

where R = θjc + θca, and Q is the rate of heat produced, equal to the power generated. The junction temperature is thus the air temperature plus ΔT.

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Heat Transfer

11.8 Analysis of Fins As noted in Section 11.7, cooling of equipment is facilitated by the addition of fins to the base surface. Usually the surface temperature is fixed as is the ambient temperature, so to improve heat transfer, fins provide additional surface area with a minimum of additional weight and cost. The radiator in an automobile is a good example of the usage of fins. Fins projecting from the base can be of varying geometries, but the most often used are rectangular in cross section. Such a fin, shown in Figure 11.35, will be analyzed. The additional heat transfer provided by the fin is expressed as a fraction of the convective heat transfer that the fin’s surface area would provide using the same temperature difference between the base surface and the ambient air. The fraction is given as fin efficiency, η, in the following equation:

Q f = ηhc Af (Δt) (11.47)

where Q f is the added heat transfer rate, hc is the convective coefficient of the base’s geometry (plate or cylinder), and Af is the fin area exposed to the air, equal to 2L(d + δ/2). The δ/2 term accounts for the convection at the tip of the fin. As fins are quite thin, Af is approximately 2Ld, and the area of the base that is lost to the fin is negligible. The fin efficiency, between 0 and 1, is found from

η=

tanh(md) (11.48) md

where m is defined as

m=

Bas

e

Phc . (11.48a) ka

L

d FIGURE 11.35 Fin with extended surface.

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Thermodynamics and Heat Power

with P the perimeter of the fin’s cross section equal to 2(L + δ), k the thermal conductivity of the fin material, and a the cross-sectional area of the fin equal to Lδ. Tanh is the hyperbolic tangent, defined as tanh x =



ex − e− x (11.48b) ex + e− x

with e the base of the natural logarithm. Here, x is md, a dimensionless variable. The orientation of the fin is immaterial as this is accounted for in the determination of hc. The effectiveness of the fin depends on its projection length d. While it may seem that the longer the fin, the more effective it will be, this is not so. The temperature distribution in the fin with length drops from the base temperature to the ambient temperature rather quickly. Thus, additional length does somewhat increase the heat transfer but not enough to compensate for the extra weight, space required, and cost. As a rule of thumb, the fin’s length should be such that md is approximately equal to 1. The heat transfer rate can be increased by adding more fins once the proper size is selected. However, to prevent choking of the convective process, the fins should be spaced at least 0.6 in. or 1.5 cm apart. For fins other than rectangular, the reader is referred to textbooks on heat transfer. ILLUSTRATIVE PROBLEM 11.30 To increase the heat transfer rate from the box in Illustrative Problem 11.17, a vertical fin is added to each of the four sides (see Figure 11.36). The fins are aluminum, 15 cm high and 0.15 cm thick, and protrude 3 cm from the box. Find the new heat loss rate. SOLUTION The fins are vertical plates with the same characteristic length as the sides of the box, so the fin’s heat transfer coefficient is the same as in Problem 11.17: hc = 5.102 W/m2 °C.

15 cm cube

15 cm 0.15 cm

3 cm

FIGURE 11.36 Illustrative Problem 11.30.

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Heat Transfer

Here P = 0.303 m, k = 204.2 W/m °C per Table 11.1, d = 0.03 m, Af = 0.0369 m2 (4 fins) and a = 0.000225 m2. The value of m in Equation 11.48a is thus

m=

Phc ka

0.303 × 5.102 = 5.80 m −1 204.2 × 0.000225

and md = 0.174. The tanh of md = 0.172 and (tanh md)/md = 0.99. Thus, the fin heat transfer rate is

Q f = ηhc Af (Δt) = 0.99 × 5.102 × 0.0369 × 25 = 4.66 W

This rate added to the rate for the box brings the total heat transfer rate to 18.81 watts, which is an increase of 33% due to the usage of fins. Note that when fins are added, the surface area of the box exposed to convection is diminished. In this example, the reduction is negligible.

11.9 Heat Pipes The heat pipe is a device for enhanced thermal conduction. It can transfer large amounts of heat quickly, especially over large distances. The exterior of the pipe is sealed metal of good conductivity such as aluminum or copper. It looks no different from a solid pipe but has an effective thermal conductivity that exceeds that of a solid pipe by many orders of magnitude. It is utilized by placing one end of the pipe in contact with the material to be cooled and the other end in a cold reservoir. It is not unusual for fins to be placed at the cold end to facilitate heat transfer. The heat pipe is hollow and includes a working fluid and a concentric wick running the length of the pipe (see Figure 11.37). The operation of the heat pipe depends on the fluid being able to vaporize at the temperature of the material to be cooled. Thus, the fluid interior must be set at the saturation pressure that corresponds to that material’s temperature. That pressure could be either above or below atmospheric. Often the fluid can be as common as water. When the pipe is placed in contact with the heat source, the fluid at that end evaporates, absorbing heat and increasing its vapor pressure. That pressure forces the Pipe wall

Wick

Liquid Vapor Liquid Vapor core

FIGURE 11.37 Heat pipe—section view.

Hot end

Cold end

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vapor to the cold end of the pipe where it condenses, giving up heat to the cold reservoir. The condensed liquid returns by capillary action along the wick to the hot end where it revaporizes to repeat the heat transfer process. The resistance to heat transfer is minimal in the boiling and condensing processes, so the net thermal resistance is only that through the thin pipe wall. To maximize the heat pipe’s effectiveness, the hot end should be below the cold end so that gravity can help return the liquid to the hot end. If this is not possible, a fine wick will work better than a coarse one. For a horizontal pipe, the coarse wick usually works best. A simple heat pipe using water can have a thermal conductivity that exceeds that of copper by up to 1000 times. The materials used in the heat pipe for the fluid, the wick, and the pipe should be chemically compatible. Otherwise, noncondensible gases may form that can degrade the heat pipe’s performance. Heat pipes are usually cylindrical but can be formed in a variety of shapes and can include bends to match the shape of the material to be cooled. For example, a flat pipe can be attached to a flat electronic circuit board to keep the components cool.

11.10 Review In this chapter, we have surveyed the three mechanisms of heat transfer: conduction, convection, and radiation. We studied conduction through a simple plane wall and a wall consisting of several resistances. Using the electrical analogy where Ohm’s law is compared to Fourier’s law, it was found that the treatment of resistances in series and parallel could be handled readily. The same reasoning was used when conduction in a hollow cylinder was considered. In convection heat transfer, there is motion of a fluid relative to a body. It therefore becomes necessary to consider the character of the flow of the fluid. That is, is the flow laminar or turbulent, and is the flow due to natural or forced convection? Because of the complexity of the subject, we could only treat several common cases in a rather simplified manner. Radiation heat transfer differs from the other modes of heat transfer in that a medium is not required to transfer the heat. Using the concept of a blackbody and the Stefan–Boltzmann equation, we were able to calculate the radiation heat transfer and to combine it with the other modes of heat transfer. We studied heat exchangers and the application of Newton’s law of cooling to the calculation of their performance. When different modes of heat transfer are available, they can be combined into an overall heat transfer coefficient. Heat transfer principles were also applied to the cooling of electronic equipment and to heat pipes. Finally, the usage of fins to enhance the rate of heat transfer was introduced. The general subject of heat transfer is a vast field that encompasses many technical disciplines. In this chapter, we have been able to cover only briefly some of the basic concepts and topics of interest. In the past, empirical test data were used extensively, but in recent decades, great strides have been made in developing analytical and numerical procedures for the calculation of many heat-transfer problems. As examples from the space program alone, we have radiation to and from space vehicles, ablation, lightweight “super” insulation, heat transfer in high-speed flow, transpiration cooling, thermal contact resistances, heat transfer from plasmas, and compact heat exchangers. Many other examples could be cited from every branch of engineering and technology. The point to be made is that this is a truly fertile field with an almost infinite number of unsolved problems that represents great potential for original work. We hope that this chapter will serve as an introduction for the understanding and evaluation of industrial heat-transfer equipment as well as for more advanced work.

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Key Terms Terms used for the first time in this chapter are as follows: absorptivity (α): The fraction of the incident radiant heat that is absorbed by a body. blackbody: A body that absorbs all the radiation that strikes it. coefficient of heat transfer (h): The factor of proportionality in Newton’s law of cooling, Q = hA∆t. conduction: The transfer of heat from one part of a body to another part of the same body without appreciable displacement of the particles of the body. convection: The transfer of heat due primarily to the motion of a fluid. dimensionless numbers: The arrangement of physical parameters that form dimensionless groups. Among these are the Nusselt, Prandtl, and Grashof numbers. emissivity: The effectiveness of a body as a thermal radiator at a given temperature. fin: An extended surface that increases the rate of heat transfer from a body. forced convection: The motion of a fluid or gas that is produced primarily by mechanical means. Fourier’s law: The law of thermal conduction. geometric factor (FA): A factor in the Stefan–Boltzmann equation to allow for the average solid angle through which one surface “sees” the other. heat pipe: A hollow metal pipe containing a fluid and a wick that greatly accelerates conduction heat transfer. heat-transfer coefficient: See coefficient of heat transfer. junction: The place where heat is maximized in an electronic component. laminar flow: A flow regime in which the fluid moves in layers or paths parallel to each other. logarithmic mean temperature difference [(Δt)m]: The appropriate temperature difference to use for parallel flow, counterflow, and constant-temperature heat exchangers. natural convection: Motion caused by the differences in density due to the difference in temperature at various locations in the fluid. Ohm’s law: The basic electrical equation for direct current circuits. It is analogous to Fourier’s law for heat conduction. overall heat transfer coefficient (U): The proportionality term in Newton’s law of cooling for heat exchangers, Q = UA(∆t)m. radiation: Heat that is transferred from one body to another without the need for a medium to effect the transfer; an electromagnetic phenomenon similar to the transmission of light. reflectivity (ρ): The fraction of the incident radiant heat that is reflected from a body, known as the reflectivity of the body. Stefan–Boltzmann law: An equation governing the radiant interchange of heat between two bodies. thermal conductivity (k): The proportionality constant in Fourier’s equation; also a physical property of a material. Q = − kA∆t/∆x. thermal resistance (Rt): As a consequence of the analogy with Ohm’s law, the thermal resistance can be written as Rt = Δx/kA. transmissivity (τ): The fraction of incident radiant heat that is transmitted. turbulent flow: The flow regime characterized by eddies that cause the mixing of the layers of fluid until no layers are distinguishable.

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Equations Developed in This Chapter Fourier’s equation

− kA∆t Q = ∆x

Ohm’s law

∆t Q = Rt

(11.3a)

Ohm’s law

i=

∆E Re

(11.4)

Series thermal circuit overall resistance

Roe = R1 + R2 + R3

Series thermal circuit overall resistance

Rot = R1 + R2 + R3 =

Parallel thermal circuit heat flow

Q = Q 1 + Q 2 + Q 3

Parallel thermal circuit overall resistance

Rot =

Hollow cylinder

ti − to =

Hollow cylinder

(t − t )2 πkL Q = 1 o ln(ro/ri )

(11.3)

(11.5) ∆x1 ∆x2 ∆x3 + + k1 A k 2 A k 3 A

1 1 1 1 + + ∆x/k1 A1 ∆x/k2 A2 ∆x/k3 A3 Q r ln o 2πkL ri

ro ri Rt = 2πkL

(11.6) (11.8) (11.10)

(11.14a)

(11.14b)

ln

Hollow cylinder

(11.14c)

(t1 − t3 )2 πL (1/k1 )ln(r2/r1 ) + (1/k2 )ln(r3/r2 )

Compound cylinder

Q =

Newton’s law of cooling

Q = hA(∆t)

Convective thermal resistance

Rc =

Natural convection from gases— laminar flow Natural convection from gases— turbulent flow

h = CL

Natural convection—vertical plates (laminar) Natural convection—vertical plates (turbulent)

h = 0.29

Natural convection—horizontal pipes (laminar)

h = 0.25

(11.15) (11.16)

1 hA

(11.17) ∆t L

1/ 4

(11.21a)

h = CTʹ (Δt)1/3 ∆t L

1/ 4

(11.22)

h = 0.21(Δt)1/3 ∆t D

(11.21b)

(11.23)

1/ 4

(11.24)

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Natural convection—horizontal pipes (turbulent)

h = 0.18(Δt)1/3

Natural convection—horizontal square plates: hot side up (laminar) Natural convection—horizontal square plates: hot side up (turbulent)

h = 0.27

Natural convection—horizontal square plates: hot side down

h = 0.12

Forced convection inside tubes— turbulent flow

(11.25)

1/ 4

∆t L

(11.26) (11.27)

h = 0.22(Δt)1/3 1/ 4

∆t L

(11.28) 1/3

Cp hD = 0.023 k k

DVρ

0.8

Stefan–Boltzmann equation

Q r = 0.173 × 108− AT 4

Stefan–Boltzmann equation

Q r = σFe FA A T 41 − T 42

Radiation heat-transfer coefficient

hr =

Heat exchanger

Q = UA(∆t)m

Overall heat-transfer coefficient for a cylinder

Uo =

Overall heat-transfer coefficient for a cylinder

Ui =

Logarithmic mean temperature difference

(∆t)m =

Heat exchanger heat balance

 c (c p )c tc − tc = m  h (c p ) h th − th m 2 1 1 2

Fin efficiency

η=

(

(

σFe FA T 41 − T 42 T1 − T2

(11.29b) (11.30)

)

(11.31)

)

(11.33) (11.42) 1

1 1 r r r r + 3 ln 2 + 3 ln 3 + ho hi (r1/r3 ) k1 r1 k2 r2

r 1 r1 + ln 2 hi k1 r1

1 r1 r 1 + ln 3 + k2 r2 ho (r3/r1 )

θ A − θB ln(θ A/θB )

(

tanh(md) md

)

Illustrative Problem 11.25, Equation (e) Illustrative Problem 11.25, Equation (f)

(11.43)

(

)

(11.44) (11.48)

QUESTIONS 11.1 11.2 11.3 11.4

Explain why gases have a much lower thermal conductivity than liquids. Compare the terms in Ohm’s law and Fourier’s law, and discuss their similarity. Show how you can go from a series electrical circuit to a series thermal circuit. Show how you can go from a parallel electrical circuit to a parallel thermal circuit. 11.5 In what way does heat transfer in a hollow cylinder differ from heat transfer in a plane wall? 11.6 What is the effect of thermal contact resistance in a series thermal circuit?

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11.7 11.8 11.9 11.10

How does convection differ from conduction? Discuss natural and forced convection. How do they differ? What are the two flow regimes in convection heat transfer? State Newton’s law of cooling and define the thermal resistance for convective heat transfer. 11.11 How is it possible to simplify the calculation of natural convection heat transfer for gases? 11.12 Which situation did we consider when we discussed forced convection? 11.13 How does radiant heat transfer differ from conduction and convection heat transfer? 11.14 What is the temperature dependence in radiation heat transfer? 11.15 How is combined convection and radiation handled? 11.16 How does the emissivity of metals vary with the condition of the surface? 11.17 How is Newton’s law of cooling written for a heat exchanger? 11.18 What is the appropriate mean temperature difference in a heat exchanger? 11.19 How is the true mean temperature difference determined in heat exchangers with differing flow paths? 11.20 Would you expect that the condensation or boiling of water in a heat exchanger would yield high or low overall heat-transfer coefficients? 11.21 Describe the effect of fouling on the performance of a heat exchanger. 11.22 How do fins increase the heat transfer rate of objects they are attached to? PROBLEMS Unless indicated otherwise, use the data of Table 11.1 and Figure 11.4 for these problems. Problems Involving Conduction Heat Transfer 11.1 A common brick wall is 4 in. thick. Determine the rate of heat transfer through the wall if one face is at 95°F while the other is at 32°F. 11.2 Compare the insulating qualities of the wall in Problem 11.1 with that of a wooden white pine wall 2 in. thick. 11.3 Compare the insulating qualities of a conducting air gap 1/4 in. thick with the brick wall of Problem 11.1. 11.4 A furnace wall has a thermal conductivity of 0.5 Btu/(h·ft.·°F). If the wall is 9 in. thick with the hot face at 2000°F and the cold face at 470°F, determine the heat loss. 11.5 A concrete wall having a thermal conductivity of 1.385 W/m·°C is made 0.2 m thick. If the outer surface is kept at 0°C while the inner surface is kept at 21°C, determine the heat loss through the wall. Assume the wall is 12 m long and 2.5 m high. 11.6 A test is conducted to determine the thermal conductivity of a material. If the test specimen is 1 ft. × 1 ft. and 6 in. thick and steady-state surface temperatures are found to be 100°F and 92°F, respectively, while 60 Btu/h is being applied, determine the thermal conductivity of the unknown material.

Heat Transfer

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11.7 A test panel is made 3 ft. × 3 ft. × 1 in. thick. The panel is found to conduct 950 Btu in a test that lasts for 3 1/2 h. If the surfaces of the panel are kept at 140°F and 110°F, respectively, determine the thermal conductivity of the panel. 11.8 A wall has a thermal conductivity of 0.4 W/m·°C. If the wall conducts 200 W/m2 while one side is maintained at 100°C, determine the temperature of the colder surface. Assume the wall to be 2 cm thick. 11.9 A wall consists of a material that is 1 in. thick. If the surface area of the panel is 10 ft.2 and the k of the wall is 0.2 Btu/(h·ft.·°F), determine the temperature of the “cold” side of the wall. The “hot” side of the wall is to be kept at 100°F, and there is a heat flow of 1000 Btu/h through it. 11.10 A brick wall is 100 mm thick. How much heat is transferred through the wall if one face is held at 40°C while the other is held at 0°C? 11.11 A test is conducted in which the test specimen is 1 m2 × 150 mm thick. Steadystate temperatures are found to be 35°C and 30°C, respectively. If 20 W is applied, determine the thermal conductivity of the material. 11.12 A furnace wall is 12 in. thick and is made of firebrick whose thermal conductivity can be taken to be 0.11 Btu/(h·ft.·°F). If the heat loss is designed not to exceed 100 Btu/h·ft.2, determine the outside wall temperature if the inside wall temperature is 1400°F. 11.13 A wall is designed to limit the heat transfer through it to 500 W/m2. If it is of firebrick whose k = 0.22 W/m·°C and it is 500 mm thick, what is the design temperature differential across the wall? 11.14 A corkboard wall has an area of 14 ft.2 and allows a heat flow of 120 Btu/h. If the surface temperatures are 70°F and 32°F, respectively, determine the thickness of the wall. 11.15 A glass window is 3 ft. × 4 ft. and 3/8 in. thick. The glass has a thermal conductivity of 0.5 Btu/(h·ft.·°F). When the inner surface temperature of the glass is 20°C, the outer surface is 10°C. Determine the heat transfer due to heat conduction only. 11.16 A portion of a wall is tested to determine its heat transfer characteristics. Assume that the wall is 6 in. thick and that 3500 Btu/h is transferred through the wall. If a temperature differential of 60°F is maintained across the wall, determine the thermal conductivity of the wall if the area is 80 ft.2. 11.17 It is desired to limit the heat loss of a furnace wall to 500 Btu/h·ft.2. The inner temperature of the wall is 2100°F, and the outer wall surface temperature is 470°F. If the material of the wall has a thermal conductivity of 0.5 Btu/(h·ft.·°F), determine the necessary wall thickness. 11.18 A mild steel sheet is used to separate two gas streams that are at different temperatures. The steel sheet is 10 ft. × 10 ft. × 1/16 in. thick, and the temperatures of the faces of the sheet differ by 32°F. Calculate the heat flow through the wall. 11.19 A building has a wall composed of 3/4 in. of white pine wood, 4 in. of mineral wool insulation, and 1/2 in. of gypsum board. The value of k for each material can be taken from Table 11.1. Calculate the overall heat transfer coefficient for the wall. 11.20 If the temperature drop across the wall in Problem 11.19 is 40°F, determine the heat loss per square foot of the wall.

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11.21 A composite series wall has an inside surface temperature of 125°F and an outside surface temperature of 52°F. If it consists of 3 in. of mineral wool, 1/2 in. of plaster on the outside, and 1/2 in. of corkboard on the inside, determine the heat loss per square foot of the wall. 11.22 Determine the interface temperatures in Problem 11.21. 11.23 A wall is 10 ft. × 12 ft. In the wall, there is a window that is 4 ft. × 4 ft. If the overall conductance of the wall is 0.28 Btu/(h·ft.2·°F) and of the window is 1.13 Btu/ (h·ft.2·°F), determine the total heat transfer if the outside temperature is 0°F and the inside temperature is 70°F. 11.24 If a wall is 3 m × 4 m and the outside temperature is −20°C while the room is maintained at 20°C, determine the heat transfer through the wall. The overall heat transfer coefficient of the wall is 0.07 W/m2·°C. Assume also that a 1 m × 1 m window exists in the wall and that the window has an overall heat transfer coefficient of 0.2 W/m2·°C. 11.25 A so-called “solid brick” construction consists of three courses of a common brick, each 4 in. thick. Comment on the insulating qualities of this wall when compared to a hollow wall filled with 3 in. of mineral wool. 11.26 A bar of steel 1 in. in diameter and 6 in. long is cut in half, and the cut ends are pressed together. If the thermal contact resistance can be thought of as an equivalent air gap of 0.001 in. thick (k = 0.01 Btu/(h·ft.·°F)), determine the percent increase in resistance to heat transfer from one end of the bar to the other due to the cutting of the bar, that is, [(cut resistance − uncut resistance)/uncut resistance] × 100. 11.27 A wall is to be made of 4 in. of a common brick, 2 in. of mineral wool, and 1/2 in. of wallboard (k = 0.04 Btu/(h·ft.·°F) from Appendix 2). Determine the heat transfer from the wall if the inside wall temperature is at 74°F when the outside wall is at 0°F. 11.28 Determine the interface temperatures in Problem 11.27. 11.29 A wall consists of 100 mm of mineral wool, 12 mm of plaster, and 12 mm of corkboard. If a temperature difference of 30°C is maintained across the wall, what is the steady-state heat transfer? 11.30 What is the heat loss from a bare steel pipe (k = 45 W/m·°C) whose inside temperature is 190°C and whose outer temperature is 100°C? The inside diameter of the pipe is 25 mm, and the outside diameter is 40 mm. Its length is 2 m. 11.31 Solve Problem 11.30 for a copper pipe (k = 390 W/m·°C). Compare your results. *11.32 The equation for the heat transfer through a cylindrical wall is given by Equation 11.14b. By comparison with a plane wall, show that the mean conducting area for a cylindrical shell is 2πL(r2 − r1)/ln(r2/r1). If S1 and S2 are the inner and outer surface areas, respectively, show that the mean conducting area is also (S2 − S1) ln(S2/S1). *11.33 The heat transfer through a spherical shell of radii r2 and r1 is

Q=

4πkr1r2 (t1 − t2 ) r2 − r1

Show that the mean conducting area for a spherical shell is 4πr1r2 or S1S2 , where S1 and S2 are the inner and outer spherical surface areas, respectively.

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11.34 A steel pipe having a 4 1/2 in. outside diameter is insulated with a molded pipe covering of diatomaceous earth (k = 0.036 Btu/(h·ft.·°F)) 1 1/2 in. thick. Thermocouples embedded in the insulation read 212°F on the inside and 130°F on the outside. Find the heat loss per foot length of the pipe. 11.35 Determine the heat loss from 50 ft. of 3 1/2 in. outside diameter pipe covered with 1 in. insulation (k = 0.03 Btu/(h·ft.·°F)) if the inner temperature of the insulation is 350°F and the outer temperature is 100°F. 11.36 A large steel pipe having an 8 in. outside diameter carries superheated steam. If the inside insulation temperature is 800°F and the pipe is insulated with 3 in. of molded pipe covering (k = 0.036 Btu/(h·ft.·°F)), determine the heat loss per foot of the pipe if the outside insulation temperature does not exceed 140°F. 11.37 If the steel pipe in Problem 11.36 has a wall thickness of 1/2 in. and ksteel = 26 Btu/ (h·ft.·°F), determine the heat loss per foot of the pipe. Assume that the inside of the pipe is at 800°F and the outside of the insulation remains at 140°F. Compare the results with those for Problem 11.36. 11.38 A steel boiler tube is 0.18 in. thick and has an outside diameter of 4 in. If the inside surface is at 500°F and there is a heat loss of 3800 Btu/h per foot length of the pipe, determine the outside tube temperature. 11.39 If the boiler tube in Problem 11.38 has a scale thickness of 0.1 in. built up on the inside of the tube, determine the outside tube temperature. Assume that the inside of the scale is at 500°F and that the scale has a thermal conductivity of 1.5 Btu/(h·ft.2·°F). 11.40 A 3 in. thick brick wall separates 75°F air from the outside air at 25°F. What thickness of gypsum plaster overlay will keep the heat loss through the wall to 50 Btu/h·ft.2? 11.41 A composite wall 8 ft. × 10 ft. is made up of 2 in. thick gypsum plaster and 1 in. thick fir. When a temperature difference of 80°F exists across the wall, what thickness of mineral wool insulation must be added to limit heat transfer through the wall to 800 Btu/h? 11.42 A 20 cm thick aluminum plate is to be insulated to keep the heat loss through it down to 100 W/m2 when a Δt of 40°C exists across it. What thickness of corkboard will accomplish this? 11.43 What is the heat loss rate per meter of a 10 cm outside diameter × 5 mm thick copper pipe covered with 1 cm of asbestos when a 50°C temperature difference exists across the insulated pipe wall? *11.44 What thickness of mineral wool insulation is required to limit the heat loss rate from a 6 in. outside diameter porcelain pipe, 1 in. thick, to 50 Btu/h per feet of pipe when an overall temperature gradient of 100°F exists? *11.45 In Problem 11.44, if the outside of the insulation is at 40°F, what is the temperature at the interface of the pipe and the insulation? Problems Involving Convection Heat Transfer 11.46 A bare horizontal pipe with 6 in. outside diameter has its outer surface at 140°F in a room whose air temperature is 65°F. Determine the natural convection heattransfer coefficient on the outside of the pipe.

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11.47 If instead of a pipe the surface in Problem 11.46 was a 1 ft. × 1 ft. square plate with the hot side facing up, determine the convection heat-transfer coefficient. 11.48 Determine the heat loss to the room by convection if the pipe in Problem 11.46 is 10 ft. long. 11.49 If the hot surface of the plate in Problem 11.47 faces down, determine the convection heat transfer coefficient. 11.50 Atmospheric air flows in a 1 in. inside diameter tube at the rate of 0.2 lbm/s. If the average air temperature is 150°F, determine the film coefficient on the inside of the tube. 11.51 Air flows in a 1.5 in. inside diameter tube at the rate of 0.4 lbm/s and has an average temperature of 500°F. If the air is at atmospheric pressure, determine the heat-transfer coefficient on the inside of the tube. 11.52 Solve Problem 11.50 if the average air temperature is raised to 250°F. Compare your results. 11.53 Solve Problem 11.51 for a 2.0 in. inside diameter tube. Compare the results of these two problems. 11.54 If water flows in a 1 in. inside diameter tube at the rate of 1 lbm/s, determine the film coefficient on the inside of the tube. The average temperature is 150°F. 11.55 Solve Problem 11.54 for a 2 in. inside diameter tube. Compare the results of these problems. 11.56 Water having an average temperature of 200°F flows in a 2 in. inside diameter pipe at the rate of 1.5 lbm/s. Determine the heat-transfer coefficient on the inside of the pipe. 11.57 If the flow rate in Problem 11.56 is increased to 2.0 lbm/s, determine the heattransfer coefficient of the inside of the pipe. 11.58 A square, hollow tube is made of steel and has a thermal conductivity of 26 Btu/ (h·ft.·°F). On one side, the film coefficient is 500 Btu/(h·ft.2·°F), while on the other side, the film coefficient is 250 Btu/(h·ft.2·°F). Estimate the overall heat-transfer coefficient if the tube is 1/2 in. thick. 11.59 A bare vertical pipe, 5 in. outside diameter has its outer surface at 120°F in a 70°F room. Find the convective heat loss per foot of the pipe. 11.60 A vertical plate, 3 ft. × 3 ft., is at 180°F on one side; the other side is insulated. Find the convective heat-loss rate to 65°F still air. 11.61 In Problem 11.51, find the heat-transfer rate per foot of the tube if the temperature of the inside of the tube is 350°F. 11.62 In Problem 11.56, find the heat-transfer rate if the pipe is 4 ft. long and its inside surface is at 150°F. Problems Involving Radiation Heat Transfer 11.63 Calculate the rate of heat radiation from a blackbody per square foot of radiating area if the temperature of the body is 1000°F, 100°F, and 0°F. 11.64 Two opposed, parallel infinite black planes are at 350°F and 450°F, respectively. Determine their net heat interchange. 11.65 If the upper temperature in Problem 11.64 is made 550°F, by what percentage is the net heat transfer increased over that in Problem 11.64?

Heat Transfer

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11.66 Assume that the planes in Problem 11.64 are gray with emissivities of 0.8 and 0.7, respectively. Determine the net heat interchange, and compare your answer to Problem 11.64. 11.67 Two perfectly black squares, 10 ft. × 10 ft., are spaced 20 ft. apart. What is the net rate of heat exchange between them if their temperatures are 500°F and 200°F, respectively? The planes are parallel and directly opposite each other. 11.68 Solve Problem 11.67 if the planes have emissivities of 0.8 and 0.9, respectively. 11.69 Two perfectly black rectangles, 6 ft. × 9 ft., are spaced 6 ft. apart. Their temperatures are 800°F and 200°F, respectively. If the planes are parallel and directly opposite each other, determine the net heat interchange. 11.70 Solve Problem 11.69 if both planes have emissivities of 0.8. 11.71 Solve Problem 11.69 if one plane has an emissivity of 0.85 and the other has an emissivity of 0.75. 11.72 A 3 1/2 in. outside diameter oxidized iron pipe whose outer temperature is 175°F passes through a room at 75°F. If εpipe = 0.8, determine hr, the radiation heattransfer coefficient. 11.73 A body whose emissivity is 0.9 is placed in a large room whose walls are at 20°C. If the body is at 250°C, determine the heat radiated to the walls per square meter of body surface. Assume that the body is small compared to the dimensions of the room. 11.74 Calculate the radiant heat interchange between two square plates having 1 ft. sides if they are separated by 1/2 ft. Assume that one square has an emissivity of 0.8 and that the other has an emissivity of 0.6. The hotter surface is at 1000°F, and the colder surface is at 100°F. 11.75 A rough metal sphere having an emissivity of 0.85 and a 12 in. diameter is hung by a nonconducting wire in a large room. Inside the sphere is an electrical heater that maintains the surface at 200°F. If the room is at 70°F, determine the wattage of the heater. 11.76 A light bulb filament may be considered to be a blackbody. If such a filament has a diameter of 0.12 mm and a length of 4 cm, determine the filament temperature. Consider radiation only, and ignore the temperature of the room or the glass envelope. The bulb is rated at 60 W. *11.77 Consider two parallel, infinite planes having the same emissivity. The planes are at temperatures T1 and T2, respectively. A third plane having the same emissivity is placed between the original planes and allowed to come to its equilibrium temperature T3. Show that the presence of the third plane reduces the heat transfer between the original two planes to half the value obtained when no plane (shield) is present. 11.78 What is the net radiation heat-transfer rate between the floor of a furnace at 1000°F and one of its walls at 500°F? The emissivity of each is 0.8. The floor is 6 ft. × 12 ft., and the wall is 6 ft. × 9 ft. with the 6 ft. length common to both. 11.79 Two 3 ft. diameter disks hang vertically 9 in. apart in a 75°F room. The emissivity of each is 0.7. One disk is at 200°F, and the other is at room temperature. Find the radiant heat-transfer rate between the two disks.

594

Thermodynamics and Heat Power

Problems Involving Heat Exchangers 11.80 A condenser operates with steam condensing at 1 psia (101.7°F). If the cooling water enters at 46°F and leaves at 90°F, determine the log mean temperature difference. *11.81 The log mean temperature difference in a condenser operating at 1.5 psia (115.65°F) is 30°F. If the cooling water enters at 50°F, determine the exit temperature of the water. *11.82 In an air heater operating as a counterflow heat exchanger, the air enters at 70°F and is heated to 200°F. The flue gas enters the heater at 620°F. The mass flow rate of the flue gas is 12% greater than the mass flow rate of the air. Assuming that the specific heats of the air and the flue gas are equal, determine the log mean temperature difference in the unit. 11.83 Solve Problem 11.82 for a parallel flow heat-transfer arrangement. 11.84 A counterflow heat exchanger operates with the hot fluid entering at 850°F and leaving at 650°F. The cold fluid enters at 150°F and leaves at 550°F. Calculate the log mean temperature difference. 11.85 Solve Problem 11.84 if the unit is operated as a parallel flow heat exchanger. 11.86 Solve Problem 11.84 for the true temperature difference if the unit is operated with one shell pass and two tube passes with the hot fluid on the shell side. 11.87 A condenser has condensed steam on its shell side at 81.7°F. If the cooling water enters at 60°F and leaves at 70°F, determine the logarithmic mean temperature difference in the unit. 11.88 If the overall heat-transfer coefficient in Problem 11.87 is 1000 Btu/(h·ft.2·°F) of the outside tube surface, determine the heat transfer per square foot of the exchanger outside tube surface. 11.89 A condenser in a power plant operates at 15°C. The cooling water enters at 5°C and leaves at 10°C. Determine the logarithmic mean temperature difference in the unit. 11.90 If the overall heat transfer coefficient in Problem 11.89 is 250 W/m2·°C of the outside tube surface, determine the heat transfer per square meter of the exchanger outside tube surface. 11.91 A counterflow heat exchanger cools oil from 175°F to 125°F. The cooling water enters at 65°F and leaves at 85°F. Calculate the logarithmic mean temperature difference in the unit. 11.92 If the heat exchanger in Problem 11.91 is operated as a parallel flow unit, determine the logarithmic mean temperature difference. 11.93 A counterflow heat exchanger operates with oil cooled from 90°C to 50°C. The cooling water enters at 15°C and leaves at 25°C. If the overall heat-transfer coefficient based on the outside tube surface is 200 W/m2·°C, determine the heat transfer per square meter of the outside tube surface. 11.94 If the heat exchanger in Problem 11.93 is operated as a parallel flow unit, determine the heat transfer. 11.95 A condenser operates with steam condensing on the shell side at 27°C. Cooling water enters at 5°C and leaves at 10°C. If the overall heat transfer coefficient is 5000 W/m2·°C based on the outside tube surface, determine the heat transfer per square meter of the outside tube surface.

Heat Transfer

595

11.96 A nuclear steam generator boils water (makes steam) at 500°F on the shell side of a steam generator. Water enters the tubes at 570°F and leaves at 525°F. Determine the logarithmic mean temperature difference. 11.97 A tank-type heat exchanger is used to generate steam at 275°C. Water enters the tubes at 325°C and leaves at 300°C. Determine the logarithmic mean temperature difference. 11.98 A heat exchanger is used to transfer 1 × 106 Btu/h. At the inlet, the temperature difference between fluids is 75°F, and at the outlet, the temperature difference is 35°F. Determine the surface required if the overall heat-transfer coefficient is 175 Btu/(h·ft.2·°F) based on the outside area of the tubes. 11.99 A heat exchanger is used to transfer 300 kW. At the inlet, the temperature difference between the fluids is 40°C, and at the outlet, the difference is 20°C. Determine the surface required if the overall heat-transfer coefficient is 1000 W/m2·°C based on the outside area of the tubes. 11.100 How much heat is being exchanged in a heat exchanger having an overall heattransfer coefficient of 60 Btu/(h·ft.2·°F) based on the outside area of the tubes, 625 ft.2 of outside tube area, and temperature differences between fluids at inlet of 62°F and at outlet of 36°F? 11.101 A heat exchanger has an overall heat-transfer coefficient of 550 W/m2·°C based on the outside area of the tubes. If there is 400 m2 of outside tube area and the temperature differences between fluids at the inlet is 40°C and at the outlet is 22°C, determine the total heat transfer in the unit. *11.102 A shell-and-tube heat exchanger has a film coefficient on the inside of the tube of 100 Btu/(h·ft.2·°F), a steel tube wall thickness of 0.105 in. (k = 26 Btu/(h·ft.·°F)), a tube outside diameter of 3/4 in., and a film coefficient on the shell side (outside of tube) of 50 Btu/(h·ft.2·°F). Determine the overall film coefficient based on the inside area of the tube. *11.103 Determine the overall film coefficient of the unit in Problem 11.102 based on the outside area of the tube. 11.104 A counterflow heat exchanger is used to cool 2000 lbm/h of oil from 150°F to 100°F. Assume the cp of oil to be 0.5 Btu/lb.·°F. Water (cp = 1 Btu/lb.·°F) enters at 55°F and leaves at 75°F. U, based on the outside area of the tubes, is 30 Btu/ (h·ft.2·°F). Determine the area required. *11.105 A shell-and-tube heat exchanger is used to condense steam on the shell side at 81.7°F. Cooling water enters the tubes at 60°F and leaves at 70°F. The tubes have a 1 in. outside diameter, a 0.902 in. inside diameter, and a conductivity of 63 Btu/ (h·ft.·°F). The film coefficient on the inside of the tubes is 1200 Btu/(h·ft.2·°F) and on the outside is 950 Btu/(h·ft.2·°F). If the unit extracts 766 × 106 Btu/h, determine the outside tube area. 11.106 In Problem 11.104, what should the cooling water flow rate be? *11.107 A shell and tube heat exchanger is used to reject 400,000 kW of heat. Saturated steam enters at 40°C and leaves as 40°C saturated liquid. Cooling water (specific heat = 4.19 kJ/kg K) enters at 10°C and leaves at 15°C. The tubes have a 25 mm O.D. and have an overall heat transfer coefficient U = 2000 W/m2 °C. Determine (a) the mass flow rate of cooling water required, (b) the log mean temperature difference, and (c) the length of heat exchanger tubing required.

596

Thermodynamics and Heat Power

Problems Involving Combined Modes of Heat Transfer 11.108 Solve Problem 11.18 assuming air films exist on both sides of the wall and that the temperatures given are the temperatures of the air on each side of the wall, respectively. Calculate the heat loss through the wall if both surface heat-­transfer coefficients are equal to 1.4 Btu/(h·ft.2·°F). 11.109 Solve Problem 11.15 assuming air film exists on both sides of the window and that the given temperatures are that of the air on each side, respectively. Determine the heat transfer through the window if the heat transfer coefficients on both sides can be taken to be 1.35 Btu/(h·ft.2·°F). 11.110 Solve Problem 11.21 if there are air films on both sides of the wall having heat transfer coefficients of 1.2 Btu/(h·ft.2·°F). 11.111 Determine the heat transfer in Problem 11.27 if there is an air film on each side of the wall, each having a heat transfer coefficient of 2 Btu/(h·ft.2·°F). Assume the temperatures to be the air temperatures on both sides of the wall. 11.112 If a film coefficient of 1 W/m2·°C exists on the inside of the wall in Problem 11.29 and the temperature differential is across the film plus the composite wall, determine the heat transfer. 11.113 A wall, 7 ft. × 7 ft., conducts 500 Btu/h. If there is a film coefficient on the inside of the wall of 1 Btu/(h·ft.2·°F) and the wall has a resistance equal to 1 in. of mineral wool, determine the temperature drop across each resistance. 11.114 A composite wall consists of 1/2 in. plaster and 2 in. of fir. If the hot-side air is at 105°F, the cold-side air is at 10°F, the hot-side film coefficient is 2 Btu/(h·ft.2·°F), and the cold-side film coefficient is 4 Btu/(h·ft.2·°F), determine the heat transfer per square foot of the wall. 11.115 Determine the temperature drops through each resistance in Problem 11.114. 11.116 If the pipe in Problem 11.36 has an outside heat transfer coefficient of 2.5 Btu/ (h·ft.2·°F), and the room temperature is 140°F, determine the heat loss per foot of the pipe. Neglect the steel-wall resistance. 11.117 If in Problem 11.72 there is a convection heat-transfer coefficient of 1.5 Btu/ (h·ft.2·°F) on the outside of the pipe, determine the combined heat-transfer coefficient and the heat loss per foot of the pipe. 11.118 In Problem 11.79, find the total heat loss rate from the hotter disk if the room air is still. Consider the disk as a vertical plate with the diameter as the characteristic length. 11.119 Two 9 in. × 9 in. plates hang vertically separated by a 3 in. air space. One plate is at 350°F with an emissivity of 0.8; the other is at 100°F with an ε of 0.7. The air is still and at 200°F. Find the total heat loss rate from the hotter plate. *11.120 In a large kitchen, a small griddle of 1 ft.2 is on a horizontal table and operates at 350°F. Its surface emissivity is 0.6. If the kitchen air is still at 70°F, how much heat does the griddle add to the room whose walls are at 75°F in its 2 h of operation? 11.121 A 4 in. outside diameter horizontal pipe (ε = 0.8) whose surface is at 150°F is in a large room of still air at 70°F. What percentage of its heat loss is by convection? By radiation?

Heat Transfer

597

11.122 A 0.03 in. nichrome wire runs horizontally through a large enclosure containing 80°F air. The temperature of the wire can reach 2250°F. Find the maximum total heat loss per foot from the wire if the emissivity of the wire is 0.3. (Hint: Consider the wire as a horizontal pipe.) 11.123 A 2 ft. × 2 ft. plate, ε = 0.7, and 150°F on one side with the other side insulated, is placed in a large room at 60°F. Find its total heat loss rate when it is (a) vertical; (b) horizontal, hot side up; and (c) horizontal, hot side down. *11.124 A foot-long horizontal porcelain pipe, 5 in. outside diameter × 0.5 in. thick, is in still air at 70°F. Find the overall heat-transfer coefficient, including conduction and convection, based on the outer surface area when the surface is at 200°F. *11.125 In Problem 11.124, if the emissivity of the porcelain is 0.9, find the overall heattransfer coefficient including radiation.

Appendix 1: Answers to Even-Numbered Problems

Chapter 1 1.2 1.4 1.6 1.8 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62

9.78 cm 2.894 tons 2.95 ft. 3900.9 g 256.54 cm 943.9 L/s 0.2103 L/s 0.00333 m3/s 5.07 × 10 –5 m3/s 102,600 L/min 1579.9 gpm 0.00946 m3/s 3650 L/s 135.92 L/s 0.0774 m2 0.01416 m3 0.003218 m3 3.93 L 29.05 m3 3.123 m3 0.932 mi. 39.77 mi./h 5339.7 N; 2.54 × 10 –5 m 68°F, 104°F, 140°F 4.44°C, 227°C, 87.8°C 160°C, 320°F –160°F, –106.7°C –130.15°ARB 490.5 N (c) 979.063 N

599

600

1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 1.100 1.102 1.104 1.106 1.108 1.110 1.112 1.114 1.116 1.118

Appendix 1

10.198 kg 61.19 kg 0.39 lbf 38.22 N 10 m/s2 2 kg 2.4 N 25 lbm/ft.3, 0.04 ft.3/lbm 149.6 lbf/ft.3, 149.6 lbm/ft.3 56.16 lbf/ft.3, 8829 N/m3 2057.7 lbf 7848 N/m3, 800 kg/m3, 0.00125 m3/kg 1.26 10.37 lbf/ft.3 8.14 N 8.679 lbf 435.6 N 1.95 ft.3 40.7 psia 273.73 kPa 0.87 psig 250 kg/m3, 0.25 39.5 psia, 7.0 ft. 10.3 psia 2576.4 psfa 10.33 psf 18.72 psia 80,902 kPa, 3964 kN

Chapter 2 2.2 2.4 2.6 2.8 2.10 2.12 2.14 2.16

300 ft. lbf, 600 ft. lbf; 380 ft. lbf, 600 ft. lbf 294.3 J 250 J 38.86 ft. lbf 9810 J, 6.26 m/s 1000 ft. lbf, 80.2 ft./s 7.67 m/s 288.86 ft. lbf, 250 ft. lbf, 38.86 ft. lbf

Appendix 1

2.18 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54

4 kJ, 9 kJ 2000 N/m, 62.5 J 10.4 ft. lbf 2500 N/m 3.37 ft. 4330 J 234.38 kJ Derivation 13 625 kW 50 J 693.1 kJ/kg –1800 ft. lbf (work in) 14,400 ft. lbf 161.25 kJ 2818 ft. lbf/lbm 60.54 kJ 1920 ft. lbf 100 kJ 19.31 kJ

Chapter 3 3.2 3.4 3.6 3.8 3.10 3.12 3.14 3.16 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34

215 kJ (into) 70 Btu/lbm (increase) 45 kJ/kg –17.78 Btu/lbm cp = 1 kJ/kg·K, ΔV = 0.214 m3 120 kJ –240 ft. lbf/lbm –8.84 Btu/lbm 171.5 Btu/lbm 0.005 kJ/kg·K 1 kJ/kg·K 75 kJ/kg 149.4°C, 28.6 kJ/kg 2 Btu/lbm·°R 354.17 kJ/kg –17.5 kJ (into), –24.5 kJ (decrease) x = 100, y = 150, z = –300, t = –400

601

602

3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.50 3.52 3.54 3.56 3.58 3.60 3.62 3.64 3.66 3.68 3.70 3.72 3.74 3.76 3.78 3.80 3.82 3.84 3.86

Appendix 1

2.04 ft./s 1.8 × 106 kg/h 13.33 ft./s 55 ft./s, 24.4 ft./s, 1872 lbm/s 13.48 ft./s 4.69 ft./s 4.59 ft./s, 47 ft./s 6367.3 ft. lbf/s, 11.6 hp –61.8 hp (in) 100 J/kg 500 Btu/lbm, not necessarily –350 kJ/kg 212.13 Btu/lbm 44.96 Btu/lbm –100 kJ/kg (in) 79.5 Btu/lbm 2730 kW 188.05 kJ/kg 2451 ft./s 4002 ft./s 634.4 m/s 1808 ft./s 1793.9 ft./s 2155.2 kJ/kg 1.86 ft.3/lbm, 240.02 Btu/lbm (into system) 0.689 lbm/lbm

Chapter 4 4.2 4.4 4.6 4.8 4.10 4.12 4.14 4.16 4.18 4.20

845.84 Btu/min, 33.4% 1370.6 MW requires an upper temperature of 5000°R! 34.35% 1 636 380 kJ/h; 40.73 L/h 32.54% 34.2%, 38.5%, 41.1%, lower T2 127.27 hp, 47.27 hp, 62.86% 115.17 Btu 70.8%, Qr = 146 Btu/min, work = 354 Btu/min

Appendix 1

4.22 4.24 4.26 4.28 4.30 4.32 4.34 4.36 4.38 4.40 4.42 4.44 4.46 4.48 4.50 4.52 4.54 4.56 4.58 4.60 4.62 4.64 4.66 4.68 4.70 4.72 4.74 4.76 4.78 4.80 4.82

retest Derivation 30.77% 3.37 h/day, $2.27/day 51.5%, 39.9 Btu/min 65.5%, 392.9 W 0.57 hp 7.88% 68.86%, 217.8 kJ, 67.8 kJ 42.1%, T1 = 932.9°R 1428.6 Btu/h 1.429 MJ 509.4 Btu/h 0.82 hp 463.8 K 54.3 kW, 35.3 kW, 427.7 K 85.2°F; 6.74 Btu/min·°R Δs = 1.8528 vs. 1.8526 Btu/lbm·°R 0.312 Btu/lbm·°R 0.1607 Btu/lbm·°R –0.1607 Btu/lbm·°R 0.4241 kJ/kg·K 0.2267 Btu/lbm·°R 150 Btu/lbm 0.1552 Btu/lbm·°R 1.2 MJ, 4 kJ/K 0.6390 kJ/kg·K 530°R 1105°R 0 58.6 kJ/kg, 63.6 kJ/kg total Δs = 0.026 Btu/lbm·°R

Chapter 5 5.2

at 1.0 MPa hg = 2778.1 kJ/kg sg = 6.5865 kJ/kg·K vg = 194.44 × 10 –3 m3/kg ug = 2583.6 kJ/kg

603

604

5.4

5.6 5.8 5.10

5.12 5.14 5.16 5.18 5.20 5.22 5.24 5.26 5.28 5.30 5.32 5.34 5.36 5.38

5.40 5.42

Appendix 1

at 1.1 MPa hg = 2781.7 kJ/kg sg = 6.5536 kJ/kg·K vg = 177.53 × 10 –3 m3/kg ug = 2586.4 kJ/kg at 350°F p = 134.53 psia vf = 0.017988 ft.3/lbm hf = 321.80 Btu/lbm at 500°F p = 680 psia vf = 0.02043 ft.3/lbm hf = 487.7 Btu/lbm hfg = 826.8 Btu/lbm 897.44 Btu/lbm, 897.5 Btu/lbm h = 1143.35 Btu/lbm s = 1.54694 Btu/lbm·°R v = 4.213 ft.3/lbm u = 1065.41 Btu/lbm 82.3% 2.9261 ft.3/lbm 819.71 Btu/lbm 11,064 ft.3/lbm 0.396, 41.85 psia 1.109 MPa 1098.58 Btu/lbm, 467.13°F (wet) 2,004 ft.3/lbm 541.7 psia 0.3066 m3/kg 1327.3 Btu/lbm 1333.2 Btu/lbm 66,179 ft.3/lbm, 1030.98 Btu/lbm, 969.76 ft.3/lbm h = 487.5 Btu/lbm v = 0.019766 ft.3/lbm u = 472.9 Btu/lbm s = 0.6758 Btu/lbm·°R 2.18 MPa at 100 psia hg = 1187.7 Bm/lbm sg = 1.6034 Btu/lbm·°R vg = 4.4329 ft.3/lbm ug = 1105.7 Btu/lbm

Appendix 1

5.44

5.46 5.48 5.50

5.52

5.54 5.56 5.58 5.60 5.62 5.64 5.66 5.68 5.70 5.72 5.74 5.76 5.78 5.80 5.82 5.84 5.86 5.88 5.90

at 1000 psia hg = 1192.2 Btu/lbm sg = 1.3902 Btu/lbm·°R vg = 0.4459 ft.3/lbm ug = 1109.7 Btu/lbm at 1.0 MPa hf = 762.88 kJ/kg sf = 2.1388 kJ/kg·K vf = 0.001127 m3/kg uf = 761.75 kJ/kg at 1.1 MPa hf = 781.38 kJ/kg sf = 2.1793 kJ/kg vf = 0.001133 m3/kg uf = 780.14 kJ/kg u = 3046.2 kJ/kg sfg = 1.6529 Btu/lbm·°R p = 5.6267 kPa vf = 0.001006 m3/kg sf = 0.5050 kJ/kg·K h = 2582.2 kJ/kg v = 0.1571 m3/kg s = 6.1107 kJ/kg·K u = 2406.2 kJ/kg 0.3162 0.6723 0.07685 m3/kg x = 0.0517, t = 78.186°C x = 0.0909, 0.019612 m3, 0.00238 m3, 2.3178 MPa 2.347 psia, 132.02°F, 0.01626 ft.3/lbm 212.42°C, 2422.5 kJ/kg 1563.7 Btu/lbm 0.5166 ft.3/lbm 2835 kJ/kg 2811.7 kJ/kg 2245.9 kJ/kg 2620.1 kJ/kg 487.50 Btu/lbm 1039.0°F, 1541.8 Btu/lbm 6.47 kg 247.1 psia, 10.72 lbm 8.581 MPa, 230.73 kg 52.78 lbm vapor 1063.4 lbm liquid

605

606

5.92 5.94 5.96 5.98 5.100 5.102 5.104 5.106 5.108 5.110 5.112 5.114 5.116 5.118 5.120 5.122 5.124 5.126 5.128 5.130 5.132 5.134 5.136 5.138 5.140 5.142 5.144 5.146 5.148 5.150 5.152 5.154 5.156 5.158 5.160 5.162 5.164 5.166 5.168 5.170 5.172

Appendix 1

39.37 kg liquid 9.84 kg vapor 0.644 0.5157 235.1 Btu vapor = 57.52%, liquid = 42.49% 6238.7 Btu (removed) 557,600 Btu 1019.73 Btu/lbm 316.9 Btu/lbm 756.44°F; from chart approx. 755°F 312.07°F, moisture = 7.6% moisture 2% –130 Btu/lbm 1058.08 Btu/lbm 1179.88 Btu/lbm 0.531 Btu/lbm·°F 350 Btu/lbm 891.31 Btu/lbm 4030.6 kJ 412.87 psia 74.7 Btu/lbm 32.69 Btu/lbm 76.6 Btu/lbm 4497 ft./s 1311.7 m/s 1354.3 m/s 6.46 kg 247.05 psia, 10.72 lbm 8.583 kPa, 230.73 kg 52.80 lbm vapor 1063.3 lbm liquid 39.38 kg vapor 9.85 kg liquid 0.644 0.5156 235.4 Btu/lbm vapor = 57.51%, liquid = 42.49% 6259.5 Btu (removed) 567,285 Btu 1019.62 Btu/lbm 317.0 Btu/lbm 756.56°F 312.09°F, 7.64%

Appendix 1

5.174 5.176 5.178 5.180 5.182 5.184 5.186 5.188 5.190 5.192 5.194 5.196 5.198 5.200 5.202

moisture = 2.05% 129.6 Btu/lbm 1058.0 Btu/lbm 1179.9 Btu/lbm 0.531 Btu/lbm·°R 353.2 Btu/lbm 890.99 Btu/lbm 4029.64 kJ/kg 412.87 psia 74.8 Btu/lbm 31.1 Btu/lbm 76.6 Btu/lbm 4496.4 ft./s 1306.4 m/s 1354.1 m/s

Chapter 6 6.2 6.4 6.6 6.8 6.10 6.12 6.14 6.16 6.18 6.20 6.22 6.24 6.26 6.28 6.30 6.32 6.34 6.36 6.38 6.40 6.42

163.8 K 0.4 lbm/ft.3 13.29 ft.3/lbm 0.813 lbm/ft.3 425 psia 1.283 kJ/kg·K, 6.48 0.171 m3/kg 1.06 kJ/kg·K 70.94 kg 0.706 ft.3/lbm 0.6062 ft.3 337.9°R 232.7 kPa 40.93 ft.3 cv = 0.4725 kJ/kg·K, cp = 0.6615 kJ/kg·K cv = 0.9556 kJ/kg·K, cp = 1.2423 kJ/kg·K R = 0.316 kJ/kg·K, MW = 26.31 MW = 29.21 MW = 27.97, k = 1.4 MW = 28.57, R = 0.291 kJ/kg·K, cv = 0.9091 kJ/kg·K 11.5 ft.3/lbm

607

608

6.44 6.46 6.48 6.50 6.52 6.54 6.56 6.58 6.60 6.62 6.64 6.66 6.68 6.70 6.72 6.74 6.76 6.78 6.80 6.82 6.84 6.86 6.88 6.90 6.92 6.94 6.96 6.98 6.100 6.102 6.104 6.106 6.108 6.110 6.112 6.114 6.116 6.118 6.120 6.122 6.124 6.126 6.128

Appendix 1

–193.4 kJ (in) –0.6601 kJ/K –71744 ft. lbf 218.2 kJ Q = 16.9 Btu, 0.02777 Btu/°R v = 0.251 ft.3/lbm, Δs = –0.16928 Btu/lbm·°R, Q = –94.8 Btu 80 psia, 105 557 ft. lbf, Δu = 0, Q = 135.7 Btu 24.42 ft.3, 15.0 lbm 524.2 kJ, 0, 524.2 kJ, 1.1082 kJ/kg·K 61.70 lbm 33.33 psia 0.00852 Btu/°R, 1.47 0.11853 Btu/lbm·°R 85.5 Btu/lbm 0.17446 Btu/lbm·°R 0.01760 kJ/K 68.8 psia, 611.3°F, 0.1283 Btu/°R 641.6°F 792.4 K, 676.8 kJ 4480°R, 208,696 ft. lbf/lbm 28.8 Btu/lbm 0.2405 Btu/lbm·°R 0.2472 Btu/lbm·°R 0.30525 Btu/lbm·°R +0.3529 m3, 4.0 kJ/kg·K 5.83 ft.3 –96 Btu/lbm work = 91.1 Btu/lbm, Δu = 225.7 Btu/lbm, q = 316.0 Btu/lbm q = 64.8 Btu/lbm, Δs = 0.088 Btu/lbm·°R work = 5517.9 ft. lbf, V2 = 5.76 ft.3 331.4 psia 1948.5°R 425.3°R 395.2°R 395.2°R 1.37 1.29 342.4 Btu/lbm 1.24 1.30 –85.4 Btu/lbm(in) –133.6 kJ/kg (in) 858.8·°R, 104.4 psia

Appendix 1

6.130 6.132 6.134 6.136 6.138 6.140 6.142 6.144

0.2516 Btu/lbm·°R 0.226 Btu/lbm·°R 0.242 ft.3/lb (ideal gas), 0.244 ft.3/lbm (real) 10 194 lbm 7.23 lbm/ft.3 13.3°F 320.8°F, 27.5 psia 960.2°R

Chapter 7 7.2

7.4

7.6 7.8 7.10

7.12 7.14 7.16 7.18

7.20

moles CH4 = 0.06238 moles O2 = 0.03125 total moles = 0.09363 xCH 4 = 0.666 xO2 = 0.334 MW = 21.36 CO2 = 40.4% N2 = 56.6% He = 2.9% C2H2 = 34.53 MPa C4H10 = 15.47 MPa MW = 29.38 R = 52.59 ft. lbf/lbm·°R R = 210.72 ft. lbf/lbm·°R CO2 = 8.33% He = 91.67% 62.6 m3 MW = 37.68 MW = 34.62 ft. lbf/lbm·°R CH4 = 93.5% CO2 = 2.98% N2 = 1.90% H2 = 1.60% MW = 14.75 R = 104.75 ft. lbf/lbm·°R volume = 69.5 ft.3 CH4 = 53.5 ft.3 O2 = 16.2 ft.3

609

610

7.22

7.24 7.26 7.28

7.30

7.32

7.34 7.36 7.38 7.40 7.42 7.44 7.46 7.48 7.50 7.52

Appendix 1

pCH 4 = 57.6 psia PO2 = 17.4 psia xCH 4 = 0.768 xO2 = 0.232 MW = 19.73 pCO = 44.98 kPa pHe = 629.80 kPa ptotal = 674.77 kPa MW = 38.0 R = 40.66 ft. lbf/lbm·°R MW = 30.4 R = 0.2735 kJ/kg·K MW = 10.69 R = 0.778 kJ/kg·K p = 200 kPa CO = 43.1% CH4 = 12.3% N2 = 32.3% O2 = 12.3% MW = 26.02 R = 59.4 ft. lbf/lbm·°R pN2 = 40 psia pO2 = 40 psia pCO2 = 20 psia N2 = 0.342 O2 = 0.390 CO2 = 0.268 MW = 32.81 R = 47.1 ft. lbf/lbm·°R t = 90°F p = 167 4 psia t = 42.1°C p = 1.053 MPa t = 89.9°F p = 86.5 psia p = 83.68 psia t = 79.05°F 0.3801 psia, 71°F 51.4%, 51.5°F 69°F, 0.3494 psia, 105 grains/lbm dry air 59.8% 45.9%, 57°F, 0.233 psia 42.1%, 73°F

Appendix 1

7.54 7.56 7.58 7.60 7.62 7.64 7.66 7.68 7.70 7.72 7.74 7.76 7.78 7.80

30%, 26.5 Btu/lbm dry air, 46 grains/lbm dry air 30%, 64°F 0.0526 lbm 46°F, 45.5 grains/lbm dry air 4.9 Btu/lbm dry air 6.69 Btu/lbm dry air 62°F, 54°F, 59°F 35.8% 89 grains/lbm dry air, 65°F 81%, 21 grains/lbm dry air, 6.0 Btu/lbm dry air 20% 63°F, 55%, 48 grains/lbm dry air 0.9642 lbm/lbm dry air, 0.0358 lbm/lbm dry air 8.19 lbm/s, 359.81 lbm/s

Chapter 8 8.2 8.4 8.6 8.8 8.10 8.12 8.14 8.16 8.18 8.20 8.22 8.24 8.26 8.28 8.30 8.32 8.34 8.36 8.38 8.40 8.42 8.44

182.5 Btu, 68.67% 466.7 K Derivation 1326°R 200 kJ/h, 80%, 800 kJ/h h = 1032 Btu/lbm, p = 5.2 psia h = 1031.3 Btu/lbm, p = 5.167 psia 90% 578.26 Btu/lbm, 1439.175 Btu/lbm, 40.2% 34.9% 1.79 Btu/lbm 1.78 Btu/lbm 32.9% 38.54%, 488.9 Btu/lbm 32.91% 32.85% 35.4% 35.65% 32.8% 36.1% 36.86% 86%

611

612

8.46 8.48 8.50 8.52 8.54 8.56 8.58 8.60 8.62 8.64 8.66 8.68 8.70 8.72 8.74 8.76 8.78 8.80 8.82 8.84 8.86 8.88 8.90 8.92 8.94 8.96 8.98 8.100

Appendix 1

78.50% 73% 59.7% 12,365 Btu/kWh 10.9 lbm/kWh 1170°F 11.7% 43.65% 7819 Btu/kWh 2% 82.9% 41.47% 42.26% 43.80% 35.7% 35.5% 45.67% 33.7% 37.3% 37.26% 37.9% 46.6% 41.8% 41.8% 42.06% 43.9%, a gain of 0.7% 47.73% Efficiency 41.9%, 23.1%

Chapter 9 9.2 9.4 9.6 9.8 9.10 9.12 9.14 9.16

54.6% 11, 61.68% 292.4 kJ/kg, 207.6 kJ/kg, 58.48% 117 Btu/lbm, 133 Btu/lbm, 6.68 47.47% 187.6 kPa 2475.2°R, 56.47% 579 kPa, 54.08%

Appendix 1

9.18 9.20 9.22 9.24 9.26 9.28

9.30 9.32 9.34 9.36 9.38 9.40 9.42 9.44 9.46 9.48 9.50 9.52 9.54 9.56

54.08%, 209 psia 54.08%, 173.9 psia 65.5 hp 69.7% 65.15% Ratio% 0.01 68.7% 0.04 65.7% 0.08 62.4% 0.10   61.3% 66.1%, 86.29 psia 23.07, 331.1 Btu/lbm, 66.22% Derivation 1325.78 psia, 3839°R 36.86% 359.04 Btu/lbm, 1295°R, 48.21% 44.8% 880 kJ/kg, 424.2 kJ/kg, 48.21% 893.17 K 47.47% 79.7% 63.2% 61%, 166.1 Btu/lbm 124.8 Btu/lbm

Chapter 10 10.2 10.4 10.6 10.8 10.10 10.12 10.14 10.16 10.18 10.20 10.22 10.24

6.58, 3.8 kW, 28.8 kW Derivation 9.11 23.9 tons, 1.238 8.02 hp 2 25.13 hp 5.33 kW, 25.33 kW 5.74 5.68 6.3 lbm/min 43.26 lbm/min

613

614

10.26 10.28 10.30 10.32 10.34 10.36 10.38 10.40 10.42 10.44 10.46 10.48 10.50 10.52 10.54 10.56 10.58 10.60 10.62 10.64 10.66 10.68 10.70

Appendix 1

45.1 Btu/lbm 46.26 lbm/min 47.91 Btu/lbm, COP 3.73 56.6 Btu/lbm 36.1 lbm/min 60.7 Btu/lbm, COP 3.63 1.075, 342°R 2.06, 4.4 hp 9.58 lbm/min/ton 16.5 hp 0.0282 lbm/lbm 0.02808 lbm/lbm, 0.972 lbm/lbm, 29.23 Btu/lbm 0.020286 kg/kg, 0.979714 kg/kg, 49.34 kJ/kg 86.5% 86.1%, 43.36 hp, 0.30 lb/s 848.3 Btu/min, T1/T2 = 1.25 3.36 10.62, 20.8 Btu/min 4.05 hp 16.63, 1505 Btu/min 28.81 kW, 17.36 329.1 kJ, 545.9 kJ 30189 Btu/h

Chapter 11 11.2 11.4 11.6 11.8 11.10 11.12 11.14 11.16 11.18 11.20 11.22 11.24 11.26

pine wall = 3.08 × brick wall Q = 1020 Btu/h 3.75 Btu/h·ft.°F 90°C 276.8 W/m2 491°F 1.33 in. 0.365 Btu/h·ft.°F 15.98 × 106 Btu/h 2.87 Btu/h·ft.2 114.3°F at cork/mineral wool; 52.9°F at mineral wool/plaster 38.8 W 43.3%

Appendix 1

11.28 11.30 11.32 11.34 11.36 11.38 11.40 11.42 11.44 11.46 11.48 11.50 11.52 11.54 11.56 11.58 11.60 11.62 11.64 11.66 11.68 11.70 11.72 11.74 11.76 11.78 11.80 11.82 11.84 11.86 11.88 11.90 11.92 11.94 11.96 11.98 11.100 11.102 11.104 11.106 11.108 11.110 11.112

65°F at wallboard/mineral wool; 9.6°F at mineral wool/brick 108.3 kW Derivation 36.3 Btu/h·ft. 267 Btu/h·ft. 497.8°F 1.35 in. 17.2 mm 1.11 in. 0.9 Btu/h·ft.2·°F 1060 Btu/h 85 Btu/h·ft.2·°F 86 Btu/h·ft.2·°F 900 Btu/h·ft.2·°F 435 Btu/h·ft.2·°F 147 Btu/h·ft.2·°F 1056.96 Btu/h 45,553 Btu/h 441.6 Btu/h·ft.2 263.1 Btu/h·ft.2 58.7 Btu/h·ft.2 675 Btu/h·ft.2 1.1 Btu/h·ft.2°F 1513 Btu/h·ft.2 2894.3 K 41,229 Btu/h 28.2°F 427°F 391.5°F 344.5°F 16,200 Btu/h·ft.2 1800 W/m2 69.2°F 9.1 kW/m2 43.7°F 108.8 ft.2 1.794 × 106 Btu/h 40.5 Btu/h·ft.2·°F 28.4 ft.2 2500 lb/h 2241 Btu/h 5.6 Btu/h·ft.2·°F 8.51 W/m2

615

616

11.114 11.116 11.118 11.120 11.122 11.124

Appendix 1

34.7 Btu/h·ft.2 255.5 Btu/h·ft. 1568.9 Btu/h 1510.43 Btu 349.54 Btu/h·ft. 1.308 Btu/h·ft.2·°F

Appendix 2: Supplemental Tables Contents of Supplemental Tables A.l A.2 A.3 A.4 A.5 A.l (SI) A.2 (SI) A.3 (SI) A.4 (SI) A.5 (SI) A.6 A.7 A.8 A.9 A.10 A.11 A.12 A.13 A.14 A.15 A.16 A.15 (SI) A.16 (SI) A.17 A.17 (SI) A.18 A.19

A.18 (SI) A.19 (SI)

A.20 A.21 A.21 (SI) A.22 A.23 A.23 (SI)

Saturation: Temperature (Steam) Saturation Pressures (Steam) Properties of Superheated Steam Properties of Compressed Liquid (Steam) Enthalpy–Entropy Diagram for Steam—A Mollier Chart for Steam Saturation: Temperature (Steam) Saturation Pressures (Steam) Properties of Superheated Steam Properties of Compressed Liquid (Steam) Enthalpy–Entropy Diagram for Steam, SI Units Thermal Conductives of Some Building and Insulating Materials (k = Btu/h. ft.°F) Ammonia: Properties of Liquid and Saturated Vapor Ammonia: Properties of Superheated Vapor Pressure–Enthalpy Diagram for Ammonia Dichlorodifluoromethane (Freon-12): Properties of Liquid and Saturated Vapor Dichlorodifluoromethane (Freon-12): Properties of Superheated Vapor Pressure–Enthalpy Diagram for Freon-12 Gas Constant Values Critical Constants HFC-134a Saturation Properties—Temperature Table HFC-134a Superheated Vapor–Constant Pressure Tables HFC-134a Saturation Properties—Temperature Table HFC-134a Superheated Vapor–Constant Pressure Tables Pressure–Enthalpy Diagram for HCF-134a Pressure–Enthalpy Diagram for HCF-134a Suva® 410A Saturation Properties—Temperature Table Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parenthesis) Pressure–Enthalpy Diagram for SUVA 410A Suva® 410A Saturation Properties—Temperature Table Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parenthesis) Pressure–Enthalpy Diagram for SUVA 410A (SI) Thermodynamic Properties of Air at Low Pressure Properties of Some Gases at Low Pressure Properties of Some Gases at Low Pressure Normal Total Emissivity of Various Surfaces Psychrometric Chart for Air–Water Vapor Mixtures Psychrometric Chart for Air–Water Vapor Mixtures

Page 618 620 623 637 639 641 644 647 654 656 657 660 664 671 672 677 685 686 687 688 690 707 708 723 724 725 736 764 765 771 798 799 801 803 804 809 810

617

Press. lbf Sq. In. p

.08859 .08866 .09992 .12166 .14748 .17803 .2563 .3632 .5073 .6988 .9503 1.2763 1.6945 2.225 2.892 3.722 4.745 5.996 7.515 9.343 11.529 14.125 17.188 20.78 24.97

Temp. Fahr. t

32 32.018 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240

.016022 .016022 .016021 .016020 .016021 .016024 .016035 .016051 .016073 .016099 .016130 .016166 .016205 .016247 .016293 .016343 .016395 .016450 .016509 .016570 .016634 .016702 .016772 .016845 .016922

Sat. Liquid vf

3305 3302 2948 2445 2037 1704.2 1206.9 867.7 632.8 467.7 350.0 265.1 203.0 157.17 122.88 96.99 77.23 62.02 50.20 40.95 33.63 27.82 23.15 19.386 16.327

Sat. Vapor vg

Specific Volume (ft.3/lbm)

Saturation: Temperature (Steam)

TABLE A.1

.01 .00 .2.99 .8.02 13.04 18.06 28.08 38.09 48.08 58.07 68.04 78.02 87.99 97.97 107.95 117.95 127.94 137.95 147.97 158.0 168.04 178.10 188.17 198.26 208.36

Sat. Liquid uf 1021.2 1021.2 1019.2 1015.8 1012.5 1009.1 1002.4 995.6 988.9 982.2 975.4 968.7 961.9 955.1 948.2 941.3 934.4 927.4 920.4 913.3 906.2 898.9 891.7 884.3 876.9

Evap. ufg 1021.2 1021.2 1022.2 1023.9 1025.5 1027.2 1030.4 1033.7 1037.0 1040.2 1043.5 1046.7 1049.9 1053.0 1056.2 1059.3 1062.3 1065.4 1068.3 1071.3 1074.2 1077.0 1079.8 1082.6 1085.3

Sat. Vapor ug

Internal Energy (Btu/lbm)

.01 .01 3.00 8.02 13.04 18.06 28.08 38.09 48.09 58.07 68.05 78.02 88.00 97.98 107.96 117.96 127.96 137.97 147.99 158.03 168.07 178.14 188.22 198.32 208.44

Sat. Liquid hf 1075.4 1075.4 1073.7 1070.9 1068.1 1065.2 1059.6 1054.0 1048.3 1042.7 1037.0 1031.3 1025.5 1019.8 1014.0 1008.1 1002.2 996.2 990.2 984.1 977.9 971.6 965.3 958.8 952.3

Evap. hfg

Enthalpy (Btu/lbm)

1075.4 1075.4 1076.7 1078.9 1081.1 1083.3 1087.7 1092.0 1096.4 1100.7 1105.0 1109.3 1113.5 1117.8 1121.9 1126.1 1130.1 1134.2 1138.2 1142.1 1145.9 1149.7 1153.5 1157.1 1160.7

Sat. Vapor hg .00003 .00000 .00607 .01617 .02618 .03607 .05555 .07463 .09332 .11165 .12963 .14730 .16465 .18172 .19851 .21503 .23130 .24732 .26311 .27866 .29400 .30913 .32406 .33880 .35335

Sat. Liquid sf 2.1870 2.1869 2.1704 2.1430 2.1162 2.0899 2.0388 1.9896 1.9423 1.8966 1.8526 1.8101 1.7690 1.7292 1.6907 1.6533 1.6171 1.5819 1.5478 1.5146 1.4822 1.4508 1.4201 1.3901 1.3609

Evap. sfg

2.1870 2.1869 2.1764 2.1592 2.1422 2.1259 2.0943 2.0642 2.0356 2.0083 1.9822 1.9574 1.9336 1.9109 1.8892 1.8684 1.8484 1.8293 1.8109 1.7932 1.7762 1.7599 1.7441 1.7289 1.7143

Sat. Vapor sg

Entropy (Btu/lbm·°R)

618 Appendix 2

250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 425 450 475 500 525 550 575 600 625 650 675 700 705.44

29.82 35.42 41.85 49.18 57.53 66.98 77.64 89.60 103.00 117.93 134.53 152.92 173.23 195.60 220.2 247.1 325.6 422.1 539.3 680.0 847.1 1044.0 1274.0 1541.0 1849.7 2205 2616 3090 3204

.017001 .017084 .017170 .017259 .017352 .017448 .017548 .017652 .017760 .017872 .017988 .018108 .018233 .018363 .018498 .018638 .019014 .019433 .019901 .02043 .02104 .02175 .02259 .02363 .02494 .02673 .02951 .03666 .05053

13.826 11.768 10.066 8.650 7.467 6.472 5.632 4.919 4.312 3.792 3.346 2.961 2.628 2.339 2.087 1.8661 1.4249 1.1011 .8594 .6761 .5350 .4249 .3378 .2677 .2103 .16206 .11952 .07438 .05053

218.49 228.64 238.82 249.02 259.25 269.52 279.81 290.14 300.51 310.91 321.35 331.84 342.37 352.95 363.58 374.27 401.24 428.6 456.6 485.1 514.5 544.9 576.5 609.9 645.7 685.0 731.0 801.7 872.6

869.4 861.8 854.1 846.3 838.5 830.5 822.3 814.1 805.7 797.1 788.4 779.6 770.6 761.4 752.0 742.4 717.4 690.9 662.6 632.3 599.5 563.7 524.3 480.1 429.4 368.7 289.3 145.9 0

1087.9 1090.5 1093.0 1095.4 1097.7 1100.0 1102.1 1104.2 1106.2 1108.0 1109.8 1111.4 1112.9 1114.3 1115.6 1116.6 1118.6 1119.5 1119.2 1117.4 1113.9 1108.6 1100.8 1090.0 1075.1 1053.7 1020.3 947.7 872.6

218.59 228.76 238.95 249.18 259.44 269.73 280.06 290.43 300.84 311.30 321.80 332.35 342.96 353.62 364.34 375.12 402.38 430.2 458.5 487.7 517.8 549.1 581.9 616.7 654.2 695.9 745.3 822.7 902.5

945.6 938.8 932.0 924.9 917.8 910.4 903.0 895.3 887.5 879.5 871.3 862.9 854.2 845.4 836.2 826.8 802.1 775.4 746.4 714.8 680.0 641.6 598.6 549.7 492.9 423.9 332.9 167.5 0

1164.2 1167.6 1170.9 1174.1 1177.2 1180.2 1183.0 1185.8 1188.4 1190.8 1193.1 1195.2 1197.2 1199.0 1200.6 1202.0 1204.5 1205.6 1204.9 1202.5 1197.8 1190.6 1180.4 1166.4 1147.0 1119.8 1078.2 990.2 902.5

.36772 .38193 .39597 .40986 .42360 .47320 .45067 .46400 .47722 .49031 .50329 .51617 .52894 .54163 .55422 .56672 .59767 .6282 .6586 .6888 .7191 .7497 .7808 .8130 .8467 .8831 .9252 .9902 1.0580

1.3324 1.3044 1.2771 1.2504 1.2241 1.1984 1.1731 1.1483 1.1238 1.0997 1.0760 1.0526 1.0295 1.0067 .9841 .9617 .9066 .8523 .7985 .7448 .6906 .6354 .5785 .5187 .4544 .3820 .2934 .1444 0

1.7001 1.6864 1.6731 1.6602 1.6477 1.6356 1.6238 1.6123 1.6010 1.5901 1.5793 1.5688 1.5585 1.5483 1.5383 1.5284 1.5043 1.4806 1.4571 1.4335 1.4007 1.3851 1.3593 1.3317 1.3010 1.2651 1.2186 1.1346 1.0580

Appendix 2 619

Temp. Fahr. t

79.56 101.70 115.65 126.04 141.43 152.93 162.21 179.91 193.19 211.99 213.03 227.96 240.08 250.34 259.30 267.26 274.46 281.03 287.10 292.73

Press. Lbf Sq. In. p

.50 1.0 1.5 2.0 3.0 4.0 5.0 7.5 10 14.696 15 20 25 30 35 40 45 50 55 60

.016071 .016136 .016187 .016230 .016300 .016358 .016407 .016508 .016590 .016715 .016723 .016830 .016922 .017004 .017078 .017146 .017209 .017269 .017325 .017378

Sat. Liquid vf

641.5 333.6 227.7 173.75 118.72 90.64 73.53 50.30 38.42 26.80 26.29 20.09 16.306 13.748 11.900 10.501 9.403 8.518 7.789 7.177

Sat. Vapor vg

Specific Volume (ft.3/lbm)

Saturation Pressures (Steam)

TABLE A.2

47.64 69.74 83.65 94.02 109.38 120.88 130.15 147.88 161.20 180.10 181.14 196.19 208.44 218.84 227.93 236.03 243.37 250.08 256.28 262.06

Sat. Liquid uf 989.2 974.3 964.8 957.8 947.2 939.3 932.9 920.4 911.0 897.5 896.8 885.8 867.9 869.2 862.4 856.2 850.7 845.5 840.8 836.3

Evap. ufg 1036.9 1044.0 1048.5 1051.8 1056.6 1060.2 1063.0 1068.3 1072.2 1077.6 1077.9 1082.0 1085.3 1088.0 1090.3 1092.3 1094.0 1095.6 1097.0 1098.3

Sat. Vapor ug

Internal Energy (Btu/lbm)

47.65 69.74 83.65 94.02 109.39 120.89 130.17 147.90 161.23 180.15 181.19 196.26 208.52 218.93 228.04 236.16 243.51 250.24 256.46 262.25

Sat. Liquid hf 1048.6 1036.0 1028.0 1022.1 1013.1 1006.4 1000.9 990.2 982.1 970.4 969.7 960.1 952.2 945.4 939.3 933.8 928.8 924.2 919.9 915.8

Evap. hfg

Enthalpy (Btu/lbm)

1096.2 1105.8 1111.7 1116.1 1122.5 1127.3 1131.0 1138.1 1143.3 1150.5 1150.9 1156.4 1160.7 1164.3 1167.4 1170.0 1172.3 1174.4 1176.3 1178.0

Sat. Vapor hg

.09250 .13266 .15714 .17499 .20089 .21983 .23486 .26297 .28358 .31212 .31367 .33580 .35345 .36821 .38093 .39214 .40218 .41129 .41963 .42733

Sat. Liquid sf

1.9443 1.8453 1.7867 1.7448 1.6852 1.6426 1.6093 1.5481 1.5041 1.4446 1.4414 1.3962 1.3607 1.3314 1.3064 1.2845 1.2651 1.2476 1.2317 1.2170

Evap. sfg

2.0368 1.9779 1.9438 1.9198 1.8861 1.8624 1.8441 1.8110 1.7877 1.7567 1.7551 1.7320 1.7142 1.6996 1.6873 1.6767 1.6673 1.6589 1.6513 1.6444

Sat. Vapor sg

Entropy (Btu/lbm·°R)

620 Appendix 2

65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 160 170 180 190 200 225 250 275 300

298.00 302.96 307.63 312.07 316.29 320.31 324.16 327.86 331.41 334.82 338.12 341.30 344.39 347.37 350.27 353.08 355.82 358.48 363.60 368.47 373.13 377.59 381.86 391.87 401.04 409.52 417.43

.017429 .017478 .017524 .017570 .017613 .017655 .017696 .017736 .017775 .017813 .017850 .017886 .017922 .017957 .017991 .018024 .018057 .018089 .018152 .018214 .018273 .018331 .018387 .018523 .018653 .018777 .018896

6.657 6.209 5.818 5.474 5.170 4.898 4.654 4.434 4.234 4.051 3.884 3.730 3.588 3.457 3.335 3.221 3.115 3.016 2.836 2.676 2.533 2.405 2.289 2.043 1.8448 1.6813 1.5442

267.46 272.56 277.37 281.95 286.30 290.46 294.45 298.28 301.97 305.52 308.95 312.27 315.49 318.61 321.64 324.58 327.45 330.24 335.63 340.76 345.68 350.39 354.9 365.6 375.4 384.5 393.0

832.1 828.1 824.3 820.6 817.1 813.8 810.6 807.5 804.5 801.6 798.8 796.0 793.3 790.7 788.2 785.7 783.3 781.0 776.4 772.0 767.7 763.6 759.6 750.2 741.4 733.0 725.1

1099.5 1100.6 1101.6 1102.6 1103.5 1104.3 1105.0 1105.8 1106.5 1107.1 1107.7 1108.3 1108.8 1109.4 1109.8 1110.3 1110.8 1111.2 1112.0 1112.7 1113.4 1114.0 1114.6 1115.8 1116.7 1117.5 1118.2

267.67 272.79 277.61 282.21 286.58 290.76 294.76 298.61 302.31 305.88 309.33 312.67 315.90 319.04 322.08 325.05 327.93 330.75 336.16 341.33 346.29 351.04 355.6 366.3 376.2 385.4 394.1

911.9 908.3 904.8 901.4 898.2 895.1 892.1 889.2 886.4 883.7 881.0 878.5 875.9 873.5 871.1 868.7 866.4 864.2 859.8 855.6 851.5 847.5 843.7 834.5 825.8 817.6 809.8

1179.6 1181.0 1182.4 1183.6 1184.8 1185.9 1186.9 1187.8 1188.7 1189.6 1190.4 1191.1 1191.8 1192.5 1193.2 1193.8 1194.4 1194.9 1196.0 1196.9 1197.8 1198.6 1199.3 1200.8 1202.1 1203.1 1203.9

.43450 .44120 .44749 .45344 .45907 .46442 .46952 .47439 .47906 .48355 .48786 .49201 .49602 .49989 .50364 .50727 .51079 .51422 .52078 .52700 .53292 .53857 .5440 .5566 .5680 .5786 .5883

1.2035 1.1909 1.1790 1.1679 1.1574 1.1475 1.1380 1.1290 1.1204 1.1122 1.1042 1.0966 1.0893 1.0822 1.0754 1.0688 1.0624 1.0562 1.0443 1.0330 1.0223 1.0122 1.0025 .9799 .9594 .9406 .9232

1.6380 1.6321 1.6265 1.6214 1.6165 1.6119 1.6076 1.6034 1.5995 1.5957 1.5921 1.5886 1.5853 1.5821 1.5790 1.5761 1.5732 1.5704 1.5651 1.5600 1.5553 1.5507 1.5464 1.5365 1.5274 1.5192 1.5115 (continued)

Appendix 2 621

Temp. Fahr. t

431.82 444.70 456.39 467.13 477.07 486.33 503.23 518.36 532.12 544.75 572.56 596.39 617.31 649.20 652.90 668.31 682.46 695.52 705.44

Press. Lbf Sq. In. p

350 400 450 500 550 600 700 800 900 1000 1250 1500 1750 2000 2250 2500 2750 3000 3203.6

.019124 .019340 .019547 .019748 .019943 .02013 .02051 .02087 .02123 .02159 .02250 .02346 .02450 .02565 .02698 .02860 .03077 .03431 .05053

Sat. Liquid vf

1.3267 1.1620 1.0326 .9283 .8423 .7702 .6558 .5691 .5009 .4459 .3454 .2769 .2268 .8813 .15692 .13059 .10717 .08404 .05053

Sat. Vapor vg

Specific Volume (ft.3/lbm)

Saturation Pressures (Steam)

TABLE A.2 (Continued)

408.7 422.8 435.7 447.7 458.9 469.4 488.9 506.6 523.0 538.4 573.4 605.0 634.4 662.4 689.9 717.7 747.3 783.4 872.6

Sat. Liquid uf 710.3 696.7 683.9 671.7 660.2 649.1 628.2 608.4 589.6 571.5 528.3 486.9 445.9 404.2 360.7 313.4 258.6 185.4 0

Evap. ufg 1119.0 1119.5 1119.6 1119.4 1119.1 1118.6 1117.0 1115.0 1112.6 1109.9 1101.7 1091.8 1080.2 1066.6 1050.6 1031.0 1005.9 968.8 872.6

Sat. Vapor ug

Internal Energy (Btu/lbm)

409.9 424.2 437.4 449.5 460.9 471.7 491.5 509.7 526.6 542.4 578.6 611.5 642.3 671.9 701.1 730.9 763.0 802.5 902.5

Sat. Liquid hf 795.0 781.2 768.2 755.8 743.9 732.4 710.5 689.6 669.5 650.0 603.0 557.2 511.4 464.4 414.8 360.5 297.4 213.0 0

Evap. hfg

Enthalpy (Btu/lbm)

1204.9 1205.5 1205.6 1205.3 1204.8 1204.1 1202.0 1199.3 1196.0 1192.4 1181.6 1168.7 1153.7 1136.3 1115.9 1091.4 1060.4 1015.5 902.5

Sat. Vapor hg .6060 .6218 .6360 .6490 .6611 .6723 .6927 .7110 .7277 .7432 .7778 .8082 .8361 .8623 .8876 .9131 .9401 .9732 1.0580

Sat. Liquid sf

.8917 .8638 .8385 .8154 .7941 .7742 .7378 .7050 .6750 .6471 .5841 .5276 .4748 .4238 .3728 .3196 .2604 .1843 0

Evap. sfg

1.4978 1.4856 1.4746 1.4645 1.4551 1.4464 1.4305 1.4160 1.4027 1.3903 1.3619 1.3359 1.3109 1.2861 1.2604 1.2327 1.2005 1.1575 1.0580

Sat. Vapor sg

Entropy (Btu/lbm·°R)

622 Appendix 2

1077.6 1054.5 1058.2 1062.0 1065.7 1069.5 1073.2 1076.9 1080.6 1084.2 1087.9 1091.5 1095.2 1098.8 1102.4 1106.0 1109.6 1113.2 1116.8 1120.4 1124.0

1150.5 1120.0 1125.0 1129.9 1134.9 1139.8 1144.7 1149.5 1154.4 1159.2 1164.0 1168.8 1173.6 1178.4 1183.1 1187.9 1192.6 1197.4 1202.1 1206.8 1211.6

h

u

v

26.80 24.10 24.54 24.98 25.42 25.85 26.29 26.72 27.15 27.57 28.00 28.42 28.85 29.27 29.69 30.11 30.52 30.94 31.36 31.77 32.19

t

Sat. 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340

14.696 (211.99)

p (t Sat.)

Properties of Superheated Steam

TABLE A.3

s 1.7567 1.7090 1.7171 1.7251 1.7328 1.7405 1.7479 1.7553 1.7624 1.7695 1.7764 1.7832 1.7899 1.7965 1.8030 1.8094 1.8157 1.8219 1.8280 1.8340 1.8400

v 20.09 17.532 17.870 18.204 18.535 18.864 19.191 19.515 19.837 20.157 20.475 20.79 21.11 21.42 21.73 22.05 22.36 22.67 22.98 23.28 23.59

u 1082.0 1052.0 1056.0 1059.9 1063.8 1067.6 1071.4 1075.2 1079.0 1082.8 1086.5 1090.3 1094.0 1097.7 1101.4 1105.0 1108.7 1112.4 1116.0 1119.7 1123.3

h 1156.4 1116.9 1122.1 1127.2 1132.4 1137.4 1142.5 1147.5 1152.4 1157.4 1162.3 1167.2 1172.1 1177.0 1181.8 1186.6 1191.5 1196.3 1201.0 1205.8 1210.6

20 (227.96)

Vapor (psia)

s 1.7320 1.6710 1.6795 1.6877 1.6957 1.7036 1.7113 1.7188 1.7762 1.7335 1.7405 1.7475 1.7543 1.7610 1.7676 1.7741 1.7805 1.7868 1.7930 1.7991 1.8051

v 13.748 11.460 11.701 11.938 12.172 12.403 12.631 12.857 13.081 13.303 13.523 13.741 13.958 14.173 14.387 14.600 14.812 15.023 15.233 15.442 15.651

u 1088.0 1047.3 1051.6 1055.8 1059.9 1064.0 1068.1 1072.1 1076.1 1080.0 1084.0 1087.9 1091.7 1095.6 1099.4 1103.2 1106.9 1110.7 1114.4 1118.2 1121.9

h 1164.3 1111.0 1116.5 1122.0 1127.5 1132.9 1138.2 1143.5 1148.7 1153.9 1159.0 1164.1 1169.2 1174.2 1179.2 1184.2 1189.2 1194.1 1199.0 1203.9 1208.8

30 (250.34) s 1.6996 1.6185 1.6275 1.6364 1.6449 1.6533 1.6615 1.6694 1.6771 1.6847 1.6921 1.6994 1.7064 1.7134 1.7202 1.7269 1.7334 1.7399 1.7462 1.7525 1.7586 (continued)

Appendix 2 623

Sat. 350 360 370 380 390 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800

26.80 32.60 33.02 33.43 33.84 34.26 34.67 35.49 36.31 37.13 37.95 38.77 39.59 40.41 41.22 42.04 42.86 43.67 44.49 45.30 46.12 46.93 47.75 48.56 49.37 50.19 51.00

1077.6 1127.6 1131.2 1134.8 1138.4 1142.0 1145.6 1152.8 1160.1 1167.3 1174.6 1181.8 1189.1 1196.5 1203.8 1211.2 1218.6 1226.1 1233.5 1241.0 1248.6 1256.1 1263.7 1271.4 1279.0 1286.7 1294.4

1150.5 1216.3 1221.0 1225.7 1230.5 1235.2 1239.9 1249.3 1258.8 1268.3 1277.8 1287.3 1296.8 1306.4 1315.9 1325.5 1335.2 1344.8 1354.5 1364.2 1374.0 1383.8 1393.6 1403.4 1413.3 1423.2 1433.1

h

u

t

v

14.696 (211.99)

p (t Sat.)

Properties of Superheated Steam

TABLE A.3 (Continued)

1.7567 1.8458 1.8516 1.8574 1.8630 1.8686 1.8741 1.8850 1.8956 1.9060 1.9162 1.9263 1.9361 1.9457 1.9552 1.9645 1.9737 1.9827 1.9916 2.0004 2.0090 2.0175 2.0259 2.0342 2.0424 2.0504 2.0584

s 20.09 23.90 24.21 24.51 24.82 25.12 25.43 26.03 26.64 27.25 27.85 28.46 29.06 29.66 30.26 30.87 31.47 32.07 32.67 33.27 33.87 34.47 35.07 35.66 36.26 36.86 37.46

v 1082.0 1126.9 1130.6 1134.2 1137.8 1141.4 1145.1 1152.3 1159.6 1166.9 1174.2 1181.5 1188.8 1196.1 1203.5 1210.9 1218.4 1225.8 1233.3 1240.8 1248.3 1255.9 1263.5 1271.2 1278.8 1286.5 1294.3

u

h 1156.4 1215.4 1220.1 1224.9 1229.7 1234.4 1239.2 1248.7 1258.2 1267.7 1277.2 1286.8 1296.3 1305.9 1315.5 1325.2 1334.8 1344.5 1354.2 1363.9 1373.7 1383.5 1393.3 1403.2 1413.0 1423.0 1432.9

20 (227.96)

Vapor (psia)

1.7320 1.8110 1.8168 1.8226 1.8283 1.8340 1.8395 1.8504 1.8611 1.8716 1.8819 1.8919 1.9018 1.9114 1.9210 1.9303 1.9395 1.9485 1.9575 1.9662 1.9749 1.9834 1.9918 2.0001 2.0082 2.0163 2.0243

s 13.748 15.859 16.067 16.273 16.480 16.686 16.891 17.301 17.709 18.116 18.523 18.928 19.333 19.737 20.140 20.543 20.95 21.35 21.75 22.15 22.55 22.95 23.35 23.75 24.15 24.55 24.95

v 1088.0 1125.6 1129.3 1133.0 1136.7 1140.3 1144.0 1151.4 1158.7 1166.1 1173.4 1180.8 1188.2 1195.5 1203.0 1210.4 1217.8 1225.3 1232.8 1240.4 1247.9 1255.5 1263.2 1270.8 1278.5 1286.2 1294.0

u

h 1164.3 1213.6 1218.5 1223.3 1228.1 1233.0 1237.8 1247.4 1257.0 1266.6 1276.2 1285.9 1295.5 1305.1 1314.8 1324.4 1334.1 1343.8 1353.6 1363.3 1373.1 1383.0 1392.8 1402.7 1412.6 1422.5 1432.5

30 (250.34)

1.6996 1.7646 1.7706 1.7765 1.7822 1.7880 1.7936 1.8047 1.8155 1.8260 1.8364 1.8465 1.8564 1.8661 1.8757 1.8851 1.8943 1.9034 1.9123 1.9211 1.9298 1.9384 1.9468 1.9551 1.9633 1.9714 1.9793

s

624 Appendix 2

Sat. 200 210 220 230 240 250 260 270 280 290 300 310 320 330

t

p (t Sat.)

850 900 950 1000 1100 1200 1300 1400 1500 1600 1800 2000 2200 2400

10.501 9.346 9.523 9.699 9.872 10.043 10.212 10.380 10.546 10.711 10.875 11.038 11.200 11.360 11.520

v

53.03 55.07 57.10 59.13 63.19 67.25 71.30 75.36 79.42 83.47 91.58 99.69 107.80 115.91

1092.3 1064.6 1068.8 1073.0 1077.2 1081.3 1085.4 1089.4 1093.4 1097.3 1101.2 1105.1 1109.0 1112.8 1116.6

u

1170.0 1133.8 1139.3 1144.8 1150.3 1155.6 1161.0 1166.2 1171.4 1176.6 1181.7 1186.8 1191.9 1196.9 1201.9

h

1458.1 1483.4 1508.8 1534.5 1586.4 1639.3 1693.2 1747.9 1803.6 1860.2 1976.1 2095.5 2218.0 2343.4

40 (267.26)

1313.9 1333.6 1353.5 1373.7 1414.6 1456.5 1499.3 1543.0 1587.6 1633.2 1727.0 1824.4 1924.8 2028.1

1.6767 1.6243 1.6327 1.6409 1.6488 1.6565 1.6641 1.6714 1.6786 1.6857 1.6926 1.6993 1.7059 1.7124 1.7188

s

2.0778 2.0967 2.1151 2.1330 2.1674 2.2003 2.2318 2.2621 2.2912 2.3194 2.3731 2.4237 2.4716 2.5170

8.518 7.370 7.519 7.665 7.810 7.952 8.092 8.231 8.368 8.504 8.639 8.772 8.904 9.036 9.166

v

38.96 40.45 41.94 43.44 46.42 49.41 52.39 55.37 58.35 61.33 67.29 73.25 79.21 85.17

1095.6 1060.9 1065.4 1069.9 1074.2 1078.6 1082.8 1087.0 1091.1 1095.2 1099.2 1103.2 1107.2 1111.2 1115.1

u 1174.4 1129.1 1135.0 1140.8 1146.5 1152.1 1157.7 1163.1 1168.5 1173.9 1179.2 1184.4 1189.6 1194.8 1199.9

h

1457.9 1483.2 1508.6 1534.3 1586.3 1639.2 1693.1 1747.9 1803.5 1860.1 1976.1 2095.4 2218.0 2343.3

50 (281.03)

1313.8 1333.5 1353.4 1373.5 1414.5 1456.4 1499.2 1542.9 1587.6 1633.2 1727.0 1824.3 1924.8 2028.1

1.6589 1.5940 1.6029 1.6115 1.6198 1.6279 1.6358 1.6434 1.6509 1.6582 1.6653 1.6722 1.6790 1.6857 1.6922

s

2.0438 2.0627 2.0810 2.0989 2.1334 2.1663 2.1978 2.2281 2.2572 2.2854 2.3391 2.3897 2.4376 2.4830

7.177 6.047 6.178 6.307 6.432 6.556 6.677 6.797 6.915 7.031 7.146 7.260 7.373 7.485 7.596

v

25.95 26.95 27.95 28.95 30.94 32.93 34.92 36.91 38.90 40.88 44.86 48.83 52.81 56.78

1098.3 1057.1 1061.9 1066.6 1071.2 1075.7 1080.1 1084.5 1088.8 1093.0 1097.2 1101.3 1105.4 1109.5 1113.5

u

1178.0 1124.2 1130.5 1136.6 1142.6 1148.5 1154.3 1160.0 1165.6 1171.1 1176.5 1181.9 1187.3 1192.6 1197.8

h

1457.6 1482.8 1508.3 1534.0 1586.1 1639.1 1692.9 1747.7 1803.4 1860.0 1976.0 2095.3 2217.9 2343.3 60 (292.73)

1313.5 1333.2 1353.2 1373.3 1414.3 1456.2 1499.1 1542.8 1587.5 1633.1 1726.9 1824.2 1924.7 2028.0

1.6444 1.5680 1.5774 1.5864 1.5952 1.6036 1.6118 1.6198 1.6275 1.6351 1.6424 1.6496 1.6565 1.6634 1.6700 (continued)

s

1.9988 1.0178 2.0362 2.0541 2.0886 2.1215 2.1530 2.1833 2.2125 2.2407 2.2944 2.3450 2.3929 2.4383

Appendix 2 625

340 350 360 370 380 390 400 420 440 460 480 500 520 540 560 580 600 620 640 660

t

p (t Sat.)

v

11.680 11.838 11.996 12.153 12.310 12.467 12.623 12.933 13.243 13.551 13.858 14.164 14.469 14.774 15.078 15.382 15.685 15.988 16.291 16.593

u

1120.4 1124.2 1128.0 1131.7 1135.5 1139.2 1143.0 1150.4 1157.8 1165.2 1172.7 1180.1 1187.5 1194.9 1202.4 1209.9 1217.3 1224.8 1232.4 1239.9

h

1206.9 1211.8 1216.8 1221.7 1226.6 1231.5 1236.4 1246.1 1255.8 1265.5 1275.2 1284.9 1294.6 1304.3 1314.0 1323.7 1333.4 1343.2 1353.0 1362.8

40 (267.26)

Properties of Superheated Steam

TABLE A.3 (Continued)

s 1.7251 1.7312 1.7373 1.7432 1.7491 1.7549 1.7606 1.7718 1.7828 1.7934 1.8038 1.8140 1.8240 1.8338 1.8434 1.8529 1.8621 1.8713 1.8802 1.8891

v 9.296 9.425 9.553 9.681 9.808 9.935 10.061 10.312 10.562 10.811 11.059 11.305 11.551 11.796 12.041 12.285 12.529 12.772 13.015 13.258

u 1119.0 1122.8 1126.7 1130.5 1134.3 1138.1 1141.9 1149.4 1156.9 1164.4 1171.9 1179.4 1186.8 1194.3 1201.8 1209.3 1216.8 1224.4 1231.9 1239.5

h 1205.0 1210.0 1215.1 1220.1 1225.0 1230.0 1235.0 1244.8 1254.6 1264.4 1274.2 1284.0 1293.7 1303.5 1313.2 1323.0 1332.8 1342.5 1352.4 1362.2

50 (281.03)

Vapor (psia)

s 1.6986 1.7049 1.7110 1.7171 1.7231 1.7290 1.7348 1.7461 1.7572 1.7679 1.7784 1.7887 1.7988 1.8086 1.8183 1.8277 1.8371 1.8462 1.8552 1.8641

v 7.706 7.815 7.924 8.032 8.139 8.246 8.353 8.565 8.775 8.984 9.192 9.399 9.606 9.811 10.016 10.221 10.425 10.628 10.832 11.035

u 1117.4 1121.4 1125.3 1129.2 1133.1 1136.9 1140.8 1148.4 1156.0 1163.6 1171.1 1178.6 1186.2 1193.7 1201.2 1208.8 1216.3 1223.9 1231.5 1239.1

h 1203.0 1208.2 1213.3 1218.4 1223.5 1228.5 1233.5 1243.5 1253.4 1263.3 1273.2 1283.0 1292.8 1302.6 1312.4 1322.2 1332.1 1341.9 1351.7 1361.6

60 (292.73) s 1.6766 1.6830 1.6893 1.6955 1.7015 1.7075 1.7134 1.7249 1.7360 1.7469 1.7575 1.7678 1.7780 1.7879 1.7976 1.8071 1.8165 1.8257 1.8347 1.8436

626 Appendix 2

680 700 720 740 760 780 800 850 900 950 1000 1100 1200 1300 1400 1500 1600 1800 2000 2200 2400

16.895 17.196 17.498 17.799 18.100 18.401 18.701 19.452 20.202 20.951 21.700 23.20 24.69 26.18 27.68 29.17 30.66 33.64 36.62 39.61 42.59

1247.5 1255.1 1262.8 1270.5 1278.2 1285.9 1293.7 1313.2 1333.0 1352.9 1373.1 1414.2 1456.1 1498.9 1542.7 1587.4 1633.0 1726.9 1824.2 1924.7 2028.0

1372.6 1382.4 1392.3 1402.2 1412.1 1422.1 1432.1 1457.2 1482.5 1508.0 1533.8 1585.9 1638.9 1692.8 1747.6 1803.3 1859.9 1975.9 2095.3 2217.8 2343.2

1.8977 1.9063 1.9147 1.9231 1.9313 1.9394 1.9474 1.9669 1.9859 2.0043 2.0223 2.0568 2.0897 2.1212 2.1515 2.1807 2.2089 2.2626 2.3132 2.3611 2.4066

13.500 13.742 13.984 14.226 14.467 14.708 14.949 15.551 16.152 16.753 17.352 18.551 19.747 20.943 22.138 23.332 24.53 26.91 29.30 31.68 34.07

1247.1 1254.8 1262.4 1270.1 1277.8 1285.6 1293.3 1312.9 1332.7 1352.7 1372.9 1414.0 1456.0 1498.8 1542.6 1587.3 1632.9 1726.8 1824.1 1924.6 2027.9

1372.0 1381.9 1391.8 1401.7 1411.7 1421.7 1431.7 1456.8 1482.2 1507.7 1533.5 1585.6 1638.7 1692.6 1747.4 1803.2 1859.8 1975.8 2095.2 2217.8 2343.1

1.8728 1.8814 1.8898 1.8982 1.9064 1.9145 1.9225 1.9421 1.9611 1.9796 1.9975 2.0321 2.0650 2.0966 2.1269 2.1561 2.1843 2.2380 2.2886 2.3365 2.3820

11.237 11.440 11.642 11.844 12.045 12.247 12.448 12.951 13.452 13.954 14.454 15.454 16.452 17.449 18.445 19.441 20.44 22.43 24.41 26.40 28.39

1246.7 1254.4 1262.0 1269.7 1277.5 1285.2 1293.0 1312.7 1332.5 1352.5 1372.7 1413.8 1455.8 1498.7 1542.5 1587.2 1632.8 1726.7 1824.0 1924.5 2027.8

1371.5 1381.4 1391.3 1401.2 1411.2 1421.2 1431.2 1456.4 1481.8 1507.4 1533.2 1585.4 1638.5 1692.4 1747.3 1803.0 1859.7 1975.7 2095.1 2217.7 2343.1

1.8523 1.8609 1.8694 1.8778 1.8860 1.8942 1.9022 1.9218 1.9408 1.9593 1.9773 2.0119 2.0448 2.0764 2.1067 2.1359 2.1641 2.2179 2.2685 2.3164 2.3618

Appendix 2 627

Sat. 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490

5.474 4.902 4.998 5.093 5.186 5.277 5.367 5.456 5.544 5.631 5.717 5.802 5.886 5.970 6.053 6.135 6.217 6.299 6.380 6.460 6.541 6.621 6.700 6.780 6.859 6.938

1102.6 1074.5 1079.3 1083.9 1088.5 1092.9 1097.4 1101.7 1106.0 1110.2 1114.3 1118.5 1122.5 1126.6 1130.6 1134.6 1138.5 1142.5 1146.4 1150.3 1154.2 1158.0 1161.9 1165.7 1169.6 1173.4

1183.6 1147.1 1153.3 1159.3 1165.2 1171.1 1176.8 1182.5 1188.0 1193.5 1199.0 1204.3 1209.7 1215.0 1220.2 1225.4 1230.6 1235.7 1240.8 1245.9 1251.0 1256.0 1261.1 1266.1 1271.1 1276.1

h

u

t

v

80 (312.07)

p (t Sat.)

Properties of Superheated Steam

TABLE A.3 (Continued)

1.6214 1.5720 1.5806 1.5890 1.5970 1.6049 1.6125 1.6199 1.6271 1.6341 1.6409 1.6476 1.6541 1.6605 1.6668 1.6730 1.6790 1.6850 1.6908 1.6966 1.7022 1.7078 1.7133 1.7188 1.7241 1.7294

s 1105.8

1093.1 1097.7 1102.3 1106.7 1111.1 1115.4 1119.7 1123.9 1128.0 1132.1 1136.2 1140.3 1144.3 1148.3 1152.3 1156.2 1160.1 1164.1 1168.0 1171.8

4.228 4.303 4.377 4.449 4.521 4.592 4.662 4.731 4.799 4.867 4.934 5.001 5.068 5.134 5.199 5.265 5.330 5.394 5.459 5.523

u

4.434

v

1171.4 1177.4 1183.3 1189.1 1194.8 1200.4 1205.9 1211.4 1216.8 1222.2 1227.5 1232.8 1238.1 1243.3 1248.5 1253.6 1258.8 1263.9 1269.0 1274.0

1187.8

h

100 (327.86)

1.5822 1.5900 1.5976 1.6050 1.6121 1.6191 1.6259 1.6326 1.6391 1.6455 1.6517 1.6578 1.6638 1.6697 1.6755 1.6812 1.6868 1.6923 1.6978 1.7032

1.6034

s

2.978 3.037 3.094 3.150 3.205 3.259 3.312 3.364 3.415 3.466 3.517 3.567 3.616 3.665 3.713 3.762 3.810 3.857 3.904

3.221

v

Vapor (psia)

1089.2 1094.3 1099.3 1104.1 1108.9 1113.5 1118.1 1122.6 1127.0 1131.4 1135.7 1139.9 1144.1 1148.3 1152.4 1156.5 1160.6 1164.7 1168.7

1110.3

u

1166.4 1173.0 1179.4 1185.7 1191.9 1198.0 1203.9 1209.7 1215.5 1221.2 1226.8 1232.3 1237.8 1243.3 1248.6 1254.0 1259.3 1264.6 1269.9

1193.8

h

140 (353.08)

1.5414 1.5499 1.5581 1.5661 1.5737 1.5812 1.5884 1.5954 1.6022 1.6088 1.6153 1.6217 1.6279 1.6339 1.6399 1.6458 1.6515 1.6572 1.6627

1.5761

s

2.429 2.475 2.520 2.563 2.606 2.648 2.690 2.731 2.771 2.811 2.850 2.889 2.928 2.966 3.005

2.533

v

1101.7 1106.9 1111.9 1116.7 1121.5 1126.2 1130.8 1135.3 1139.8 1144.2 1148.5 1152.8 1157.0 1161.3 1165.4

1113.4

u

1182.6 1189.3 1195.8 1202.1 1208.3 1214.4 1220.4 1226.3 1232.1 1237.8 1243.4 1249.0 1254.6 1260.1 1265.5

1197.8

h

180 (373.13)

1.5368 1.5450 1.5529 1.5605 1.5678 1.5749 1.5818 1.5886 1.5951 1.6015 1.6078 1.6139 1.6199 1.6257 1.6315

1.5553

s

628 Appendix 2

1352.0

10.455

8.053 8.174 8.295

1312.1

9.700

1332.0

1215.3 1222.9 1230.5 1238.2 1245.9 1253.6 1261.3 1269.0 1276.8 1284.6 1292.4

7.794 7.948 8.102 8.255 8.408 8.561 8.714 8.866 9.018 9.170 9.321

10.078

1207.7

7.640

1506.8

1481.2

1455.7

1330.7 1340.6 1350.5 1360.4 1370.4 1380.3 1390.3 1400.3 1410.3 1420.3 1430.4

1320.8

1310.9

1.9273

1.9087

1.8897

1.7838 1.7930 1.8021 1.8111 1.8199 1.8285 1.8371 1.8455 1.8538 1.8619 1.8700

1.7743

1.7647

1.7549

8.416

6.216 6.340 6.464 6.588 6.711 6.834 6.957 7.079 7.201 7.324 7.445 7.567 7.689

6.091

5.966

5.840

5.714

900 920 940 950 960

1200.1

7.485

1300.9

1.7449

5.587

7.932

1192.4

7.329

1291.0

1.7346

7.810

1184.8

7.173

1281.1

880

1177.2

7.017

500 510 520 530 540 550 560 570 580 590 600 620 640 660 680 700 720 740 760 780 800 820 840 850 860

1355.6

1331.5 1339.5 1347.5

1323.5

1315.5

1214.2 1221.9 1229.6 1237.3 1245.0 1252.8 1260.5 1268.3 1276.1 1283.9 1291.8 1299.7 1307.6

1206.6

1198.9

1191.2

1183.5

1175.7

1511.3

1480.5 1490.7 1501.0

1470.2

1460.0

1329.3 1339.3 1349.2 1359.2 1369.2 1379.2 1389.3 1399.3 1409.4 1419.5 1429.6 1439.7 1449.9

1319.3

1309.3

1299.2

1289.2

1279.1

1.9060

1.8838 1.8913 1.8987

1.8762

1.8685

1.7582 1.7675 1.7767 1.7857 1.7946 1.8033 1.8118 1.8203 1.8286 1.8368 1.8449 1.8529 1.8607

1.7487

1.7390

1.7290

1.7189

1.7085

6.000

5.739 5.826 5.913

5.651

5.564

4.412 4.502 4.592 4.682 4.771 4.860 4.949 5.037 5.125 5.214 5.301 5.389 5.477

4.321

4.230

4.138

4.045

3.952

1354.7

1330.4 1338.5 1346.6

1322.4

1314.4

1212.1 1219.9 1227.7 1235.6 1243.4 1251.2 1259.0 1266.9 1274.7 1282.6 1290.5 1298.5 1306.4

1204.3

1196.5

1188.6

1180.7

1172.7

1510.1

1479.1 1489.4 1499.8

1468.8

1458.5

1326.4 1336.6 1346.7 1356.8 1367.0 1377.1 1387.2 1397.4 1407.5 1417.7 1427.9 1438.1 1448.3

1316.2

1306.0

1295.8

1285.5

1275.1

1.8683

1.8459 1.8535 1.8609

1.8383

1.8306

1.7191 1.7286 1.7379 1.7470 1.7560 1.7648 1.7735 1.7820 1.7904 1.7986 1.8068 1.8148 1.8228

1.7094

1.6995

1.6893

1.6789

1.6682

4.657

4.453 4.521 4.589

4.385

4.316

3.042 3.080 3.117 3.154 3.191 3.228 3.264 3.301 3.337 3.373 3.409 3.481 3.552 3.623 3.693 3.763 3.833 3.903 3.972 4.041 4.110 4.179 4.248

1353.8

1329.4 1337.5 1345.6

1321.3

1313.3

1169.6 1173.7 1177.8 1181.9 1185.9 1190.0 1194.0 1198.0 1202.0 1206.0 1210.0 1217.9 1225.8 1233.8 1241.7 1249.6 1257.5 1265.4 1273.4 1281.3 1289.3 1297.3 1305.3

1508.9

1477.7 1488.1 1498.5

1467.4

1457.1

1270.9 1276.3 1281.6 1286.9 1292.2 1297.5 1302.7 1307.9 1313.1 1318.3 1323.5 1333.9 1344.1 1354.4 1364.7 1374.9 1385.2 1395.4 1405.7 1415.9 1426.2 1436.5 1446.7

1.8399 (continued)

1.8175 1.8250 1.8325

1.8098

1.8020

1.6372 1.6427 1.6482 1.6536 1.6589 1.6642 1.6693 1.6744 1.6795 1.6844 1.6893 1.6990 1.7084 1.7177 1.7268 1.7357 1.7445 1.7531 1.7615 1.7699 1.7781 1.7862 1.7942

Appendix 2 629

2.289 2.361

2.399

2.437

2.475 2.511

Sat. 400

410

420

430 440

1137.5 1142.0

1132.9

1128.2

1114.6 1123.5

1229.1 1234.9

1223.1

1217.0

1199.3 1210.8

h

u

v

1584.9 1638.1 1692.1 1747.0 1802.8 1859.5 1975.5 2094.9 2217.5 2342.9

t

1413.5 1455.5 1498.4 1542.3 1587.0 1632.6 1726.5 1823.9 1924.4 2027.7

11.583 12.333 13.081 13.830 14.577 15.324 16.818 18.310 19.802 21.294

1532.6

200 (381.86)

1372.3

10.831

p (t Sat.)

980 1000 1020 1040 1060 1080 1100 1200 1300 1400 1500 1600 1800 2000 2200 2400

h

u

t

v

80 (312.07)

p (t Sat.)

Properties of Superheated Steam

TABLE A.3 (Continued)

1.5809 1.5874

1.5741

1.5672

1.5464 1.5600

s

1.9799 2.0130 2.0446 2.0749 2.1041 2.1323 2.1861 2.2367 2.2846 2.3301

1.9453

s

1.5805 1.6086

1.5517

1.5221

1.5442 1.4915

v

8.537 8.657 8.778 8.899 9.019 9.140 9.260 9.861 10.461 11.060 11.659 12.257 13.452 14.647 15.842 17.036

v 1521.7 1532.1 1542.5 1552.9 1563.4 1573.9 1584.5 1637.7 1691.8 1746.7 1802.5 1859.3 1975.3 2094.8 2217.4 2342.8

h

1125.0 1130.3

1119.6

1114.0

1118.2 1108.2

u

1212.7 1219.6

1205.7

1198.5

1203.9 1191.0

h

300 (417.43)

1363.7 1371.9 1380.1 1388.3 1396.5 1404.8 1413.1 1455.2 1498.2 1542.0 1586.8 1632.4 1726.4 1823.7 1924.3 2027.5

u

100 (327.86)

1.5216 1.5292

1.5136

1.5054

1.5115 1.4967

s

1.9132 1.9204 1.9275 1.9345 1.9414 1.9483 1.9551 1.9882 2.0198 2.0502 2.0794 2.1076 2.1614 2.2121 2.2600 2.3054

s

1.3219 1.3480

1.2950

1.3267

v

6.086 6.173 6.260 6.346 6.433 6.519 6.605 7.036 7.466 7.895 8.324 8.752 9.607 10.461 11.315 12.169

v

Vapor (psia)

1520.5 1531.0 1541.4 1551.9 1562.4 1573.0 1583.6 1636.9 1691.1 1746.1 1802.0 1858.8 1975.0 2094.5 2217.1 2342.5

h

1117.9 1123.7

1112.0

1119.0

u

1203.6 1211.0

1195.9

1204.9

h

350 (431.82)

1362.9 1371.0 1379.3 1387.5 1395.8 1404.1 1412.4 1454.6 1497.7 1541.6 1586.4 1632.1 1726.1 1823.5 1924.0 2027.3

u

140 (353.08)

1.4962 1.5045

1.4875

1.4978

s

1.8755 1.8827 1.8898 1.8969 1.9039 1.9107 1.9176 1.9507 1.9824 2.0129 2.0421 2.0704 2.1242 2.1749 2.2228 2.2682

s

1.1257 1.1506

1.1620

v

4.725 4.793 4.861 4.928 4.996 5.063 5.131 5.467 5.802 6.137 6.471 6.804 7.470 8.135 8.800 9.465

v

1519.4 1529.8 1540.3 1550.9 1561.4 1572.0 1582.6 1636.1 1690.4 1745.6 1801.5 1858.4 1974.6 2094.2 2216.8 2342.2

h

1110.3 1116.6

1119.5

u

1193.6 1201.7

1205.5

h

400 (444.70)

1362.0 1370.2 1378.4 1386.7 1395.0 1403.4 1411.7 1454.0 1497.2 1541.2 1586.0 1631.7 1725.8 1823.2 1923.7 2027.0

u

180 (373.13)

1.4723 1.4814

1.4856

s

1.8472 1.8545 1.8616 1.8687 1.8757 1.8826 1.8894 1.9227 1.9544 1.9849 2.0142 2.0425 2.0964 2.1470 2.1950 2.2404

s

630 Appendix 2

450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920

2.548 2.584 2.619 2.654 2.689 2.724 2.758 2.792 2.826 2.860 2.893 2.926 2.960 2.993 3.025 3.058 3.123 3.188 3.252 3.316 3.379 3.442 3.505 3.568 3.631 3.693 3.755 3.818 3.879 3.941 4.003 4.064

1146.4 1150.8 1155.2 1159.5 1163.7 1168.0 1172.2 1176.3 1180.5 1184.6 1188.7 1192.7 1196.8 1200.8 1204.9 1208.9 1216.9 1224.9 1232.8 1240.8 1248.8 1256.7 1264.7 1272.7 1280.6 1288.6 1296.6 1304.7 1312.7 1320.8 1328.9 1337.0

1240.7 1246.5 1252.1 1257.7 1263.3 1268.8 1274.2 1279.7 1285.0 1290.4 1295.7 1301.0 1306.3 1311.6 1316.8 1322.1 1332.5 1342.9 1353.2 1363.5 1373.8 1384.1 1394.4 1404.7 1415.0 1425.3 1435.6 1446.0 1456.3 1466.7 1477.1 1487.5

1.5938 1.6001 1.6062 1.6122 1.6181 1.6239 1.6295 1.6351 1.6405 1.6459 1.6512 1.6565 1.6616 1.6667 1.6717 1.6767 1.6864 1.6959 1.7053 1.7144 1.7234 1.7322 1.7408 1.7493 1.7577 1.7660 1.7741 1.7821 1.7900 1.7978 1.8055 1.8131

1.6361 1.6630 1.6894 1.7154 1.7410 1.7662 1.7910 1.8156 1.8399 1.8640 1.8878 1.9114 1.9348 1.9580 1.9811 2.004 2.049 2.094 2.139 2.183 2.227 2.270 2.314 2.357 2.400 2.442 2.485 2.527 2.569 2.611 2.653 2.695

1135.4 1140.4 1145.3 1150.1 1154.8 1159.5 1164.1 1168.6 1173.1 1177.5 1181.9 1186.2 1190.5 1194.8 1199.0 1203.2 1211.6 1220.0 1228.2 1236.4 1244.6 1252.8 1261.0 1269.1 1277.3 1285.4 1293.6 1301.7 1309.9 1318.1 1326.3 1334.5

1226.2 1232.7 1239.1 1245.3 1251.5 1257.5 1263.5 1269.4 1275.2 1281.0 1286.7 1292.3 1297.9 1303.5 1309.0 1314.5 1325.4 1336.2 1347.0 1357.6 1368.3 1378.9 1389.4 1400.0 1410.5 1421.0 1431.5 1442.0 1452.5 1463.1 1473.6 1484.1

1.5365 1.5436 1.5505 1.5572 1.5637 1.5701 1.5763 1.5823 1.5882 1.5940 1.5997 1.6052 1.6107 1.6161 1.6214 1.6266 1.6368 1.6467 1.6564 1.6658 1.6751 1.6841 1.6930 1.7017 1.7103 1.7187 1.7270 1.7351 1.7432 1.7511 1.7589 1.7666

1.3733 1.3979 1.4220 1.4455 1.4686 1.4913 1.5136 1.5356 1.5572 1.5786 1.5998 1.6207 1.6414 1.6619 1.6823 1.7025 1.7424 1.7818 1.8207 1.8593 1.8975 1.9354 1.9731 2.0104 2.0476 2.085 2.121 2.158 2.194 2.231 2.267 2.303

1129.2 1134.6 1139.9 1145.0 1150.0 1154.9 1159.7 1164.5 1169.1 1173.7 1178.3 1182.8 1187.2 1191.6 1196.0 1200.3 1208.9 1217.4 1225.8 1234.2 1242.5 1250.8 1259.1 1267.3 1275.6 1283.8 1292.0 1300.3 1308.5 1316.7 1325.0 1333.3

1218.2 1225.2 1232.0 1238.6 1245.1 1251.5 1257.8 1263.9 1270.0 1276.0 1281.9 1287.7 1293.5 1299.3 1304.9 1310.6 1321.8 1332.8 1343.8 1354.6 1365.4 1376.2 1386.9 1397.5 1408.2 1418.8 1429.4 1440.0 1450.6 1461.2 1471.8 1482.5

1.5125 1.5201 1.5275 1.5346 1.5415 1.5482 1.5546 1.5610 1.5671 1.5731 1.5790 1.5848 1.5904 1.5960 1.6014 1.6068 1.6172 1.6274 1.6372 1.6469 1.6562 1.6654 1.6744 1.6832 1.6919 1.7004 1.7088 1.7170 1.7251 1.7331 1.7409 1.7487

1.1745 1.1977 1.2202 1.2421 1.2634 1.2843 1.3048 1.3249 1.3447 1.3642 1.3833 1.4023 1.4210 1.4395 1.4579 1.4760 1.5118 1.5471 1.5819 1.6163 1.6503 1.6840 1.7175 1.7506 1.7836 1.8163 1.8489 1.8813 1.9135 1.9456 1.9776 2.0094

1122.6 1128.5 1134.1 1139.6 1144.9 1150.1 1155.2 1160.2 1165.0 1169.8 1174.6 1179.2 1183.8 1188.4 1192.9 1197.3 1206.1 1214.8 1223.4 1231.9 1240.4 1248.8 1257.2 1265.5 1273.8 1282.1 1290.5 1298.8 1307.1 1315.4 1323.7 1332.0

1209.6 1.4901 1217.1 1.4984 1224.4 1.5063 1231.5 1.5139 1238.4 1.5212 1245.2 1.5282 1251.8 1.5351 1258.2 1.5417 1264.6 1.5481 1270.8 1.5544 1277.0 1.5605 1283.0 1.5665 1289.0 1.5723 1294.9 1.5781 1300.8 1.5837 1306.6 1.5892 1318.0 1.5999 1329.3 1.6103 1340.5 1.6203 1351.6 1.6301 1362.5 1.6397 1373.4 1.6490 1384.3 1.6581 1395.1 1.6670 1405.9 1.6758 1416.6 1.6844 1427.3 1.6928 1438.0 1.7011 1448.7 1.7093 1459.4 1.7173 1470.1 1.7252 1480.8 1.7330 (continued)

Appendix 2 631

1.0326 1.0183

1.0405

1.0620

460

470

v

4.126 4.187 4.249 4.310 4.371 4.432 4.493 4.554 4.615 4.918 5.220 5.521 5.822 6.123 6.722 7.321 7.920 8.518

Sat. 450

t

p (t Sat.)

940 960 980 1000 1020 1040 1060 1080 1100 1200 1300 1400 1500 1600 1800 2000 2200 2400

1497.9 1508.3 1518.8 1529.3 1539.8 1550.3 1560.9 1571.5 1582.2 1635.7 1690.1 1745.3 1801.3 1858.2 1974.4 2094.0 2216.7 2342.1

1128.0

1121.8

1119.6 1115.5

u

1216.4

1208.5

1205.6 1200.3

h

450 (456.39)

1345.2 1353.3 1361.6 1369.8 1378.0 1386.3 1394.6 1403.0 1411.4 1453.7 1496.9 1540.9 1585.8 1631.6 1725.6 1823.0 1923.6 2026.8

h

u

t

v

200 (381.86)

p (t Sat.)

Properties of Superheated Steam

TABLE A.3 (Continued)

1.4863

1.4777

1.4746 1.4687

s

1.8206 1.8280 1.8353 1.8425 1.8497 1.8568 1.8638 1.8707 1.8776 1.9109 1.9427 1.9732 2.0025 2.0308 2.0847 2.1354 2.1833 2.2288

s

.9342

.9133

.9283

v

2.736 2.778 2.819 2.860 2.902 2.943 2.984 3.025 3.066 3.270 3.473 3.675 3.877 4.078 4.479 4.879 5.280 5.679

v 1494.7 1505.3 1515.8 1526.5 1537.1 1547.7 1558.4 1569.1 1579.8 1633.8 1688.4 1743.8 1800.0 1857.0 1973.5 2093.2 2216.0 2341.4

h

1121.3

1114.7

1119.4

u

1207.8

1199.2

1205.3

h

500 (467.13)

1342.8 1351.1 1359.3 1367.7 1376.0 1384.4 1392.7 1401.2 1409.6 1452.2 1495.6 1539.8 1584.8 1630.7 1724.9 1822.3 1922.9 2026.1

u

300 (417.43)

1.4671

1.4578

1.4645

s

1.7742 1.7817 1.7891 1.7964 1.8036 1.8108 1.8178 1.8248 1.8317 1.8653 1.8973 1.9279 1.9573 1.9857 2.0396 2.0904 2.1384 2.1838

s

.8283

.8423

v

2.339 2.375 2.411 2.446 2.482 2.517 2.553 2.588 2.624 2.799 2.974 3.148 3.321 3.494 3.838 4.182 4.525 4.868

v

Vapor (psia)

1493.1 1503.7 1514.4 1525.0 1535.7 1546.4 1557.1 1567.9 1578.6 1632.8 1687.6 1743.1 1799.4 1856.5 1973.1 2092.8 2215.6 2341.1

h

1114.1

1119.1

u

1198.4

1204.8

h

550 (477.07)

1341.6 1349.9 1358.2 1366.6 1375.0 1383.4 1391.8 1400.2 1408.7 1451.5 1495.0 1539.3 1584.3 1630.2 1724.5 1822.0 1922.5 2025.8

u

350 (431.82)

1.4483

1.4551

s

1.7563 1.7639 1.7713 1.7787 1.7859 1.7931 1.8002 1.8072 1.8142 1.8478 1.8799 1.9106 1.9401 1.9685 2.0225 2.0733 2.1212 2.1667

s

.7702

v

2.0411 2.0727 2.1043 2.136 2.167 2.198 2.229 2.261 2.292 2.446 2.599 2.752 2.904 3.055 3.357 3.658 3.959 4.260

v

1491.5 1502.2 1512.9 1523.6 1534.3 1545.1 1555.9 1566.6 1577.4 1631.8 1686.8 1742.4 1798.8 1855.9 1972.6 2092.4 2215.2 2340.8

h

1118.6

u

1204.1

h

600 (486.33)

1340.4 1348.7 1357.1 1365.5 1373.9 1382.4 1390.8 1399.3 1407.8 1450.7 1494.3 1538.7 1.583.8 1629.8 1724.1 1821.6 1922.2 2025.4

u

400 (444.70)

1.4464

s

1.7407 1.7483 1.7558 1.7632 1.7705 1.7777 1.7849 1.7919 1.7989 1.8327 1.8648 1.8956 1.9251 1.9535 2.0076 2.0584 2.1064 2.1519

s

632 Appendix 2

480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 720 740 760 780 800 820 840 860 880

1.0828 1.1029 1.1226 1.1417 1.1605 1.1788 1.1969 1.2146 1.2320 1.2492 1.2662 1.2830 1.2996 1.3160 1.3323 1.3484 1.3644 1.3803 1.3960 1.4116 1.4272 1.4426 1.4580 1.4884 1.5186 1.5485 1.5782 1.6077 1.6369 1.6660 1.6950 1.7238

1133.8 1139.5 1145.1 1150.4 1155.7 1160.8 1165.8 1170.7 1175.6 1180.3 1185.0 1189.7 1194.3 1198.8 1203.3 1207.8 1212.2 1216.6 1221.0 1225.3 1229.6 1233.9 1238.2 1246.7 1255.2 1263.7 1272.1 1280.5 1288.9 1297.3 1305.6 1314.0

1224.0 1231.4 1238.5 1245.5 1252.3 1258.9 1265.5 1271.9 1278.2 1284.4 1290.5 1296.5 1302.5 1308.4 1314.2 1320.0 1325.8 1331.5 1337.2 1342.9 1348.5 1354.1 1359.6 1370.7 1381.7 1392.6 1403.5 1414.4 1425.2 1436.0 1446.8 1457.5

1.4944 1.5022 1.5097 1.5170 1.5239 1.5307 1.5372 1.5436 1.5498 1.5559 1.5618 1.5675 1.5732 1.5788 1.5842 1.5896 1.5948 1.6000 1.6051 1.6101 1.6151 1.6199 1.6248 1.6342 1.6435 1.6525 1.6614 1.6701 1.6786 1.6870 1.6952 1.7033

.9543 .9736 .9924 1.0106 1.0283 1.0456 1.0625 1.0792 1.0955 1.1115 1.1273 1.1429 1.1583 1.1735 1.1885 1.2033 1.2181 1.2327 1.2472 1.2615 1.2758 1.2899 1.3040 1.3319 1.3594 1.3867 1.4138 1.4407 1.4673 1.4938 1.5201 1.5463

1127.7 1133.8 1139.7 1145.4 1150.9 1156.3 1161.6 1166.7 1171.8 1176.7 1181.6 1186.4 1191.1 1195.8 1200.4 1205.0 1209.5 1214.0 1218.4 1222.9 1227.3 1231.7 1236.0 1244.7 1253.3 1261.8 1270.3 1278.8 1287.3 1295.7 1304.2 1312.6

1216.0 1223.9 1231.5 1238.9 1246.1 1253.1 1259.9 1266.6 1273.1 1279.5 1285.9 1292.1 1298.3 1304.3 1310.4 1316.3 1322.2 1328.0 1333.8 1339.6 1345.3 1351.0 1356.7 1367.9 1379.1 1390.1 1401.1 1412.1 1423.0 1433.9 1444.8 1455.7

1.4759 1.4843 1.4923 1.4999 1.5073 1.5144 1.5212 1.5279 1.5343 1.5406 1.5467 1.5527 1.5585 1.5642 1.5698 1.5753 1.5807 1.5860 1.5912 1.5963 1.6014 1.6063 1.6112 1.6208 1.6302 1.6394 1.6483 1.6571 1.6657 1.6742 1.6825 1.6906

.8480 .8669 .8850 .9056 .9196 .9361 .9522 .9679 .9834 .9985 1.0133 1.0280 1.0424 1.0566 1.0706 1.0845 1.0982 1.1118 1.1252 1.1386 1.1518 1.1649 1.1779 1.2037 1.2291 1.2543 1.2793 1.3040 1.3285 1.3528 1.3770 1.4010

1121.1 1127.7 1134.0 1140.1 1146.0 1151.7 1157.2 1162.6 1167.8 1173.0 1178.0 1183.0 1187.9 1192.7 1197.4 1202.1 1206.7 1211.3 1215.9 1220.4 1224.9 1229.4 1233.8 1242.6 1251.3 1260.0 1268.6 1277.1 1285.7 1294.2 1302.7 1311.2

1207.4 1215.9 1224.1 1232.0 1239.6 1246.9 1254.1 1261.1 1267.9 1274.6 1281.1 1287.6 1293.9 1300.2 1306.4 1312.5 1318.5 1324.5 1330.4 1336.3 1342.1 1347.9 1353.7 1365.1 1376.4 1387.6 1398.8 1409.8 1420.9 1431.9 1442.9 1453.8

1.4579 1.4669 1.4755 1.4836 1.4914 1.4989 1.5061 1.5131 1.5198 1.5263 1.5327 1.5388 1.5448 1.5507 1.5565 1.5621 1.5676 1.5730 1.5783 1.5836 1.5887 1.5938 1.5987 1.6085 1.6180 1.6273 1.6364 1.6452 1.6539 1.6625 1.6708 1.6791 .7582 .7769 .7947 .8118 .8283 .8443 .8598 .8749 .8896 .9040 .9181 .9320 .9456 .9590 .9722 .9853 .9982 1.0109 1.0235 1.0360 1.0483 1.0606 1.0727 1.0968 1.1205 1.1439 1.1671 1.1900 1.2128 1.2353 1.2577 1.2800

1113.9 1121.1 1128.0 1134.5 1140.7 1146.8 1152.6 1158.2 1163.7 1169.1 1174.3 1179.5 1184.5 1189.5 1194.4 1199.2 1203.9 1208.6 1213.3 1217.9 1222.5 1227.0 1231.5 1240.4 1249.3 1258.1 1266.8 1275.4 1284.1 1292.7 1301.2 1309.8

1198.1 1.4401 1207.4 1.4500 1216.2 1.4592 1224.6 1.4679 1232.7 1.4762 1240.5 1.4841 1248.0 1.4917 1255.4 1.4990 1262.5 1.5060 1269.5 1.5128 1276.3 1.5194 1282.9 1.5253 1289.5 1.5320 1295.9 1.5381 1302.3 1.5440 1308.6 1.5497 1314.8 1.5554 1320.9 1.5609 1326.9 1.5664 1332.9 1.5717 1338.9 1.5769 1344.8 1.5821 1350.6 1.5872 1362.2 1.5971 1373.7 1.6067 1385.1 1.6161 1396.3 1.6253 1407.6 1.6343 1418.7 1.6430 1429.8 1.6517 1440.9 1.6601 1451.9 1.6684 (continued)

Appendix 2 633

900 920 940 960 980 1000 1020 1040 1060 1080 1100 1150 1200 1250 1300 1350 1400 1450 1500 1600 1800 2000 2200 2400

1.7524 1.7810 1.8094 1.8377 1.8660 1.8941 1.9221 1.9501 1.9780 2.0058 2.034 2.103 2.172 2.240 2.308 2.376 2.444 2.512 2.580 2.715 2.983 3.251 3.519 3.787

1322.4 1330.8 1339.2 1347.6 1356.0 1364.4 1372.9 1381.4 1389.9 1398.4 1406.9 1428.4 1450.0 1471.8 1493.7 1515.8 1538.1 1560.6 1583.3 1629.3 1723.7 1821.3 1921.8 2025.1

1468.3 1479.1 1489.8 1500.6 1511.4 1522.2 1533.0 1543.8 1554.6 1565.4 1576.3 1603.5 1630.8 1658.3 1685.9 1713.7 1741.7 1769.8 1798.2 1855.4 1972.1 2092.0 2214.9 2340.4

h

u

t

v

450 (456.39)

p (t Sat.)

Properties of Superheated Steam

TABLE A.3 (Continued)

1.7113 1.7191 1.7269 1.7345 1.7420 1.7495 1.7568 1.7641 1.7712 1.7783 1.7853 1.8025 1.8192 1.8355 1.8515 1.8670 1.8823 1.8972 1.9119 1.9403 1.9944 2.0453 2.0933 2.1388

s 1.5723 1.5982 1.6240 1.6497 1.6753 1.7008 1.7262 1.7515 1.7768 1.8020 1.8271 1.8896 1.9518 2.0137 2.075 2.137 2.198 2.259 2.320 2.442 2.684 2.926 3.167 3.408

v 1321.0 1329.5 1337.9 1346.4 1354.9 1363.3 1371.8 1380.4 1388.9 1397.4 1406.0 1427.5 1449.2 1471.1 1493.1 1515.2 1537.6 1560.1 1582.8 1628.9 1723.3 1820.9 1921.5 2024.7

u 1466.5 1477.4 1488.2 1499.0 1509.9 1520.7 1531.6 1542.4 1553.3 1564.2 1575.1 1602.4 1629.8 1657.4 1685.1 1712.9 1741.0 1769.2 1797.5 1854.8 1971.7 2091.6 2214.5 2340.1

h

500 (467.13)

1.6987 1.7066 1.7144 1.7221 1.7296 1.7371 1.7445 1.7518 1.7590 1.7661 1.7731 1.7904 1.8072 1.8235 1.8395 1.8551 1.8704 1.8853 1.9000 1.9285 1.9827 2.0335 2.0815 2.1270

s 1.4249 1.4487 1.4723 1.4958 1.5193 1.5426 1.5659 1.5890 1.6121 1.6352 1.6581 1.7152 1.7720 1.8285 1.8848 1.9409 1.9967 2.0525 2.1080 2.219 2.440 2.660 2.879 3.098

v

Vapor (psia)

1319.7 1328.2 1336.7 1345.2 1353.7 1362.3 1370.8 1379.3 1387.9 1396.5 1405.1 1426.7 1448.5 1470.3 1492.4 1514.6 1537.0 1559.6 1582.3 1628.4 1722.9 1820.6 1921.1 2024.4

u 1464.7 1475.6 1486.6 1497.5 1508.4 1519.3 1530.2 1541.1 1552.0 1562.9 1573.9 1601.3 1628.8 1656.5 1684.2 1712.2 1740.2 1768.5 1796.9 1854.3 1971.2 2091.2 2214.2 2339.7

h

550 (477.07)

1.6872 1.6951 1.7030 1.7107 1.7183 1.7259 1.7333 1.7406 1.7478 1.7550 1.7620 1.7793 1.7962 1.8126 1.8286 1.8443 1.8596 1.8746 1.8892 1.9178 1.9720 2.0229 2.0709 2.1164

s 1.3021 1.3240 1.3459 1.3676 1.3893 1.4108 1.4322 1.4536 1.4749 1.4961 1.5173 1.5699 1.6222 1.6742 1.7260 1.7775 1.8289 1.8801 1.9312 2.033 2.236 2.438 2.639 2.840

v 1318.4 1326.9 1335.5 1344.0 1352.6 1361.2 1369.7 1378.3 1386.9 1395.6 1404.2 1425.9 1447.7 1469.6 1491.7 1514.0 1536.5 1559.1 1581.9 1628.0 1722.6 1820.2 1920.8 2024.0

u

1462.9 1473.9 1484.9 1495.9 1506.8 1517.8 1528.8 1539.7 1550.7 1561.7 1572.7 1600.2 1627.8 1655.5 1683.4 1711.4 1739.5 1767.8 1796.3 1853.7 1970.8 2090.8 2213.8 2339.4

h

600 (486.33)

1.6766 1.6846 1.6925 1.7003 1.7079 1.7155 1.7230 1.7303 1.7376 1.7448 1.7519 1.7692 1.7861 1.8026 1.8186 1.8343 1.8497 1.8647 1.8794 1.9080 1.9622 2.0131 2.0612 2.1067

s

634 Appendix 2

Sat. 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 720 740 760 780 800 820 840 860 880

t

p (t Sat.)

1107.9 1116.4 1124.3 1131.8 1138.8 1145.6 1152.0 1158.3 1164.3 1170.1 1175.8 1181.3 1186.7 1192.0 1197.2 1202.3 1207.4 1212.3 1217.2 1222.1 1231.6 1241.0 1250.3 1259.4 1268.5 1277.4 1286.4 1295.2 1304.1

.5554 .5717 .5870 .6015 .6154 .6287 .6415 .6539 .6659 .6776 .6890 .7002 .7111 .7218 .7324 .7428 .7530 .7631 .7730 .7829 .8023 .8212 .8399 .8583 .8764 .8943 .9120 .9295 .9468

u

1115.0

v

.5691

800 (518.36) h

1190.1 1201.0 1211.2 1220.8 1229.9 1238.6 1247.0 1255.1 1262.9 1270.4 1277.8 1285.0 1292.0 1298.9 1305.6 1312.3 1318.8 1325.3 1331.7 1338.0 1350.4 1362.6 1374.6 1386.5 1398.2 1409.8 1421.4 1432.8 1444.2

1199.3

s

1.4066 1.4178 1.4282 1.4378 1.4469 1.4555 1.4637 1.4714 1.4789 1.4861 1.4930 1.4997 1.5062 1.5125 1.5186 1.5245 1.5304 1.5361 1.5416 1.5471 1.5577 1.5680 1.5779 1.5875 1.5969 1.6061 1.6150 1.6238 1.6324

1.4160

v

.4389 .4534 .4669 .4795 .4915 .5030 .5140 .5245 .5348 .5447 .5543 .5637 .5730 .5820 .5908 .5995 .6080 .6247 .6410 .6569 .6725 .6878 .7028 .7176 .7323 .7467

.4459

u

1105.2 1114.8 1123.6 1131.7 1139.4 1146.7 1153.7 1160.3 1166.7 1172.9 1178.9 1184.7 1190.4 1196.0 1201.4 1206.8 1212.0 1222.3 1232.3 1242.1 1251.7 1261.2 1270.6 1279.9 1289.1 1298.2

1109.9

h

1186.4 1198.7 1210.0 1220.5 1230.4 1239.8 1248.8 1257.4 1265.7 1273.7 1281.5 1289.1 1296.5 1303.7 1310.8 1317.7 1324.6 1337.9 1350.9 1363.7 1376.2 1388.5 1400.6 1412.7 1424.6 1436.4

1192.4

1000 (544.75) s

1.3844 1.3966 1.4077 1.4179 1.4275 1.4365 1.4450 1.4531 1.4609 1.4682 1.4754 1.4822 1.4889 1.4953 1.5015 1.5076 1.5135 1.5249 1.5359 1.5464 1.5566 1.5664 1.5760 1.5853 1.5944 1.6033 (continued)

1.3903

Appendix 2 635

900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1350 1400 1450 1500 1600 1800 2000 2200 2400

t

p (t Sat.)

.9640 .9811 .9980 1.0149 1.0316 1.0482 1.0647 1.0812 1.0975 1.1138 1.1300 1.1462 1.1623 1.1783 1.1943 1.2102 1.2261 1.2420 1.2578 1.2735 1.2892 1.3284 1.3674 1.4062 1.4448 1.5218 1.6749 1.8271 1.9789 2.1305

v

Properties of Superheated Steam

TABLE A.3 (Continued)

u

1312.9 1321.7 1330.4 1339.2 1348.0 1356.7 1365.5 1374.2 1383.0 1391.7 1400.5 1409.3 1418.1 1426.9 1435.8 1444.6 1453.5 1462.3 1471.3 1480.2 1489.1 1511.6 1534.2 1556.9 1579.9 1626.2 1721.0 1818.8 1919.4 2022.7

800 (518.36) h 1455.6 1466.9 1478.2 1489.4 1500.7 1511.9 1523.1 1534.3 1545.5 1556.6 1567.8 1579.0 1590.2 1601.4 1612.6 1623.8 1635.9 1646.2 1657.4 1668.7 1680.0 1708.2 1736.6 1765.1 1793.7 1851.5 1969.0 2089.3 2212.4 2338.1

s 1.6408 1.6490 1.6572 1.6651 1.6730 1.6807 1.6883 1.6959 1.7033 1.7106 1.7178 1.7249 1.7319 1.7389 1.7458 1.7526 1.7593 1.7659 1.7725 1.7790 1.7854 1.8013 1.8167 1.8319 1.8467 1.8754 1.9298 1.9808 2.0290 2.0745

v .7610 .7752 .7892 .8031 .8169 .8305 .8441 .8576 .8710 .8844 .8976 .9108 .9240 .9370 .9500 .9630 .9759 .9888 1.0016 1.0144 1.0272 1.0589 1.0905 1.1218 1.1531 1.2152 1.3384 1.4608 1.5828 1.7046

Vapor (psia)

u 1307.3 1316.3 1325.3 1334.3 1343.2 1352.2 1361.1 1370.0 1378.9 1387.9 1396.8 1405.7 1414.6 1423.6 1432.5 1441.5 1450.4 1459.4 1468.4 1477.4 1486.5 1509.1 1531.9 1554.8 1577.8 1624.4 1719.5 1817.4 1918.1 2021.3

h 1448.1 1459.7 1471.3 1482.9 1494.4 1505.9 1517.3 1528.7 1540.1 1551.5 1562.9 1574.3 1585.6 1597.0 1608.3 1619.7 1631.0 1642.4 1653.8 1665.1 1676.5 1705.1 1733.7 1762.4 1791.2 1849.3 1967.2 2087.7 2211.0 2336.7

1000 (544.75) s 1.6120 1.6205 1.6288 1.6370 1.6451 1.6530 1.6608 1.6684 1.6760 1.6834 1.6908 1.6980 1.7052 1.7122 1.7192 1.7261 1.7329 1.7396 1.7462 1.7528 1.7593 1.7753 1.7909 1.8061 1.8210 1.8499 1.9046 1.9557 2.0038 2.0494

636 Appendix 2

Sat. 32 50 100 150 200 250 300 350 400 450 500 510 520 530 540 550 560 570 580 590 600 610

t

p (t Sat.)

.016022 .016024 .016130 .016344 .016635 .017003 .017453 .018000 .018668 .019503 .02060 .02087 .02116 .02148 .02182 .02221 .02265 .02315

v

0.01 18.06 68.05 117.95 168.05 218.52 269.61 321.59 374.85 429.96 488.1 500.3 512.7 525.5 538.6 552.1 566.1 580.8

u

0

0.01 18.06 68.05 117.95 168.05 218.52 269.61 321.59 374.85 429.96 488.1 500.3 512.7 525.5 538.6 552.1 566.1 580.8

h

Properties of Compressed Liquid (Steam)

TABLE A.4

.00003 .03607 .12963 .21504 .29402 .36777 .43732 .50359 .56740 .62970 .6919 .7046 .7173 .7303 .7434 .7569 .7707 .7851

s

v .019748 .015994 .015998 .016106 .016318 .016608 .016972 .017416 .017954 .018608 .019420 .02048 .02073 .02100 .02130 .02162 .02198 .02237 .02281 .02332 .02392

447.70 .00 18.02 67.87 117.66 167.65 217.99 268.92 320.71 373.68 428.40 485.9 497.9 510.1 522.6 535.3 548.4 562.0 576.0 590.8 606.4

u 449.53 1.49 19.50 69.36 119.17 169.19 219.56 270.53 322.37 375.40 430.19 487.8 499.8 512.0 524.5 537.3 550.5 564.0 578.1 592.9 608.6

h

500 (467.13)

Liquid (psia)

s .64904 .00000 .03599 .12932 .21457 .29341 .36702 .43641 .50249 .56604 .63798 .6896 .7021 .7146 .7273 .7402 .7532 .7666 .7804 .7946 .8096

v .021591 .015967 .015972 .016082 .016293 .016580 .016941 .017379 .017909 .018550 .019340 .02036 .02060 .02086 .02114 .02144 .02177 .02213 .02253 .02298 .02349 .02409 .02482

u 538.39 .03 17.99 67.70 117.38 167.26 217.47 268.24 319.83 372.55 426.89 483.8 495.6 507.6 519.9 532.4 545.1 558.3 571.8 585.9 600.6 616.2 632.9

542.38 2.99 20.94 70.68 120.40 170.32 220.61 271.46 323.15 375.98 430.47 487.5 499.4 511.5 523.8 536.3 549.2 562.4 576.0 590.1 604.9 620.6 637.5

h

1000 (544.75) s .74320 .00005 .03592 .12901 .21410 .29281 .36628 .43352 .50140 .56472 .62632 .6874 .6997 .7121 .7245 .7372 .7499 .7630 .7763 .7899 .8041 .8189 .8348 (continued)

Appendix 2 637

v

.015807 .015821 .015942 .016150 .016425 .016765 .017174 .017659 .018235 .018924 .019766 .020161 .020600 .021091 .021648 .02229 .02304 .02394 .02506 .02653 .02867 .03026

t

32 50 100 150 200 250 300 350 400 450 500 520 540 560 580 600 620 640 660 680 700 710

p (t Sat)

.10 17.76 66.72 115.77 165.02 214.52 264.43 314.98 366.35 418.83 472.9 495.2 517.9 541.2 565.2 590.0 616.0 643.3 672.7 704.9 742.1 764.3

u

4000

11.80 29.47 78.52 127.73 177.18 226.93 277.15 328.05 379.85 432.84 487.5 510.1 533.1 556.8 581.2 606.5 633.0 661.1 691.2 724.5 763.4 786.7

h

Properties of Compressed Liquid (Steam)

TABLE A.4 (Continued)

s .00005 .03534 .12714 .21136 .28931 .36200 .43038 .49526 .55734 .61725 .6758 .6990 .7223 .7457 .7694 .7936 .8183 .8441 .8712 .9007 .9345 .9545

v .015188 .015227 .015372 .015572 .015813 .016096 .016422 .016791 .017207 .017669 .018183 .018404 .018636 .018879 .019134 .01940 .01968 .01998 .02030 .02064 .02099 .02118

u 0.54 16.32 62.83 109.64 156.62 203.57 250.58 297.80 345.32 393.15 441.3 460.6 480.0 499.5 519.0 538.7 558.4 578.2 598.1 618.2 638.4 648.5

h 50.05 67.04 114.03 161.51 209.29 257.19 305.28 353.73 402.63 452.00 501.9 521.9 542.1 562.4 582.8 603.3 623.9 644.8 665.7 686.9 708.3 719.1

18 000

Liquid (psia)

s .00372 .03021 .11817 .19941 .27474 .34472 .41021 .47197 .53057 .58639 .6397 .6605 .6808 .7009 .7207 .7403 .7596 .7787 .7976 .8163 .8349 .8442

v .015116 .015154 .015298 .015497 .015736 .016015 .016333 .016693 .017096 .017541 .018031 .018242 .018461 .018689 .018928 .01918 .01944 .01972 .02001 .02031 .02063 .02080

.65 16.14 62.37 108.91 155.62 202.28 248.96 295.83 342.97 390.39 438.1 457.2 476.4 495.6 514.9 534.3 553.7 573.2 592.7 612.4 632.1 642.1

u

h 55.30 72.23 118.99 166.26 213.86 261.55 309.41 357.61 406.24 455.31 504.8 524.7 544.7 564.8 585.0 605.2 625.6 646.1 666.8 687.6 708.5 719.1

20 000 s .00446 .02936 .11688 .19778 .27281 .34250 .40766 .46911 .52738 .58286 .6358 .6564 .6766 .6965 .7160 .7354 .7544 .7732 .7918 .8102 .8285 .8375

638 Appendix 2

639

Appendix 2

TABLE A.5 Enthalpy–Entropy Diagram for Steam—A Mollier Chart for Steam Abs. Press. in. Hg. 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sat. Temp. °F

Abs. Press., lb. per sq. in.

Sat. Temp. °F

Abs. Press. lb. per sq. in.

Sat. Temp. °F

34.56 40.23 44.96 49.06 52.64 55.87 58.80 61.48 63.95 66.26 68.40 70.43 72.32 74.18 75.84 77.47 79.03 81.95 84.65 87.17 89.51 91.72 93.80 95.77 97.65 99.43 101.14

1.0 2 3 4 5 6 7 8 9 10 12 14 14.696 16 18 20 25 30 35 40 45 50 60 70 80 90 100

101.74 126.08 141.18 152.97 162.24 170.06 176.83 182.86 188.28 193.21 201.96 209.56 212.00 216.32 222.41 227.96 240.07 250.33 259.28 267.25 274.44 281.01 292.71 302.92 312.03 320.27 327.81

120 140 160 180 200 220 240 260 280 300 400 500 600 700 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3206.2

341.25 353.02 363.53 373.06 381.79 389.86 397.37 404.42 411.05 417.33 444.59 467.01 486.21 503.10 518.23 544.61 567.22 587.10 604.90 621.03 635.82 649.46 662.12 673.94 684.99 695.36 705.40

Source: Modified and greatly reduced from J. H. Keenan and F. G. Keyes: Thermodynamic Properties of Steam. 1936. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

640

Appendix 2

o

o

1050

700

o

00

600

200 160 0 0 1 100200 0 800

50 er he

30 25 0 20 0 0 15 0

up

at, d

40

0o

0o

75

8

sq.

450o

per

o

o

450

10

0

o

nst

ant

400

halp

re,

lb’.

500

o

1200

Sat

1150

ura

tion

2

300o

line

200o

14

re he

16

91 F .7 o 79 72 .0 o 64 .3 o 58 .0 o 52 .8 o 45 .6 o . 34 0 o .6 o

o

1.1 3 1. 0

1. 2 5

lb. ur res s tp ns tan

30

Co

28

900

32

850

36

1.7

40

38

50

45

1.1

1.2

1.3

950

1.9

1.8

34

850

1000

2.0

e,

26

900

2.1

10

5

4

. bs q. in. a pe rs

24

Critical state

6

20 22

1050

0. 2”

nt

12

0 5” .4 0 ” .3 ”

ce

20 14 10 .69 8 8

30

5 0 40 0

10 er

2 .0 1 ” .5 M erc ” 1 ur .0 y 0 ” .8 0 ” .6 0 ” .

,p

osp

re

At m

tu

ard

ois

2.2

18

950

1100

8

nd

tm

10 8 0 6 0

tan

1000

800 1.0

100o

Sta

ns

1150

150o

6

4000 30 0 0 20250 15 0 0

60 0 5 0

80

55

00

0

0

40 0 30 00 00 20 0 16 0 0 12 0 00 1

Co

1200

250o

4 1100

1250

o Constant temperature, deg. F. 350

o

300

1300

400o

Co

350

550o 500o

in.

0

1350

600o

10

. abs

20

o

550

1250

650o

ssu

m

6

r lb

o

00

Pre

70

o

0

1400

700o

0

0

y, B t

u pe

750o

.F .

10 0 80 60 50 40 30

eg

1450

800o

0

1.0

ts

6

tan

20 14 .69

ns

30

65

1500

900o 850o

Co

60 50 0 400 0

1400

1350

1550

o

1000

o erature, deg. F. 950 Constant temp

550 0 400 0 300 0

1450

800

1.4

Entropy

TABLE A.5 Enthalpy–Entropy Diagram for Steam.

1.5

1.6

800

Copyright, 1940, by Frank O. Ellenwood, William N. Barnard, and Charles O. Mackey

Enthalpy, Btu per lb.

o

50

10

1500

2.2

900 1600

6 5

11

2.1 o

50

11

1550

Sat. temp., o F 341.25 353.02 363.53 373.06 381.79 389.86 397.37 404.42 411.05 417.33 444.59 467.01 486.21 503.10 518.23 544.61 567.22 587.10 604.90 621.03 635.82 649.46 662.12 673.94 684.99 695.36 705.40

1050

2.0

2 1.5

12

1300

Ent

1.9

1100

0o

Sat. temp., o F 101.74 126.08 141.18 152.97 162.24 170.06 176.83 182.86 188.28 193.21 201.96 209.56 212.00 216.32 222.41 227.96 240.07 250.33 259.28 267.25 274.44 281.01 292.71 302.92 312.03 320.27 327.80

Entropy (Btu/lbm·oR)

o

1 9 000 o 9 50 o 85 o00 o 0

Sat. temp., o F 34.56 40.23 44.96 49.06 52.64 55.87 58.80 61.48 63.95 66.26 68.40 70.43 72.32 74.18 75.84 77.47 79.03 81.95 84.65 87.17 89.51 91.72 93.80 95.77 97.65 99.43 101.14

1.8

80

Abs. press. in. Hg. 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Abs. press. lb. per sq. in. 120 140 160 180 200 220 240 260 280 300 400 500 600 700 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3206.2

1.7

00

Modified and greatly reduced from Keenan and Keye’s Thermodynamic Properties of Steam, published (1936) by John Wiley and Sons, Inc. Reproduced by permission of the publishers. Abs. press., lb. per sq. in. 1.0 2 3 4 5 6 7 8 9 10 12 14 14.696 16 18 20 25 30 35 40 45 50 60 70 80 90 100

1.6

4 3

1.5

1600

A Mollier chart for steam

Press. kPa P

0.6113 0.8721 1.2276 1.7051 2.339 3.169 4.246 5.628 7.384 9.593 12.349 15.758 19.940 25.03 31.19 38.58 47.39 57.83 70.14 84.55 0.101 35 0.120 82

Temp. °C T

0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

0.001 000 0.001 000 0.001 000 0.001 001 0.001 002 0.001 003 0.001 004 0.001 006 0.001 008 0.001 010 0.001 012 0.001 015 0.001 017 0.001 020 0.001 023 0.001 026 0.001 029 0.001 033 0.001 036 0.001 040 0.001 044 0.001 048

Sat. Liquid vf

206.14 147.12 106.38 77.93 57.79 43.36 32.89 25.22 19.52 15.26 12.03 9.568 7.671 6.197 5.042 4.131 3.407 2.828 2.361 1.982 1.6729 1.4194

Sat. Vapor vg

Specific Volume (m3 kg)

Saturation: Temperature (Steam)

TABLE A.1 (SI)

.00 20.97 42.00 62.99 83.95 104.88 125.78 146.67 167.56 188.44 209.32 230.21 251.11 272.02 292.95 313.90 334.86 355.84 376.85 397.88 418.94 440.02

Sat. Liquid uf 2375.3 2361.3 2347.2 2333.1 2319.0 2304.9 2290.8 2276.7 2262.6 2248.4 2234.2 2219.9 2205.5 2191.1 2176.6 2162.0 2147.4 2132.6 2117.7 2102.7 2087.6 2072.3

Evap. ugg 2375.3 2382.3 2389.2 2396.1 2402.9 2409.8 2416.6 2423.4 2430.1 2436.8 2443.5 2450.1 2456.6 2463.1 2469.6 2475.9 2482.2 2488.4 2494.5 2500.6 2506.5 2512.4

Sat. Vapor ug

Internal Energy (kJ/kg)

.01 20.98 42.01 62.99 83.96 104.89 125.79 146.68 167.57 188.45 209.33 230.23 251.13 272.06 292.98 313.93 334.91 355.90 376.92 397.96 419.04 440.15

Sat. Liquid hf 2501.3 2489.6 2477.7 2465.9 2454.1 2442.3 2430.5 2418.6 2406.7 2394.8 2382.7 2370.7 2358.5 2346.2 2333.8 2321.4 2308.8 2296.0 2283.2 2270.2 2257.0 2243.7

Evap. hfg

Enthalpy (kJ/kg)

2501.4 2510.6 2519.8 2528.9 2538.1 2547.2 2556.3 2565.3 2574.3 2583.2 2592.1 2600.9 2609.6 2618.3 2626.8 2635.3 2643.7 2651.9 2660.1 2668.1 2676.1 2683.8

Sat. Vapor hg .0000 .0761 .1510 .2245 .2966 .3674 .4369 .5053 .5725 .6387 .7038 .7679 .8312 .8935 .9549 1.0155 1.0753 1.1343 1.1925 1.2500 1.3069 1.3630

Sat. Liquid sf 9.1562 8.9496 8.7498 8.5569 8.3706 8.1905 8.0164 7.8478 7.6845 7.5261 7.3725 7.2234 7.0784 6.937.5 6.8004 6.6669 6.5369 6.4102 6.2866 6.1659 6.0480 5.9328

Evap. sfg

9.1562 9.0257 8.9008 8.7814 8.6672 8.5580 8.4533 8.3531 8.2570 8.1648 8.0763 7.9913 7.9096 7.8310 7.7553 7.6824 7.6122 7.5445 7.4791 7.4159 7.3549 7.2958 (continued)

Sat. Vapor sg

Entropy (kJ/kg. K)

Appendix 2 641

Press. kPa P

0.143 27 0.169 06 0.198 53 0.2321 0.2701 0.3130 0.3613 0.4154 0.4758 0.5431 0.6178 0.7005 0.7917 0.8920 1.0021 1.1227 1.2544 1.3978 1.5538 1.7230 1.9062 2.104

Temp. °C T

110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215

0.001 052 0.001 056 0.001 060 0.001 065 0.001 070 0.001 075 0.001 080 0.001 085 0.001 091 0.001 096 0.001 102 0.001 108 0.001 114 0.001 121 0.001 127 0.001 134 0.001 141 0.001 149 0.001 157 0.001 164 0.001 173 0.001 181

Sat. Liquid vf

1.2102 1.0366 0.8919 0.7706 0.6685 0.5822 0.5089 0.4463 0.3928 0.3468 0.3071 0.2727 0.2428 0.2168 0.194 05 0.174 09 0.156 54 0.141 05 0.127 36 0.115 21 0.104 41 0.094 79

Sat. Vapor vg

Specific Volume (m3 kg)

Saturation: Temperature (Steam)

TABLE A.1 (SI) (Continued)

461.14 482.30 503.50 524.74 546.02 567.35 588.74 610.18 631.68 653.24 674.87 696.56 718.33 740.17 762.09 784.10 806.19 828.37 850.65 873.04 895.53 918.14

Sat. Liquid uf 2057.0 2041.4 2025.8 2009.9 1993.9 1977.7 1961.3 1944.7 1927.9 1910.8 1893.5 1876.0 1858.1 1840.0 1821.6 1802.9 1783.8 1764.4 1744.7 1724.5 1703.9 1682.9

Evap. ugg 2518.1 2523.7 2529.3 2534.6 2539.9 2545.0 2550.0 2554.9 2559.5 2564.1 2568.4 2572.5 2576.5 2580.2 2583.7 2587.0 2590.0 2592.8 2595.3 2597.5 2599.5 2601.1

Sat. Vapor ug

Internal Energy (kJ/kg)

461.30 482.48 503.71 524.99 546.31 567.69 589.13 610.63 632.20 653.84 675.55 697.34 719.21 741.17 763.22 785.37 807.62 829.98 852.45 875.04 897.76 920.62

Sat. Liquid hf 2230.2 2216.5 2202.6 2188.5 2174.2 2159.6 2144.7 2129.6 2114.3 2098.6 2082.6 2066.2 2049.5 2032.4 2015.0 1997.1 1978.8 1960.0 1940.7 1921.0 1900.7 1879.9

Evap. hfg

Enthalpy (kJ/kg)

2691.5 2699.0 2706.3 2713.5 2720.5 2727.3 2733.9 2740.3 2746.5 2752.4 2758.1 2763.5 2768.7 2773.6 2778.2 2782.4 2786.4 2790.0 2793.2 2796.0 2798.5 2800.5

Sat. Vapor hg 1.4185 1.4734 1.5276 1.5813 1.6344 1.6870 1.7391 1.7907 1.8418 1.8925 1.9427 1.9925 2.0419 2.0909 2.1396 2.1879 2.2359 2.2835 2.3309 2.3780 2.4248 2.4714

Sat. Liquid sf

5.8202 5.7100 5.6020 5.4962 5.3925 5.2907 5.1908 5.0926 4.9960 4.9010 4.8075 4.7153 4.6244 4.5347 4.4461 4.3586 4.2720 4.1863 4.1014 4.0172 3.9337 3.8507

Evap. sfg

7.2387 7.1833 7.1296 7.0775 7.0269 6.9777 6.9299 6.8833 6.8379 6.7935 6.7502 6.7078 6.6663 6.6256 6.5857 6.5465 6.5079 6.4698 6.4323 6.3952 6.3585 6.3221

Sat. Vapor sg

Entropy (kJ/kg. K)

642 Appendix 2

220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 330 340 350 360 370 374.14

2.318 2.548 2.795 3.060 3.344 3.648 3.973 4.319 4.688 5.081 5.499 5.942 6.412 6.909 7.436 7.993 8.581 9.202 9.856 10.547 11.274 12.845 14.586 16.513 18.651 21.03 22.09

0.001 190 0.001 199 0.001 209 0.001 219 0.001 229 0.001 240 0.001 251 0.001 263 0.001 276 0.001 289 0.001 302 0.001 317 0.001 332 0.001 348 0.001 366 0.001 384 0.001 404 0.001 425 0.001 447 0.001 472 0.001 499 0.001 561 0.001 638 0.001 740 0.001 893 0.002 213 0.003 155

0.086 19 0.078 49 0.071 58 0.065 37 0.059 76 0.054 71 0.050 13 0.045 98 0.042 21 0.038 77 0.035 64 0.032 79 0.030 17 0.027 77 0.025 57 0.023 54 0.021 67 0.019 948 0.018 350 0.016 867 0.015 488 0.012 996 0.010 797 0.008 813 0.006 945 0.004 925 0.003 155

940.87 963.73 986.74 1009.89 1033.21 1056.71 1080.39 1104.28 1128.39 1152.74 1177.36 1202.25 1227.46 1253.00 1278.92 1305.2 1332.0 1359.3 1387.1 1415.5 1444.6 1505.3 1570.3 1641.9 1725.2 1844.0 2029.6

1661.5 1639.6 1617.2 1594.2 1570.8 1546.7 1522.0 1496.7 1470.6 1443.9 1416.3 1387.9 1358.7 1328.4 1297.1 1264.7 1231.0 1195.9 1159.4 1121.1 1080.9 993.7 894.3 776.6 626.3 384.5 0

2602.4 2603.3 2603.9 2604.1 2604.0 2603.4 2602.4 2600.9 2599.0 2596.6 2593.7 2590.2 2586.1 2581.4 2576.0 2569.9 2563.0 2555.2 2546.4 2536.6 2525.5 2498.9 2464.6 2418.4 2351.5 2228.5 2029.6

943.62 966.78 990.12 1013.62 1037.32 1061.23 1085.36 1109.73 1134.37 1159.28 1184.51 1210.07 1235.99 1262.31 1289.07 1316.3 1344.0 1372.4 1401.3 1431.0 1461.5 1525.3 1594.2 1670.6 1760.5 1890.5 2099.3

1858.5 1836.5 1813.8 1790.5 1766.5 1741.7 1716.2 1689.8 1662.5 1634.4 1605.2 1574.9 1543.6 1511.0 1477.1 1441.8 1404.9 1366.4 1326.0 1283.5 1238.6 1140.6 1027.9 893.4 720.5 441.6 0

2802.1 2803.3 2804.0 2804.2 2803.8 2803.0 2801.5 2799.5 2796.9 2793.6 2789.7 2785.0 2779.6 2773.3 2766.2 2758.1 2749.0 2738.7 2727.3 2714.5 2700.1 2665.9 2622.0 2563.9 2481.0 2332.1 2099.3

2.5178 2.5639 2.6099 2.6558 2.7015 2.7472 2.7927 2.8383 2.8838 2.9294 2.9751 3.0208 3.0668 3.1130 3.1594 3.2062 3.2534 3.3010 3.3493 3.3982 3.4480 3.5507 3.6594 3.7777 3.9147 4.1106 4.4298

3.7683 3.6863 3.6047 3.5233 3.4422 3.3612 3.2802 3.1992 3.1181 3.0368 2.9551 2.8730 2.7903 2.7070 2.6227 2.5375 2.4511 2.3633 2.2737 2.1821 2.0882 1.8909 1.6763 1.4335 1.1379 .6865 0

6.2861 6.2503 6.2146 6.1791 6.1437 6.1083 6.0730 6.0375 6.0019 5.9662 5.9301 5.8938 5.8571 5.8199 5.7821 5.7437 5.7045 5.6643 5.6230 5.5804 5.5362 5.4417 5.3357 5.2112 5.0526 4.7971 4.4298

Appendix 2 643

0.100 0.125 0.150 0.175 0.200 0.225

99.63 105.99 111.37 116.06 120.23 124.00

0.01 6.98 13.03 17.50 21.08 24.08 28.96 32.88 40.29 45.81 53.97 60.06 64.97 69.10 75.87 81.33 91.78

0.6113 1.0 1.5 2.0 2.5 3.0 4.0 5.0 7.5 10 15 20 25 30 40 50 75

MPa

Temp. °C T

Press. kPa P

0.001 043 0.001 048 0.001 053 0.001 057 0.001 061 0.001 064

0.001 000 0.001 000 0.001 001 0.001 001 0.001 002 0.001 003 0.001 004 0.001 005 0.001 008 0.001 010 0.001 014 0.001 017 0.001 020 0.001 022 0.001 027 0.001 030 0.001 037

Sat. Liquid vf

1.6940 1.3749 1.1593 1.0036 0.8857 0.7933

206.14 129.21 87.98 67.00 54.25 45.67 34.80 28.19 19.24 14.67 10.02 7.649 6.204 5.229 3.993 3.240 2.217

Sat. Vapor vg

Specific Volume (m3/ kg)

Saturation Pressures (Steam)

TABLE A.2 (SI)

417.36 444.19 466.94 486.80 504.49 520.47

.00 29.30 54.71 73.48 88.48 101.04 121.45 137.81 168.78 191.82 225.92 251.38 271.90 289.20 317.53 340.44 384.31

Sat. Liquid uf

2088.7 2069.3 2052.7 2038.1 2025.0 2013.1

2375.3 2355.7 2338.6 2326.0 2315.9 2307.5 2293.7 2282.7 2261.7 2246.1 2222.8 2205.4 2191.2 2179.2 2159.5 2143.4 2112.4

Evap. ufg

2506.1 2513.5 2519.7 2524.9 2529.5 2533.6

2375.3 2385.0 2393.3 2399.5 2404.4 2408.5 2415.2 2420.5 2430.5 2437.9 2448.7 2456.7 2463.1 2468.4 2477.0 2483.9 2496.7

Sat. Vapor ug

Internal Energy (kJ/kg)

417.46 444.32 467.11 486.99 504.70 520.72

.01 29.30 54.71 73.48 88.49 101.05 121.46 137.82 168.79 191.83 225.94 251.40 271.93 289.23 317.58 340.49 384.39

Sat. Liquid hf

2258.0 2241.0 2226.5 2213.6 2201.9 2191.3

2501.3 2484.9 2470.6 2460.0 2451.6 2444.5 2432.9 2423.7 2406.0 2392.8 2373.1 2358.3 2346.3 2336.1 2319.2 2305.4 2278.6

Evap. hfg

Enthalpy (kJ/kg)

2675.5 2685.4 2693.6 2700.6 2706.7 2712.1

2501.4 2514.2 2525.3 2533.5 2540.0 2545.5 2554.4 2561.5 2574.8 2584.7 2599.1 2609.7 2618.2 2625.3 2636.8 2645.9 2663.0

Sat. Vapor hg

1.3026 1.3740 1.4336 1.4849 1.5301 1.5706

.0000 .1059 .1957 .2607 .3120 .3545 .4226 .4764 .5764 .6493 .7549 .8320 .8931 .9439 1.0259 1.0910 1.2130

Sat. Liquid sf

6.0568 5.9104 5.7897 5.6868 5.5970 5.5173

9.1562 8.8697 8.6322 8.4629 8.3311 8.2231 8.0520 7.9187 7.6750 7.5009 7.2536 7.0766 6.9383 6.8247 6.6441 6.5029 6.2434

Evap. sfg

7.3594 7.2844 7.2233 7.1717 7.1271 7.0878

9.1562 8.9756 8.8279 8.7237 8.6432 8.5776 8.4746 8.3951 8.2515 8.1502 8.0085 7.9085 7.8314 7.7686 7.6700 7.5939 7.4564

Sat. Vapor sg

Entropy (kJ/kg. K)

644 Appendix 2

0.250 0.275 0.300 0.325 0.350 0.375 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.75 2.00 2.25 2.5 3.0 3.5 4

127.44 130.60 133.55 136.30 138.88 141.32 143.63 147.93 151.86 155.48 158.85 162.01 164.97 167.78 170.43 172.96 175.38 177.69 179.91 184.09 187.99 191.64 195.07 198.32 205.76 212.42 218.45 223.99 233.90 242.60 250.40

0.001 067 0.001 070 0.001 073 0.001 076 0.001 079 0.001 081 0.001 084 0.001 088 0.001 093 0.001 097 0.001 101 0.001 104 0.001 108 0.001 112 0.001 115 0.001 118 0.001 121 0.001 124 0.001 127 0.001 133 0.001 139 0.001 144 0.001 149 0.001 154 0.001 166 0.001 177 0.001 187 0.001 197 0.001 217 0.001 235 0.001 252

0.7187 0.6573 0.6058 0.5620 0.5243 0.4914 0.4625 0.4140 0.3749 0.3427 0.3157 0.2927 0.2729 0.2556 0.2404 0.2270 0.2150 0.2042 0.194 44 0.177 53 0.163 33 0.151 25 0.140 84 0.131 77 0.113 49 0.099 63 0.088 75 0.079 98 0.066 68 0.057 07 0.049 78

535.10 548.59 561.15 572.90 583.95 594.40 604.31 622.77 639.68 655.32 669.90 683.56 696.44 708.64 720.22 731.27 741.83 751.95 761.68 780.09 797.29 813.44 828.70 843.16 876.46 906.44 933.83 959.11 1004.78 1045.43 1082.31

2002.1 1991.9 1982.4 1973.5 1965.0 1956.9 1949.3 1934.9 1921.6 1909.2 1897.5 1886.5 1876.1 1866.1 1856.6 1847.4 1838.6 1830.2 1822.0 1806.3 1791.5 1777.5 1764.1 1751.3 1721.4 1693.8 1668.2 1644.0 1599.3 1558.3 1520.0

2537.2 2540.5 2543.6 2546.4 2548.9 2551.3 2553.6 2557.6 2561.2 2564.5 2567.4 2570.1 2572.5 2574.7 2576.8 2578.7 2580.5 2582.1 2583.6 2586.4 2588.8 2591.0 2592.8 2594.5 2597.8 2600.3 2602.0 2603.1 2604.1 2603.7 2602.3

535.37 548.89 561.47 573.25 584.33 594.81 604.74 623.25 640.23 655.93 670.56 684.28 697.22 709.47 721.11 732.22 742.83 753.02 762.81 781.34 798.65 814.93 830.30 844.89 878.50 908.79 936.49 962.11 1008.42 1049.75 1087.31

2181.5 2172.4 2163.8 2155.8 2148.1 2140.8 2133.8 2120.7 2108.5 2097.0 2086.3 2076.0 2066.3 2057.0 2048.0 2039.4 2031.1 2023.1 2015.3 2000.4 1986.2 1972.7 1959.7 1947.3 1917.9 1890.7 1865.2 1841.0 1795.7 1753.7 1714.1

2716.9 2721.3 2725.3 2729.0 2732.4 2735.6 2738.6 2743.9 2748.7 2753.0 2756.8 2760.3 2763.5 2766.4 2769.1 2771.6 2773.9 2776.1 2778.1 2781.7 2784.8 2787.6 2790.0 2792.2 2796.4 2799.5 2801.7 2803.1 2804.2 2803.4 2801.4

1.6072 1.6408 1.6718 1.7006 1.7275 1.7528 1.7766 1.8207 1.8607 1.8973 1.9312 1.9627 1.9922 2.0200 2.0462 2.0710 2.0946 2.1172 2.1387 2.1792 2.2166 2.2515 2.2842 2.3150 2.3851 2.4474 2.5035 2.5547 2.6457 2.7253 2.7964

5.4455 5.3801 5.3201 5.2646 5.2130 5.1647 5.1193 5.0359 4.9606 4.8920 4.8288 4.7703 4.7158 4.6647 4.6166 4.5711 4.5280 4.4869 4.4478 4.3744 4.3067 4.2438 4.1850 4.1298 4.0044 3.8935 3.7937 3.7028 3.5412 3.4000 3.2737

7.0527 7.0209 6.9919 6.9652 6.9405 6.9175 6.8959 6.8565 6.8213 6.7893 6.7600 6.7331 6.7080 6.6847 6.6628 6.6421 6.6226 6.6041 6.5865 6.5536 6.5233 6.4953 6.4693 6.4448 6.3896 6.3409 6.2972 6.2575 6.1869 6.1253 6.0701 (continued)

Appendix 2 645

Temp. °C T

263.99 275.64 285.88 295.06 303.40 311.06 318.15 324.75 330.93 336.75 342.24 347.44 352.37 357.06 361.54 365.81 369.89 373.80 374.14

Press. MPa P

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 22.09

0.001 286 0.001 319 0.001 351 0.001 384 0.001 418 0.001 452 0.001 489 0.001 527 0.001 567 0.001 611 0.001 658 0.001 711 0.001 770 0.001 840 0.001 924 0.002 036 0.002 207 0.002 742 0.003 155

Sat. Liquid vf

0.039 44 0.032 44 0.027 37 0.023 52 0.020 48 0.018 026 0.015 987 0.014 263 0.012 780 0.011 485 0.010 337 0.009 306 0.008 364 0.007 489 0.006 657 0.005 834 0.004 952 0.003 568 0.003 155

Sat. Vapor vg

Specific Volume (m3/ kg)

Saturation Pressures (Steam)

TABLE A.2 (SI) (Continued)

1147.81 1205.44 1257.55 1305.57 1350.51 1393.04 1433.7 1473.0 1511.1 1548.6 1585.6 1622.7 1660.2 1698.9 1739.9 1785.6 1842.1 1961.9 2029.6

Sat. Liquid uf 1449.3 1384.3 1323.0 1264.2 1207.3 1151.4 1096.0 1040.7 985.0 928.2 869.8 809.0 744.8 675.4 598.1 507.5 388.5 125.2 0

Evap. ufg 2597.1 2589.7 2580.5 2569.8 2557.8 2544.4 2529.8 2513.7 2496.1 2476.8 2455.5 2431.7 2405.0 2374.3 2338.1 2293.0 2230.6 2087.1 2029.6

Sat. Vapor ug

Internal Energy (kJ/kg)

1154.23 1213.35 1267.00 1316.64 1363.26 1407.56 1450.1 1491.3 1531.5 1571.1 1610.5 1650.1 1690.3 1732.0 1776.5 1826.3 1888.4 2022.2 2099.3

Sat. Liquid hf 1640.1 1571.0 1505.1 1441.3 1378.9 1317.1 1255.5 1193.6 1130.7 1066.5 1000.0 930.6 856.9 777.1 688.0 583.4 446.2 143.4 0

Evap. hfg

Enthalpy (kJ/kg)

2794.3 2784.3 2772.1 2758.0 2742.1 2724.7 2705.6 2684.9 2662.2 2637.6 2610.5 2580.6 2547.2 2509.1 2464.5 2409.7 2334.6 2165.6 2099.3

Sat. Vapor hg 2.9202 3.0267 3.1211 3.2068 3.2858 3.3596 3.4295 3.4962 3.5606 3.6232 3.6848 3,7461 3.8079 3.8715 3.9388 4.0139 4.1075 4.3110 4.4298

Sat. Liquid sf

3.0532 2.8625 2.6922 2.5364 2.3915 2.2544 2.1233 1.9962 1.8718 1.7485 1.6249 1.4994 1.3698 1.2329 1.0839 .9130 .6938 .2216 0

Evap. sfg

Entropy (kJ/kg. K)

5.9734 5.8892 5.8133 5.7432 5.6772 5.6141 5.5527 5.4924 5.4323 5.3717 5.3098 5.2455 5.1777 5.1044 5.0228 4.9269 4.8013 4.5327 4.4298

Sat. Vapor sg

646 Appendix 2

14.674 14.869 17.196 19.512 21.825 24.136 26.445 31.063 35.679 40.295 44.911 49.526 54.141 58.757 63.372 67.987 72.602

.8857 .9596 1.0803 1.1988 1.3162 1.5493 1.7814 2.013 2.244

Sat. 150 200 250 300 400 500 600 700

v

Sat. 50 100 150 200 250 300 400 500 600 700 800 900 1000 1100 1200 1300

T

2529.5 2576.9 2654.4 2731.2 2808.6 2966.7 3130.8 3301.4 3478.8

h

2584.7 2592.6 2687.5 2783.0 2879.5 2977.3 3076.5 3279.6 3489.1 3705.4 3928.7 4159.0 4396.4 4640.6 4891.2 5147.8 5409.7

2706.7 2768.8 2870.5 2971.0 3071.8 3276.6 3487.1 3704.0 3927.6

Ρ = .20 MPa (120.23)

2437.9 2443.9 2515.5 2587.9 2661.3 2736.0 2812.1 2968.9 3132.3 3302.5 3479.6 3663.8 3855.0 4053.0 4257.5 4467.9 4683.7

u

Ρ = .010 MPa (45.81)

Properties of Superheated Steam

TABLE A.3 (SI)

7.1272 7.2795 7.5066 7.7086 7.8926 8.2218 8.5133 8.7770 9.0194

8.1502 8.1749 8.4479 8.6882 8.9038 9.1002 9.2813 9.6077 9.8978 10.1608 10.4028 10.6281 10.8396 11.0393 11.2287 11.4091 11.5811

s

.6058 .6339 .7163 .7964 .8753 1.0315 1.1867 1.3414 1.4957

2511.6 2585.6 2659.9 2735.0 2811.3 2968.5 3132.0 3302.2 3479.4 3663.6 3854.9 4052.9 4257.4 4467.8 4683.6

3.418 3.889 4.356 4.820 5.284 6.209 7.134 8.057 8.981 9.904 10.828 11.751 12.674 13.597 14.521

2682.5 2780.1 2877.7 2976.0 3075.5 3278.9 3488.7 3705.1 3928.5 4158.9 4396.3 4640.5 4891.1 5147.7 5409.6

2645.9

h

2543.6 2570.8 2650.7 2728.7 2806.7 2965.6 3130.0 3300.8 3478.4

2725.3 2761.0 2865.6 2967.6 3069.3 3275.0 3486.0 3703.2 3927.1

Ρ = .30 MPa (133.55)

2483.9

u

3.240

v

Ρ = .050 MPa (81.33)

6.9919 7.0778 7.3115 7.5166 7.7022 8.0330 8.3251 8.5892 8.8319

7.6947 7.9401 8.1580 8.3556 8.5373 8.8642 9.1546 9.4178 9.6599 9.8852 10.0967 10.2964 10.4859 10.6662 10.8382

7.5939

s

.4625 .4708 .5342 .5951 .6548 .7726 .8893 1.0055 1.1215

1.6958 1.9364 2.172 2.406 2.639 3.103 3.565 4.028 4.490 4.952 5.414 5.875 6.337 6.799 7.260

1.6940

v

2676.2 2776.4 2875.3 2974.3 3074.3 3278.2 3488.1 3704.7 3928.2 4158.6 4396.1 4640.3 4891.0 5147.6 5409.5

2675.5

h

2553.6 2564.5 2646.8 2726.1 2804.8 2964.4 3129.2 3300.2 3477.9

2738.6 2752.8 2860.5 2964.2 3066.8 3273.4 3484.9 3702.4 3926.5

Ρ = .40 MPa (143.63)

2506.7 2582.8 2658.1 2733.7 2810.4 2967.9 3131.6 3301.9 3479.2 3663.5 3854.8 4052.8 4257.3 4467.7 4683.5

2506.1

u

Ρ = .10 MPa (99.63)

6.8959 6.9299 7.1706 7.3789 7.5662 7.8985 8.1913 8.4558 8.6987 (continued)

7.3614 7.6134 7.8343 8.0333 8.2158 8.5435 8.8342 9.0976 9.3398 9.5652 9.7767 9.9764 10.1659 10.3463 10.5183

7.3594

s

Appendix 2 647

2.475 2.706 2.937 3.168 3.399 3.630

.3749 .4249 .4744 .5226 .5701 .6173 .7109 .8041 .8969 .9896 1.0822 1.1747 1.2672 1.3596 1.4521

.194 44 .2060 .2327

Sat. 200 250 300 350 400 500 600 700 800 900 1000 1100 1200 1300

Sat. 200 250

v

800 900 1000 1100 1200 1300

T

4158.2 4395.8 4640.0 4890.7 5147.3 5409.3

h

2748.7 2855.4 2960.7 3064.2 3167.7 3271.9 3483.9 3701.7 3925.9 4156.9 4394.7 4639.1 4889.9 5146.6 5408.6

2583.6 2621.9 2709.9

2778.1 2827.9 2942.6

Ρ = 1.00 MPa (179.91)

2561.2 2642.9 2723.5 2802.9 2882.6 2963.2 3128.4 3299.6 3477.5 3662.1 3853.6 4051.8 4256.3 4466.8 4682.5

Ρ = .50 MPa (151.86)

3663.1 3854.5 4052.5 4257.0 4467.5 4683.2

u

Ρ = .010 MPa (45.81)

Properties of Superheated Steam

TABLE A.3 (SI) (Continued)

6.5865 6.6940 6.9247

6.8213 7.0592 7.2709 7.4599 7.6329 7.7938 8.0873 7.3522 8.5952 8.8211 9.0329 9.2328 9.4224 9.6029 9.7749

9.2449 9.4566 9.6563 9.8458 10.0262 10.1982

s

.163 33 .169 30 .192 34

.3157 .3520 .3938 .4344 .4742 .5137 .5920 .6697 .7472 .8245 .9017 .9788 1.0559 1.1330 1.2101

1.6499 1.8041 1.9581 2.1121 2.2661 2.4201

v 4157.8 4395.4 4639.7 4890.4 5147.1 5409.0

h

2756.8 2850.1 2957.2 3061.6 3165.7 3270.3 3482.8 3700.9 3925.3 4156.5 4394.4 4638.8 4889.6 5146.3 5408.3

2588.8 2612.8 2704.2

2784.8 2815.9 2935.0

Ρ = 1.20 MPa (187.99)

2567.4 2638.9 2720.9 2801.0 2881.2 2962.1 3127.6 3299.1 3477.0 3661.8 3853.4 4051.5 4256.1 4466.5 4682.3

Ρ = .60 MPa (158.85)

3662.9 3854.2 4052.3 4256.8 4467.2 4683.0

u

Ρ = .050 MPa (81.33)

6.5233 6.5898 6.8294

6.7600 6.9665 7.1816 7.3724 7.5464 7.7079 8.0021 8.2674 8.5107 8.7367 8.9486 9.1485 9.3381 9.5185 9.6906

9.0576 9.2692 9.4690 9.6585 9.8389 10.0110

s

.140 84 .143 02 .163 50

.2404 .2608 .2931 .3241 .3544 .3843 .4433 .5018 .5601 .6181 .6761 .7340 .7919 .8497 .9076

1.2372 1.3529 1.4685 1.5840 1.6996 1.8151

v 4157.3 4395.1 4639.4 4890.2 5146.8 5408.8

h

2769.1 2839.3 2950.0 3056.5 3161.7 3267.1 3480.6 3699.4 3924.2 4155.6 4393.7 4638.2 4889.1 5145.9 5407.9

2592.8 2603.1 2698.3

2790.0 2803.3 2927.2

Ρ = 1.40 MPa (195.07)

2576.8 2630.6 2715.5 2797.2 2878.2 2959.7 3126.0 3297.9 3476.2 3661.1 3852.8 4051.0 4255.6 4466.1 4681.8

Ρ = .80 MPa (170.43)

3662.4 3853.9 4052.0 4256.5 4467.0 4682.8

u

Ρ = .10 MPa (99.63)

6.4693 6.4975 6.7467

6.6628 6.8158 7.0384 7.2328 7.4089 7.5716 7.8673 8.1333 8.3770 8.6033 8.8153 9.0153 9.2050 9.3855 9.5575

8.9244 9.1362 9.3360 9.5256 9.7060 9.8780

s

648 Appendix 2

.2579 .2825 .3066 .3541 .4011 .4478 .4943 .5407 .5871 .6335 .6798 .7261

.123 80 .132 87 .141 84 .158 62 .174 56 .190 05 .2203 .2500 .2794

.3086 .3377 .3668 .3958 .4248 .4538

300 350 400 500 600 700 800 900 1000 1100 1200 1300

Sat. 225 250 300 350 400 500 600 700

800 900 1000 1100 1200 1300

3051.2 3157.7 3263.9 3478.5 3697.9 3923.1 4154.7 4392.9 4637.6 4888.6 5145.4 5407.4

2794.0 2857.3 2919.2 3034.8 3145.4 3254.2 3472.0 3693.2 3919.7

3658.3 3850.5 4049.0 4253.7 4464.2 4679.9

4152.1 4390.8 4635.8 4887.0 5143.9 5406.0

Ρ = 1.60 MPa (201.41)

2596.0 2644.7 2692.3 2781.1 2866.1 2950.1 3119.5 3293.3 3472.7

Ρ = 1.60 MPa (201.41)

2793.2 2875.2 2957.3 3124.4 3296.8 3475.3 3660.4 3852.2 4050.5 4255.1 4465.6 4681.3

8.2808 8.4935 8.6938 8.8837 9.0643 9.2364

6.4218 6.5518 6.6732 6.8844 7.0694 7.2374 7.5390 7.8080 8.0535

7.1229 7.3011 7.4651 7.7622 8.0290 8.2731 8.4996 8.7118 8.9119 9.1017 9.2822 9.4543

.2742 .3001 .3260 .3518 .3776 .4034

.11042 .116 73 .124 97 .140 21 .154 57 .168 47 .195 50 .2220 .2482

.2138 .2345 .2548 .2946 .3339 .3729 .4118 .4505 .4892 .5278 .5665 .6051

3045.8 3153.6 3260.7 3476.3 3696.3 3922.0 4153.8 4392.2 4637.0 4888.0 5144.9 5407.0

2797.1 2846.7 2911.0 3029.2 3141.2 3250.9 3469.8 3691.7 3918.5

3657.6 3849.9 4048.5 4253.2 4463.7 4679.5

4151.2 4390.1 4635.2 4886.4 5143.4 5405.6

Ρ = 1.80 MPa (207.15)

2598.4 2636.6 2686.0 2776.9 2863.0 2947.7 3117.9 3292.1 3471.8

Ρ = 1.80 MPa (207.15)

2789.2 2872.2 2954.9 3122.8 3295.6 3474.4 3659.7 3851.6 4050.0 4254.6 4465.1 4680.9

8.2258 8.4386 8.6391 8.8290 9.0096 9.1818

6.3794 6.4808 6.6066 6.8226 7.0100 7.1794 7.4825 7.7523 7.9983

7.0317 7.2121 7.3774 7.6759 7.9435 8.1881 8.4148 8.6272 8.8274 9.0172 9.1977 9.3698

.2467 .2700 .2933 .3166 .3398 .3631

.099 63 .103 77 .111 44 .125 47 .138 57 .151 20 .175 68 .199 60 .2232

.182 28 .2003 .2178 .2521 .2860 .3195 .3528 .3861 .4192 .4524 .4855 .5186

3040.4 3149.5 3257.5 3474.1 3694.8 3920.8 4153.0 4391.5 4636.4 4887.5 5144.4 5406.5

2799.5 2835.8 2902.5 3023.5 3137.0 3247.6 3467.6 3690.1 3917.4

3657.0 3849.3 4048.0 4252.7 4463.3 4679.0

4150.3 4389.4 4634.6 4885.9 5142.9 5405.1

Ρ = 2.00 MPa (212.42)

2600.3 2628.3 2679.6 2772.6 2859.8 2945.2 31162 3290.9 3470.9

Ρ = 2.00 MPa (212.42)

2785.2 2869.2 2952.5 3121.1 3294.4 3473.6 3659.0 3851.1 4049.5 4254.1 4464.7 4680.4

8.1765 8.3895 8.5901 8.7800 8.9607 9.1329 (continued)

6.3409 6.4147 6.5453 6.7664 6.9563 7.1271 7.4317 7.7024 7.9487

6.9534 7.1360 7.3026 7.6027 7.8710 8.1160 8.3431 8.5556 8.7559 8.9457 9.1262 9.2984

Appendix 2 649

.079 98 .080 27 .087 00 .098 90 .109 76 .120 10 .130 14 .139 98 .159 30 .178 32 .197 16 .215 90 .2346 .2532 .2718 .2905

.049 78 .054 57 .058 84 .066 45 .073 41 .080 02 .086 43 .098 85 .11095 .122 87 .134 69

Sat. 275 300 350 400 450 500 600 700 800 900

v

Sat. 225 250 300 350 400 450 500 600 700 800 900 1000 1100 1200 1300

T

2803.1 2806.3 2880.1 3008.8 3126.3 3239.3 3350.8 3462.1 3686.3 3914.5 4148.2 4387.6 4633.1 4884.6 5141.7 5404.0

h

2602.3 2667.9 2725.3 2826.7 2919.9 3010.2 3099.5 3279.1 3462.1 3650.0 3843.6

2801.4 2886.2 2960.7 3092.5 3213.6 3330.3 3445.3 3674.4 3905.9 4141.5 4382.3

Ρ = 4.0 MPa (250.40)

2603.1 2605.6 2662.6 2761.6 2851.9 2939.1 3025.5 3112.1 3288.0 3468.7 3655.3 3847.9 4046.7 4251.5 4462.1 4677.8

u

Ρ = 2.50 MPa (223.99)

Properties of Superheated Steam

TABLE A.3 (SI) (Continued)

6.0701 6.2285 6.3615 6.5821 6.7690 6.9363 7.0901 7.3688 7.6198 7.8502 8.0647

6.2575 6.2639 6.4085 6.6438 6.8403 7.0148 7.1746 7.3234 7.5960 7.8435 8.0720 8.2853 8.4861 8.6762 8.8569 9.0291

s

.044 06 .047 30 .051 35 .058 40 .064 75 .070 74 .076 51 .087 65 .098 47 .109 11 .119 65

2644.0 2750.1 2843.7 2932.8 3020.4 3108.0 3285.0 3466.5 3653.5 3846.5 4045.4 4250.3 4460.9 4676.6

.070 58 .081 14 .090 53 .099 36 .107 87 .116 19 .132 43 .148 38 .164 14 .179 80 .195 41 .210 98 .226 52 .242 06

2855.8 2993.5 3115.3 3230.9 3344.0 3456.5 3682.3 3911.7 4145.9 4385.9 4631.6 4883.3 5140.5 5402.8

2804.2

h

2600.1 2650.3 2712.0 2817.8 2913.3 3005.0 3095.3 3276.0 3459.9 3648.3 3842.2

2798.3 2863.2 2943.1 3080.6 3204.7 3323.3 3439.6 3670.5 3903.0 4139.3 4380.6

Ρ = 4.5 MPa (257.49)

2604.1

u

.066 68

v

Ρ = 3.00 MPa (233.90)

6.0198 6.1401 6.2828 6.5131 6.7047 6.8746 7.0301 7.3110 7.5631 7.7942 8.0091

6.2872 6.5390 6.7428 6.9212 7.0834 7.2338 7.5085 7.7571 7.9862 8.1999 8.4009 8.5912 8.7720 8.9442

6.1869

s

.039 44 .041 41 .045 32 .051 94 .057 81 .063 30 .068 57 .078 69 .088 49 .098 11 .107 62

.058 72 .068 42 .076 78 .084 53 .091 96 .099 18 .113 24 .126 99 .140 56 .154 02 .167 43 .180 80 .194 15 .207 49

.057 07

v

2829.2 2977.5 3104.0 3222.3 3337.2 3450.9 3678.4 3908.8 4143.7 4384.1 4630.1 4881.9 5139.3 5401.7

2803.4

h

2597.1 2631.3 2698.0 2808.7 2906.6 2999.7 3091.0 3273.0 3457.6 3646.6 3840.7

2794.3 2838.3 2924.5 3068.4 3195.7 3316.2 3433.8 3666.5 3900.1 4137.1 4378.8

Ρ = 5.0 MPa (263.99)

2623.7 2738.0 2835.3 2926.4 3015.3 3103.0 3282.1 3464.3 3651.8 3845.0 4044.1 4249,2 4459.8 4675.5

2603.7

u

Ρ = 3.50 MPa (242.60)

5.9734 6.0544 6.2084 6.4493 6.6459 6.8186 6.9759 7.2589 7.5122 7.7440 7.9593

6.1749 6.4461 6.6579 6.8405 7.0052 7.1572 7.4339 7.6837 7.9134 8.1276 8.3288 8.5192 8.7000 8.8723

6.1253

s

650 Appendix 2

.146 45 .158 17 .169 87 .181 56

.032 44 .036 16 .042 23 .047 39 .052 14 .056 65 .061 01 .065 25 .073 52 .081 60 .089 58 .097 49 .105 36 .113 21 .121 06

.020 48 .023 27 .025 80 .029 93 .033 50 .036 77 .039 87 .042 85 .045 74

1000 1100 1200 1300

Sat. 300 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300

Sat. 325 350 400 450 500 550 600 650

4628.7 4880.6 5138.1 5400.5

2784.3 2884.2 3043.0 3177.2 3301.8 3422.2 3540.6 3658.4 3894.2 4132.7 4375.3 4622.7 4875.4 5133.3 5396.0

2557.8 2646.6 2724.4 2848.4 2955.2 3055.2 3152.2 3248.1 3343.6

2742.1 2856.0 2956.6 3117.8 3256.6 3386.1 3511.0 3633.7 3755.3

Ρ = 9.0 MPa (303.40)

2589.7 2667.2 2789.6 2892.9 2988.9 3082.2 3174.6 3266.9 3453.1 3643.1 3837.8 4037.8 4243.3 4454.0 4669.6

Ρ = 6.0 MPa (275.64)

4042.9 4248.0 4458.6 4674.3

5.6772 5.8712 6.0361 6.2854 6.4844 6.6576 6.8142 6.9589 7.0943

5.8892 6.0674 6.3335 6.5408 6.7193 6.8803 7.0288 7.1677 7.4234 7.6566 7.8727 8.0751 8.2661 8.4474 8.6199

8.2662 8.4567 8.6376 8.8100

.018 026 .019 861 .022 42 .026 41 .029 75 .032 79 .035 64 .038 37 .041 01

.027 37 .029 47 .035 24 .039 93 .044 16 .048 14 .051 95 .055 65 .062 83 .069 81 .076 69 .083 50 .090 27 .097 03 .103 77

.130 13 .140 56 .150 98 .161 39

4627.2 4879.3 5136.9 5399.4

2772.1 2838.4 3016.0 3158.1 3287.1 3410.3 3530.9 3650.3 3888.3 4128.2 4371.8 4619.8 4872.8 5130.9 5393.7

2544.4 2610.4 2699.2 2832.4 2943.4 3045.8 3144.6 3241.7 3338.2

2724.7 2809.1 2923.4 3096.5 3240.9 3373.7 3500.9 3625.3 3748.2

Ρ = 10.0 MPa (311.06)

2580.5 2632.2 2769.4 2878.6 2978.0 3073.4 3167.2 3260.7 3448.5 3639.5 3835.0 4035.3 4240.9 4451.7 4667.3

Ρ = 7.0 MPa (285.88)

4041.6 4246.8 4457.5 4673.1

5.6141 5.7568 5.9443 6.2120 6.4190 6.5966 6.7561 6.9029 7.0398

5.8133 5.9305 6.2283 6.4478 6.6327 6.7975 6.9486 7.0894 7.3476 7.5822 7.7991 8.0020 8.1933 8.3747 8.5473

8.2108 8.4015 8.5825 8.7549

4625.7 4878.0 5135.7 5398.2

2758.0 2785.0 2987.3 3138.3 3272.0 3398.3 3521.0 3642.0 3882.4 4123.8 4368.3 4616.9 4870.3 5128.5 5391.5

2505.1 2624.6 2789.3 2912.5 3021.7 3125.0 3225.4 3324.4

.016 126 .020 00 .022 99 .025 60 .028 01 .030 29 .032 48

2826.2 3039.3 3199.8 3341.8 3475.2 3604.0 3730.4

2673.8

Ρ = 12.5 MPa (327.89)

2569.8 2590.9 2747.7 2863.8 2966.7 3064.3 3159.8 3254.4 3443.9 3636.0 3832.1 4032.8 4238.6 4449.5 4665.0

Ρ = 8.0 MPa (295.06)

4040.4 4245.6 4456.3 4672.0

.013 495

.023 52 .024 26 .029 95 .034 32 .038 17 .041 75 .045 16 .048 45 .054 81 .060 97 .067 02 .073 01 .078 96 .084 89 .090 80

.117 07 .126 48 .135 87 .145 26

5.7118 6.0417 6.2719 6.4618 6.6290 6.7810 6.9218 (continued)

5.4624

5.7432 5.7906 6.1301 6.3634 6.5551 6.7240 6.8778 7.0206 7.2812 7.5173 7.7351 7.9384 8.1300 8.3115 8.4842

8.1612 8.3520 8.5331 8.7055

Appendix 2 651

.010 337 .011 470 .015 649 .018 445 .020 80 .022 93 .024 91 .026 80 .028 61 .032 10 .035 46 .038 75 .042 00 .045 23 .048 45

.001 973 1 .006 004

Sat. 350 400 450 500 550 600 650 700 800 900 1000 1100 1200 1300

375 400

v

.048 57 .054 09 .059 50 .064 85 .070 16 .075 44 .080 72

700 800 900 1000 1100 1200 1300

T

h

3876.5 4119.3 4364.8 4614.0 4867.7 5126.2 5389.2

2610.5 2692.4 2975.5 3156.2 3308.6 3448.6 3582.3 3712.3 3840.1 4092.4 4343.8 4596.6 4852.6 5112.3 5376.0

1798.7 2430.1

1848.0 2580.2

Ρ = 25.0 MPa

2455.5 2520.4 2740.7 2879.5 2996.6 3104.7 3208.6 3310.3 3410.9 3610.9 3811.9 4015.4 4222.6 4433.8 4649.1

Ρ = 15.0 MPa (342.24)

3439.3 3632.5 3829.2 4030.3 4236.3 4447.2 4662.7

u

Ρ = 9.0 MPa (303.40)

Properties of Superheated Steam

TABLE A.3 (SI) (Continued)

s

4.0320 5.1418

5.3098 5.4421 5.8811 6.1404 6.3443 6.5199 6.6776 6.8224 6.9572 7.2040 7.4279 7.6348 7.8283 8.0108 8.1840

7.2221 7.4596 7.6783 7.8821 8.0740 8.2556 8.4284

v

u

2685.0 2844.2 2970.3 3083.9 3191.5 3296.0 3398.7 3601.8 3804.7 4009.3 4216.9 4428.3 4643.5

.012 447 .015 174 .017 358 .019 288 .021 06 .022 74 .024 34 .027 38 .030 31 .033 16 .035 97 .038 76 .041 54

2902.9 3109.7 3274.1 3421.4 3560.1 3693.9 3824.6 4081.1 4335.1 4589.5 4846.4 5106.6 5370.5

2528.8

1737.8 2067.4

1791.5 2151.1

Ρ = 30.0 MPa

2390.2

.001 789 2 .002 790

h 3870.5 4114.8 4361.2 4611.0 4865.1 5123.8 5387.0

Ρ = 17.5 MPa (354.75)

3434.7 3628.9 3826.3 4027.8 4234.0 4444.9 4460.5

.007 920

.043 58 .048 59 .053 49 .058 32 .063 12 .067 89 .072 65

Ρ = 10.0 MPa (311.06) s

3.9305 4.4728

5.7213 6.0184 6.2383 6.4230 6.5866 6.7357 6.8736 7.1244 7.3507 7.5589 7.7531 7.9360 8.1093

5.1419

7.1687 7.4077 7.6272 7.8315 8.0237 8.2055 8.3783

v

.001 700 3 .002 100

.009 942 .012 695 .014 768 .016 555 .018 178 .019 693 .021 13 .023 85 .026 45 .028 97 .031 45 .033 91 .036 36

.005 834

.034 60 .038 69 .042 67 .046 58 .050 45 .054 30 .058 13

h 3855.3 4103.6 4352.5 4603.8 4858.8 5118.0 5381.4

2818.1 3060.1 3238.2 3393.5 3537.6 3675.3 3809.0 4069.7 4326.4 4582.5 4840.2 5101.0 5365.1

2409.7

1702.9 1914.1

1762.4 1987.6

Ρ = 35.0 MPa

2619.3 2806.2 2942.9 3062.4 3174.0 3281.4 3386.4 3592.7 3797.5 4003.1 4211.3 4422.8 4638.0

2293.0

Ρ = 20.0 MPa (365.81)

3422.9 3620.0 3819.1 4021.6 4228.2 4439.3 4654.8

u

Ρ = 12.5 MPa (327.89) s

3.8722 4.2126

5.5540 5.9017 6.1401 6.3348 6.5048 6.6582 6.7993 7.0544 7.2830 7.4925 7.6874 7.8707 8.0442

4.9269

7.0536 7.2965 7.5182 7.7237 7.9165 8.0987 8.2717

652 Appendix 2

.007 881 .009 162 .011 123 .012 724 .014 137 .015 433 .016 646 .018912 .021 045 .023 10 .025 12 .027 11 .029 10

.001 640 7 .001 907 7 .002 532 .003 693 .005 622 .006 984 .008 094 .009 063 .009 941 .011 523 .012 962 .014 324 .015 642 .016 940 .018 229

425 450 500 550 600 650 700 800 900 1000 1100 1200 1300

375 400 425 450 500 550 600 650 700 800 900 1000 1100 1200 1300

2806.3 2949.7 3162.4 3335.6 3491.4 3637.4 3777.5 4047.1 4309.1 4568.5 4828.2 5089.9 5354.4

1677.1 1854.6 2096.9 2365.1 2678.4 2869.7 3022.6 3158.0 3283.6 3517.8 3739.4 3954.6 4167.4 4380.1 4594.3

1742.8 1930.9 2198.1 2512.8 2903.3 3149.1 3346.4 3520.6 3681.2 3978.7 4257.9 4527.6 4793.1 5057.7 5323.5

Ρ = 40.0 MPa

2609.2 2720.7 2884.3 3017.5 3137.9 3251.6 3361.3 3574.3 3783.0 3990.9 4200.2 4412.0 4626.9

3.8290 4.1135 4.5029 4.9459 5.4700 5.7785 6.0114 6.2054 6.3750 6.6662 6.9150 7.1356 7.3364 7.5224 7.6969

5.4723 5.6744 5.9592 6.1765 6.3602 6.5229 6.6707 6.9345 7.1680 7.3802 7.5765 7.7605 7.9342

.001 559 4 .001 730 9 .002 007 .002 486 .003 892 .005 118 .006 112 .006 966 .007 727 .009 076 .010 283 .011 411 .012 496 .013 561 .014 616

.005 303 .006 735 .008 678 .010 168 .011 446 .012 596 .013 661 .015 623 .017 448 .019 196 .020 903 .022 589 .024 266

2614.2 2821.4 3081.1 3275.4 3443.9 3598.9 3745.6 4024.2 4291.9 4554.7 4816.3 5079.0 5344.0

1638.6 1788.1 1959.7 2159.6 2525.5 2763.6 2942.0 3093.5 3230.5 3479.8 3710.3 3930.5 4145.7 4359.1 4572.8

1716.6 1874.6 2060.0 2284.0 2720.1 3019.5 3247.6 3441.8 3616.8 3933.6 4224.4 4501.1 4770.5 5037.2 5303.6

Ρ = 50.0 MPa

2455.1 2619.3 2820.7 2970.3 3100.5 3221.0 3335.8 3555.5 3768.5 3978.8 4189.2 4401.3 4616.0

3.7639 4.0031 4.2734 4.5884 5.1726 5.5485 5.8178 6.0342 6.2189 6.5290 6.7882 7.0146 7.2184 7.4058 7.5808

5.1504 5.4424 5.7905 6.0342 6.2331 6.4058 6.5606 6.8332 7.0718 7.2867 7.4845 7.6692 7.8432

.001 502 8 .001 633 5 .001 816 5 .002 085 .002 956 .003 956 .004 834 .005 595 .006 272 .007 459 .008 508 .009 480 .010 409 .011 317 .012 215

.003 428 .004 961 .006 927 .008 345 .009 527 .010 575 .011 533 .013 278 .014 883 .016 410 .017 895 .019 360 .020 815

2373.4 2672.4 2994.4 3213.0 3395.5 3559.9 3713.5 4001.5 4274.9 4541.1 4804.6 5068.3 5333.6

1609.4 1745.4 1892.7 2053.9 2390.6 2658.8 2861.1 3028.8 3177.2 3441.5 3681.0 3906.4 4124.1 4338.2 4551.4

1699.5 1843.4 2001.7 2179.0 2567.9 2896.2 3151.2 3364.5 3553.5 3889.1 4191.5 4475.2 4748.6 5017.2 5284.3

Ρ = 60.0 MPa

2253.4 2498.7 2751.9 2921.0 3062.0 3189.8 3309.8 3536.7 3754.0 3966.7 4178.3 4390.7 4605.1

3.7141 3.9318 4.1626 4.4121 4.9321 5.3441 5.6452 5.8829 6.0824 6.4109 6.6805 6.9127 7.1195 7.3083 7.4837

4.7747 5.1962 5.6282 5.9026 6.1179 6.3010 6.4631 6.7450 6.9886 7.2064 7.4057 7.5910 7.7653

Appendix 2 653

v

.001 285 9 .000 997 7 .000 999 5 .001 005 6 .001 014 9 .001 026 8 .001 041 0 .001 057 6 .001 076 8 .001 098 8 .001 124 0 .001 153 0 .001 186 6 .001 226 4 .001 274 9

T

Sat. 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

1147.8 .04 83.65 166.95 250.23 333.72 417.52 501.80 586.76 672.62 759.63 848.1 938.4 1031.4 1127.9

u

1154.2 5.04 88.65 171.97 255.30 338.85 422.72 507.09 592.15 678.12 765.25 853.9 944.4 1037.5 1134.3

h

Ρ = 5 MPa (263.99)

Properties of Compressed Liquid (Steam)

TABLE A.4 (SI)

s 2.9202 .0001 .2956 .5705 .8285 1.0720 1.3030 1.5233 1.7343 1.9375 2.1341 2.3255 2.5128 2.6979 2.8830

v .001 452 4 .000 995 2 .000 997 2 .001 003 4 .001 012 7 .001 024 5 .001 038 5 .001054 9 .001 073 7 .001 095 3 .001 119 9 .001 148 0 .001 180 5 .001 218 7 .001 264 5 .001 321 6 .001 397 2

1393.0 .09 83.36 166.35 249.36 332.59 416.12 500.08 584.68 670.13 756.65 844.5 934.1 1026.0 1121.1 1220.9 1328.4

u 1407.6 10.04 93.33 176.38 259.49 342.83 426.50 510.64 595.42 681.08 767.84 856.0 945.9 1038.1 1133.7 1234.1 1342.3

h

Ρ = 10 MPa (311.06) s 3.3596 .0002 .2945 .5686 .8258 1.0688 1.2992 1.5189 1.7292 1.9317 2.1275 2.3178 2.5039 2.6872 2.8699 3.0548 3.2469

v .001 658 1 .000 992 8 .000 995 0 .001 001 3 .001 010 5 .001 022 2 .001 036 1 .001 052 2 .001 070 7 .001 091 8 .001 115 9 .001 143 3 .001 1748 .001 211 4 .001 255 0 .001 308 4 .001 377 0 .001 472 4 .001 631 1

1585.6 .15 83.06 165.76 248.51 331.48 414.74 498.40 582.66 667.71 753.76 841.0 929.9 1020.8 1114.6 1212.5 1316.6 1431.1 1567.5

u

1610.5 15.05 97.99 180.78 263.67 346.81 430.28 514.19 598.72 684.09 770.50 858.2 947.5 1039.0 1133.4 1232.1 1337.3 1453.2 1591.9

h

Ρ = 15 MPa (342.24) s 3.6848 .0004 .2934 .5666 .8232 1.0656 1.2955 1.5145 1.7242 1.9260 2.1210 2.3104 2.4953 2.6771 2.8576 3.0393 3.2260 3.4247 3.6546

654 Appendix 2

Sat. 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

.002 036 .000 990 4 .000 992 8 .000 999 2 .001 008 4 .001 019 9 .001 033 7 .001 049 6 .001 067 8 .001 088 5 .001 112 0 .001 138 8 .001 169 3 .001 204 6 .001 246 2 .001 296 5 .001 359 6 .001 443 7 .001 568 4 .001 822 6

1785.6 .19 82.77 165.17 247.68 330.40 413.39 496.76 580.69 665.35 750.95 837.7 925.9 1016.0 1108.6 1204.7 1306.1 1415.7 1539.7 1702.8

1826.3 20.01 102.62 185.16 267.85 350.80 434.06 517.76 602.04 687.12 773.20 860.5 949.3 1040.0 1133.5 1230.6 1333.3 1444.6 1571.0 1739.3

Ρ = 20 MPa (365.81) 4.0139 .0004 .2923 .5646 .8206 1.0624 1.2917 1.5102 1.7193 1.9204 2.1147 2.3031 2.4870 2.6674 2.8459 3.0248 3.2071 3.3979 3.6075 3.8772 .000 985 6 .000 988 6 .000 995 1 .001 004 2 .001 015 6 .001 029 0 .001 044 5 .001 062 1 .001 082 1 .001 104 7 .001 130 2 .001 159 0 .001 192 0 .001 230 3 .001 275 5 .001 330 4 .001 399 7 .001 492 0 .001 626 5 .001 869 1

.25 82.17 164.04 246.06 328.30 410.78 493.59 576.88 660.82 745.59 831.4 918.3 1006.9 1097.4 1190.7 1287.9 1390.7 1501.7 1626.6 1781.4

29.82 111.84 193.89 276.19 358.77 441.66 524.93 608.75 693.28 778.73 865.3 953.1 1042.6 1134.3 1229.0 1327.8 1432.7 1546.5 1675.4 1837.5

Ρ = 30 MPa .0001 .2899 .5607 .8154 1.0561 1.2844 1.5018 1.7098 1.9096 2.1024 2.2893 2.4711 2.6490 2.8243 2.9986 3.1741 3.3539 3.5426 3.7494 4.0012

.000 976 6 .000 980 4 .000 987 2 .000 996 2 .001 007 3 .001 020 1 .001 034 8 .001 051 5 .001 070 3 .001 091 2 .001 114 6 .001 140 8 .001 170 2 .001 203 4 .001 241 5 .001 286 0 .001 338 8 .001 403 2 .001 483 8 .001 588 4

.20 81.00 161.86 242.98 324.34 405.88 487.65 569.77 652.41 735.69 819.7 904.7 990.7 1078.1 1167.2 1258.7 1353.3 1452.0 1556.0 1667.2

49.03 130.02 211.21 292.79 374.70 456.89 539.39 622.35 705.92 790.25 875.5 961.7 1049.2 1138.2 1229.3 1323.0 1420.2 1522.1 1630.2 1746.6

Ρ = 50 MPa .0014 .2848 .5527 .8052 1.0440 1.2703 1.4857 1.6915 1.8891 2.0794 2.2634 2.4419 2.6158 2.7860 2.9537 3.1200 3.2868 3.4557 3.6291 3.8101

Appendix 2 655

656

Appendix 2

TABLE A.5 (SI) Enthalpy–Entropy Diagram for Steam, SI Units Entropy, s, kJ/kgK 4.5 4200

5.0

6.0

7.0

8.0

9.0

9.5 4200

800

IDEAL JET VELOCITY

4100

v = 2000

780

h

4000

4100

760

h v kj/kg m/s

740

100 200

4000

60

0

720

300

3900

400

100

3800

700

660

600

200

800

560

0 3000

0

0

3500

500

ssure

460

1500

0

420

0

0

400

200

150 100

20

320

60 50

80

0

3100

280

40

20

0

3100

300

30

15

3000

3200

360 340

5

6

260

8

3200

15

800

600 500

100

3300

400 380

25

10

2000

30

300

Enthalpy, h, kJ/kg

3300

3400

440

Pre

5000

4000

0

3000

3400

480

35

6000

8000

1000

0

1000

520

1500

2000

500

3600

540

40 0

00 1000

6000 0 5000 0 4000 0

900

8000

0

400

3700

580

45

0

3500

620 600

300

3600

3800

640 500

700

3700

3900

680 55 0

500

3000

240

10

220

0

2900

Sup e

rhe

at a o t C

50

2800 Satu rati on

Temperature oC

160

line

2800

120

2700

100 80

2

60

2600

4

2600

40

6

20

00 800 0

oi

150

0

200 0

M

st

ur

e

12

60 50 0 40 0 0

16

20 0

MOLLIER CHART

80 60 50 40 30

2200 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS UNITED ENGINEERING CENTER, 345 EAST 47th STREET NEW YORK, N.Y., 10017

20

8

10

15

24

6

2100

2300

ENTHALPY_ENTROPY DIAGRAM

0

15 0 22

18

10

ur ess Pr

20

2200

2400

14

30 0 e

2300

2500

10

10 00 80 0

100

100 000 6000 80000 4000 0 0 500 00 300 00 200 00 150 00

600 0 500 0 400 0 300 0

8

2500

2900

180

140

2700

2400

200

1

28

1.5

2

3

4

5

26

2100

30

2000 4.5

5.0

6.0

Source: American Society of Mechanical Engineers.

7.0

8.0

9.0

2000 9.5

657

Appendix 2

TABLE A.6 Thermal Conductivities of Some Building and Insulating Materials (k = Btu/h·ft. °F)

Material

Apparent Density ρ lbm/ft.3 at Room Temperature

Aerogel, silica, opacified

8.5

Asbestos-cement boards Asbestos sheets Asbestos slate

120 55.5 112 112 0.2

Aluminum foil, 7 air spaces per 2.5 in. Asphalt Bricks: Alumina (92–99% Al2O3 by weight) fused Alumina (64–65% Al2O3 by weight) (See also Bricks, fire clay) Building brickwork Carbon Chrome brick (32% Cr2O3 by weight)

Diatomaceous earth, molded and fired Diatomaceous earth, high burn, large pores

132

115 96.7 200 200 200 38 38 37 37

Kaolin insulating firebrick Magnesite (86.8% MgO, 6.3% Fe2O3, 3% CaO, 2.6% SiO2 by weight) Calcium carbonate, natural White marble Chalk Calcium sulfate (4H2O), artificial Plaster, artificial Building Cardboard, corrugated Celluloid Charcoal flakes

k 0.013 0.026 0.43 0.096 0.087 0.114 0.025 0.038 0.43

801 2399 1472 68

27 27 19 19 158 158 158 162

392 1202 2399 399 1600 392 1832 392 1112 1832 2552 932 2102 392 1400 399 1202 2192 86

96 84.6 132 77.9

104 167 77

87.3 11.9 15

86 176 176

Fire clay, Missouri

Kaolin insulating brick

°F 248 554 68 124 32 140 100 351 68

1.8 2.7 0.62 0.4 3.0 0.67 0.85 1.0 0.14 0.18 0.13 0.34 0.58 0.85 0.95 1.02 0.15 0.26 0.050 0.113 2.2 1.6 1.1 1.3 1.7 0.4 0.22 0.43 0.25 0.037 0.12 0.043 0.051 (continued)

658

Appendix 2

TABLE A.6 (Continued) Thermal Conductivities of Some Building and Insulating Materials (k = Btu/h·ft. °F)

Material

Apparent Density ρ lbm/ft.3 at Room Temperature

Coke, petroleum Coke, powdered Concrete, cinder 1:4 dry Stone Cork board Cork, ground Cotton wool Diatomaceous earth power, coarse Fine Molded pipe covering Dolomite Ebonite Enamel, silicate Felt, wool Fiber insulating board Glass Borosilicate type Soda glass Window glass Granite Graphite, longitudinal Gypsum, molded and dry Hair felt, perpendicular to fibers Ice Kapok Lampblack Leather sole Limestone (15.3 vol.% H2O) Magnesia, powdered Magnesia, light carbonate Magnesium oxide, compressed

°F 212 932 32–212

10 9.4 5 20.0 20.0 17.2 17.2 26.0 26.0 167

86 86 86 100 1600 399 1600 399 1600 122

38 20.6 14.8

86 70

139

86–167

78 17 57.5 0.88 10 62.4 103 49.7 19 49.9

68 68 86 32 68 104 75 117 70 68

k 3.4 2.9 0.11 0.20 0.44 0.54 0.025 0.025 0.024 0.036 0.082 0.040 0.074 0.051 0.088 1.0 0.10 0.5–0.75 0.03 0.028 0.2–0.73 0.63 0.3–0.44 0.3–0.61 1.0–2.3 95 0.25 0.021 1.3 0.020 0.038 0.092 0.54 0.35 0.034 0.32 (continued)

659

Appendix 2

TABLE A.6 (Continued) Thermal Conductivities of Some Building and Insulating Materials (k = Btu/h·ft. °F)

Material Marble Mica, perpendicular to planes Mineral wool Paper Paraffin wax Porcelain Portland cement (see Concrete) Pumice stone Pyroxylin plastics Rubber, hard Para Soft Sand, dry Sandstone Sawdust Slag, blast furnace Slag wool Slate Snow Sulfur, monoclinic Rhombic Wallboard, insulating type Wallboard, stiff pasteboard Wood shavings Wood, across grain Balsa Oak Maple Pine, white Teak White fir Wood, parallel to grain Pine Wool, animal

Apparent Density ρ lbm/ft.3 at Room Temperature

9.4 19.7

122 86 86 32 392 194 70–151

74.8

k

°F

1.2–1.7 0.25 0.0225 0.024 0.075 0.14 0.88 0.17 0.14 0.075 0.087 0.109 0.075–0.092 0.19 1.06 0.03 0.064 0.022 0.86 0.27 0.09–0.097 0.16 0.028 0.04 0.034

14.8 43 8.8

32 70 70 68 104 70 75–261 86 201 32 212 70 70 86 86

7–8 51.5 44.7 34.0 40.0 28.1

86 59 122 59 59 140

0.025–0.03 0.12 0.11 0.087 0.10 0.062

34.4 6.9

70 86

0.20 0.021

94.6 140 12 12 34.7

Source: G. F. Babits, Thermodynamics, Allyn & Bacon, Inc., Boston, 1963, pp. 231–34. With permission.

Abs. lb./in.2 p

1.24 1.86 2.74 3.94 4.69 5.55 6.54 7.67 8.95 10.41 11.04 11.71 12.41 13.14 13.90 14.71 15.55 16.42 17.34 18.30 19.30 20.34 21.43 22.56

Temp. °F t

–100 –90 –80 –70 –65 –60 –55 –50 –45 –40 –38 –36 –34 –32 –30 –28 –26 –24 –22 –20 –18 –16 –14 –12

27.4 26.1 *24.3 *21.9 *20.4 *18.6 *16.6 *14.3 *11.7 *8.7 *7.4 *6.1 *4.7 *3.2 *1.6 0.0 0.8 1.7 2.6 3.6 4.6 5.6 6.7 7.9

*

*

Gauge lb./ in.2 pd

Pressure

182.90 124.28 86.54 61.65 52.34 44.73 38.38 33.08 28.62 24.86 23.53 22.27 21.10 20.00 18.97 18.00 17.09 16.24 15.43 14.68 13.97 13.29 12.66 12.06

Volume Vapor ft.3/ lb. vg

Ammonia: Properties of Liquid and Saturated Vapor

TABLE A.7

45.51 45.12 44.73 44.32 44.11 43.91 43.70 43.49 43.28 43.08 42.99 42.90 42.82 42.73 42.65 42.57 42.48 42.40 42.31 42.22 43.13 42.04 41.96 41.87

Density Liquid lb./ ft.3 1/vf –61.5 –51.4 –41.3 –31.1 –26.0 –20.9 –15.7 –10.5 – 5.3 0.0 2.1 4.3 6.4 8.5 10.7 12.8 14.9 17.1 19.2 21.4 23.5 25.6 27.8 30.0

Liquid Btu/ lb. hf 571.4 575.9 580.1 584.4 586.6 588.8 591.0 593.2 595.7 597.6 598.3 599.1 599.9 600.6 601.4 602.1 602.8 603.6 604.3 605.0 605.7 606.4 607.1 607.8

Vapor Btu/ lb. hg

Enthalpy from –40°F

632.9 627.3 621.4 615.5 612.6 609.7 606.7 603.7 600.7 597.6 596.2 594.8 593.5 592.1 590.7 589.3 587.9 586.5 585.1 583.6 582.2 580.8 579.3 577.8

Latent Btu/ lb. hfg –0.1579 –0.1309 –0.1036 –0.0771 –0.0642 –0.0514 –0.0382 –0.0254 –0.0128 0.0000 .0051 .0101 .0151 .0201 0.0250 .0300 .0350 .0399 .0448 0.0497 .0545 .0594 .0642 .0690

Liquid Btu/ lb. °F sf

1.6025 1.5667 1.5336 1.5026 1.4833 1.4747 1.4614 1.4487 1.4363 1.4242 1.4193 1.4144 1.4096 1.4048 1.4001 1.3955 1.3909 1.3863 1.3818 1.3774 1.3729 1.3686 1.3643 1.3600

Vapor Btu/ lb. °F sg

Entropy from –40°F

660 Appendix 2

–10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

23.74 24.97 26.26 27.59 28.98 30.42 31.92 33.47 35.09 36.77 38.51 40.31 42.18 44.12 46.13 48.21 50.36 52.59 54.90 57.28 59.74 62.29 64.91 67.63 70.43 73.32 76.31 79.38 82.55 85.82

9.0 10.3 11.6 12.9 14.3 15.7 17.2 18.8 20.4 22.1 23.8 25.6 27.5 29.4 31.4 33.5 35.7 37.9 40.2 42.6 45.0 47.6 50.2 52.9 55.7 58.6 61.6 64.7 67.9 71.1

11.50 10.97 10.47 9.991 9.541 9.116 8.714 8.333 7.971 7.629 7.304 6.996 6.703 6.425 6.161 5.910 5.671 5.443 5.227 5.021 4.825 4.637 4.459 4.289 4.126 3.971 3.823 3.682 3.547 3.418

41.78 41.69 41.60 41.52 41.43 41.34 41.25 41.16 41.07 40.98 40.89 40.80 40.71 40.61 40.52 40.43 40.34 40.25 40.15 40.06 39.96 39.86 39.77 39.67 39.50 39.49 39.39 39.29 39.19 39.10

32.1 34.3 36.4 38.6 40.7 42.9 45.1 47.2 49.4 51.6 53.8 56.0 58.2 60.3 62.5 64.7 66.9 69.1 71.3 73.5 75.7 77.9 80.1 82.3 84.6 86.8 89.0 91.2 93.5 95.7

608.5 609.2 609.8 610.5 611.1 611.8 612.4 613.0 613.6 614.3 614.9 615.5 616.1 616.6 617.2 617.8 618.3 618.9 619.4 619.9 620.5 621.0 621.5 622.0 622.5 623.0 623.4 623.9 624.4 624.8

576.4 574.9 573.4 571.9 570.4 568.9 567.3 565.8 564.2 562.7 561.1 559.5 557.9 556.3 554.7 553.1 551.4 549.8 548.1 546.4 544.8 543.1 541.4 539.7 537.9 536.2 534.4 532.7 530.9 529.1

0.0738 .0786 .0833 .0880 .0928 0.0975 .1022 .1069 .1115 .1162 0.1208 .1254 .1300 .1346 .1392 0.1437 .1483 .1528 .1573 .1618 0.1663 .1708 .1753 .1797 .1841 0.1885 .1930 .1974 .2018 .2062

1.3558 1.3516 1.3474 1.3433 1.3393 1.3352 1.3312 1.3273 1.3234 1.3195 1.3157 1.3118 1.3081 1.3043 1.3006 1.2969 1.2933 1.2897 1.2861 1.2825 1.2790 1.2755 1.2721 1.2686 1.2652 1.2618 1.2585 1.2552 1.2519 1.2486 (continued)

Appendix 2 661

50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86

Temp. °F t

89.19 92.66 96.23 99.91 103.7 107.6 111.6 115.7 120.0 124.3 128.8 133.4 138.1 143.0 147.9 153.0 158.3 163.7 169.2

Abs. lb./in.2 p

74.5 78.0 81.5 85.2 89.0 92.9 96.9 101.0 105.3 109.6 114.1 118.7 123.4 128.3 133.2 138.3 143.6 149.0 154.5

Gauge lb./ in.2 pd

Pressure

3.294 3.176 3.063 2.954 2.851 2.751 2.656 2.565 2.477 2.393 2.312 2.235 2.161 2.089 2.021 1.955 1.892 1.831 1.772

Volume Vapor ft.3/ lb. vg

Ammonia: Properties of Liquid and Saturated Vapor

TABLE A.7 (Continued)

39.00 38.90 38.80 38.70 38.60 38.50 38.40 38.30 38.20 38.10 38.00 37.90 37.79 37.69 37.58 37.48 37.37 37.26 37.16

Density Liquid lb./ ft.3 1/vf 97.9 100.2 102.4 104.7 106.9 109.2 111.5 113.7 116.0 118.3 120.5 122.8 125.1 127.4 129.7 132.0 134.3 136.6 138.9

Liquid Btu/ lb. hf 625.2 625.7 626.1 626.5 626.9 627.3 627.7 628.0 628.4 628.8 629.1 629.4 629.8 630.1 630.4 630.7 631.0 631.3 631.5

Vapor Btu/ lb. hg

Enthalpy from –40°F

527.3 525.5 523.7 521.8 520.0 518.1 516.2 514.3 512.4 510.5 508.6 506.6 504.7 502.7 500.7 498.7 496.7 494.7 492.6

Latent Btu/ lb. hfg

0.2105 .2149 .2192 .2236 .2279 0.2322 .2365 .2408 .2451 .2494 0.2537 .2579 .2622 .2664 .2706 0.2749 .2791 .2833 .2875

Liquid Btu/ lb. °F sf

1.2453 1.2421 1.2389 1.2357 1.2325 1.2294 1.2262 1.2231 1.2201 1.2170 1.2140 1.2110 1.2080 1.2050 1.2020 1.1991 1.1962 1.1933 1.1904

Vapor Btu/ lb. °F sg

Entropy from –40°F

662 Appendix 2

174.8 180.6 186.6 192.7 198.9 205.3 211.9 218.6 225.4 232.5 239.7 247.0 254.5 262.2 270.1 278.2 286.4 294.8 303.4

160.1 165.9 171.9 178.0 184.2 190.6 197.2 203.9 210.7 217.8 225.0 232.3 239.8 247.5 255.4 263.5 271.7 280.1 288.7

1.716 1.661 1.609 1.559 1.510 1.464 1.419 1.375 1.334 1.293 1.254 1.217 1.180 1.145 1.112 1.079 1.047 1.017 0.987

37.05 36.95 36.84 36.73 36.62 36.51 36.40 36.29 36.18 36.06 35.95 35.84 35.72 35.61 35.49 35.38 35.26 35.14 35.02

141.2 143.5 145.8 148.2 150.5 152.9 155.2 157.6 159.9 162.3 164.6 167.0 169.4 171.8 174.2 176.6 179.0 181.4 183.9

631.8 632.0 632.2 632.5 632.6 632.9 633.0 633.2 633.4 633.5 633.6 633.7 633.8 633.9 634.0 634.0 634.0 634.0 634.0

490.6 488.5 486.4 484.3 482.1 480.0 477.8 475.6 473.5 471.2 469.0 466.7 464.4 462.1 459.8 457.4 455.0 452.6 450.1

.2917 0.2958 .3000 .3041 .3083 .3125 0.3166 .3207 .3248 .3289 .3330 0.3372 .3413 .3453 .3495 .3535 0.3576 .3618 .3659

1.1875 1.1846 1.1818 1.1789 1.1761 1.1733 1.1705 1.1677 1.1649 1.1621 1.1593 1.1566 1.1538 1.1510 1.1483 1.1455 1.1427 1.1400 1.1372

Source: Abstracted from Tables of Thermodynamic Properties of Ammonia, U.S. Department of Commerce, Bureau of Standards Circular 142, 1945. With permission. * Inches of mercury below one atmosphere.

88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124

Appendix 2 663

Sat. –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temp. °F t

v

49.31 51.05 52.36 53.67 54.97 56.26 57.55 58.84 60.12 61.41 62.69 63.96 65.24 66.51 67.79 69.06 70.33 71.60 72.87 74.14 75.41 76.68 77.95

597.1

603.2 608.5 613.7 618.9 624.0 629.1 634.2 639.3 644.4 649.5 654.6 659.7 664.8 670.0 675.1 680.3 685.4 690.6 695.8 701.1

26.58 27.26 27.92 28.58 29.24 29.90 30.55 31.20 31.85 32.49 33.14 33.78 34.42 35.07 35.71 36.35 36.99 37.62 38.26 38.90

v 25.81

h

s

1.4857 1.5025 .5149 .5269 .5385 .5498 1.5608 .5716 .5821 .5925 .6026 1.6125 .6223 .6319 .6413 .6506 1.6598 .6689 .6778 .6865 .6952 1.7038 .7122

h

588.3 595.2 600.3 605.4 610.4 615.4 620.4 625.4 630.4 635.4 640.4 645.5 650.5 655.5 660.6 665.6 670.7 675.8 680.9 686.1 691.2 696.4 701.6

10 –41.34 s

1.4420 .4542 .4659 1.4773 .4884 .4992 .5097 .5200 1.5301 .5400 .5497 .5593 .5687 1.5779 .5870 .5960 .6049 .6136 1.6222 .6307

1.4276

v

18.01 18.47 18.92 19.37 19.82 20.26 20.70 21.14 21.58 22.01 22.44 22.88 23.31 23.74 24.17 24.60 25.03 25.46 25.88

17.67

606.4 611.9 617.2 622.5 627.8 633.0 638.2 643 4 648.5 653.7 658.9 664.0 669.2 674.4 679.6 684.8 690.0 695.3 700.5

602.4

h

15 –27.20

Absolute Pressure in lb./in.2 (Saturation Temperature in Italics)

5 –63.11

Ammonia: Properties of Superheated Vapor

TABLE A.8

s

1.4031 .4154 1.4272 .4386 .4497 .4604 .4709 1.4812 .4912 .5011 .5108 .5203 1.5296 .5388 .5478 .5567 .5655 1.5742 .5827

1.3988

v

13.74 14.09 14.44 14.78 15.11 15.45 15.78 16.12 16.45 16.78 17.10 17.43 17.76 18.08 18.41 18.73 19.05 19.37

13.50

610.0 615.5 621.0 626.4 631.7 637.0 642.3 647.5 652.8 658.0 663.2 668.5 673.7 678.9 684.2 689.4 694.7 700.0

606.2

h

20 –16.64 s

1.3784 1.3907 .4025 .4138 .4248 .4356 1.4460 .4562 .4662 .4760 .4856 1.4950 .5042 .5133 .5223 .5312 1.5399 .5485

1.3700

664 Appendix 2

10.96 11.19

11.47

11.75 12.03 12.30 12.57 12.84 13.11 13.37 13.64 13.90 14.17 14.43 14.69 14.95 15.21 15 47 15.73 15.99 16.25

10

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

v

79.21 80.48

Sat. 0

Temp. °F t

240

220

200

170 180 190

625.0 630.4 635.8 641.2 646.5 651.8 657.1 662.4 667.7 673.0 678.2 683.5 688.8 694.1 699.4 704.7 710.1 715.4

619.4

609.1 613.8

h

25 –7.96

706.8 712.1

.3855 .3967 .4077 1.4183 .4287 .4388 .4487 .4584 1.4679 .4772 .4864 .4954 .5043 1.5131 .5217 .5303 .5387 .5470

.3738

1.3515 1.3616

s

.7206 .7289

9.731 9.966 10.20 10.43 10.65 10.88 11.10 11.33 11.55 11.77 11.99 12.21 12.43 12.65 12 87 13.08 13.30 13.52

9.492

9.236

v

41.45

39.54 40.17 40.81

623.5 629.1 634.6 640.1 645.5 650.9 656.2 661.6 666.9 672.2 677.5 682.9 688.2 693.5 698 8 704.2 709.6 714.9

617.8

611.6

h

30 –0.57

722.2

706.3 711.6 716.9

.3618 .3733 .3845 1.3953 .4059 .4161 .4261 .4359 1.4456 .4550 .4642 .4733 .4823 1.4911 .4998 .5083 .5168 .5251

1.3497

1.3364

s

1.6637

.6391 .6474 .6556

8.287 8.493 8.695 8.895 9.093 9.289 9.484 9.677 9.869 10.06 10.25 10.44 10.63 10.82 11.00 11.19 11.38 11.56

8.078

7.991

v

28.44

27.59

26.31 26.74 27.16

622.0 627.7 633.4 638.9 644.4 649.9 655.3 660.7 666.1 671.5 676.8 682.2 687.6 692.9 698.3 703.7 709.1 714.5

616.1

613.6

h

35 5.89

732.4

721.7

705.8 711.1 716.4

.3413 .3532 .3646 1.3756 .3863 .3967 .4069 .4168 1.4265 .4360 .4453 .4545 .4635 1.4724 .4811 .4897 .4982 .5066

1.3289

1.3236

s

.6318

1.6158

.5911 .5995 .6077

7.203 7.387 7.568 7.746 7.922 8.096 8.268 8.439 8.609 8.777 8.945 9.112 9.278 9.444 9.609 9.774 9.938 10.10

7.047

v

21.94

21.30

20.66

19.70 20.02 20.34

620.4 626.3 632.1 637.8 643.4 648.9 654.4 659.9 665.3 670.7 676.1 681.5 686.9 692.3 697.7 703.1 708.5 714.0

615.4

h

40 11.66

742.8

732.0

721.2

705.3 710.6 715.9

1.3231 .3353 .3470 1.3583 .3692 .3797 .3900 .4000 1.4098 .4194 .4288 .4381 .4471 1.4561 .4648 .4735 .4820 .4904 (continued)

1.3125

s

.6135

.5978

1.5817

.5569 .5653 1.5736

Appendix 2 665

Sat. 30 40 50 60 70 80 90 100 110

Temp. °F t

200 220 240 260 280 300

Temp. °F t

v

5.710 5.838 5.988 6.135 6.280 6.423 6.564 6.704 6.843 6.980

v

16.50 17.02 17.53 18.04

618.2 623.4 629.5 635.4 641.2 646.9 652.6 658.2 663.7 669.2

h

50 21.67

720.8 731.6 742.5 753.4

h

25 –7.96

s

1.2939 1.3046 .3169 1.3286 .3399 .3508 .3613 .3716 1.3816 .3914

s

1.5552 .5713 .5870 .6025

v

h

620.5 626.8 632.9 639.0 644.9 650.7 656.4 662.1 667.7

4.933 5.060 5.184 5.307 5.428 5.547 5.665 5.781

h

60 30.21

720.3 731.1 742.0 753.0 764.1

4.805

v

13.73 14.16 14.59 15.02 15.45

30 –0.57 s

1.2913 1.3035 .3152 .3265 .3373 .3479 1.3581 .3681

1.2787

s

1.5334 .5495 .5653 .5808 .5960

v

4.177 4.290 4.401 4.509 4.615 4.719 4.822 4.924

4.151

v

11.75 12.12 12.49 12.86 13.23

623.9 630.4 636.6 642.7 648.7 654.6 660.4 666.1

622.4

h

70 37.70

719.9 730.7 741.7 752.7 763.7

h

35 5.89

Absolute Pressure in lb./in.2 (Saturation Temperature in Italics)

Ammonia: Properties of Superheated Vapor

TABLE A.8 (Continued)

s

1.2688 1.2816 .2937 .3054 .3166 .3274 1.3378 .3480

1.2658

s

1.5148 .5311 .5469 .5624 .5776

v

3.712 3.812 3.909 4.005 4.098 4.190 4.281

8.655

v

10.27 10.59 10.92 11.24 11.56 11.88

627.7 634.3 640.6 646.7 652.8 658.7 664.6

624.0

h

80 44.40

719.4 730.3 741.3 752.3 763.4 774.6

h

40 11.66 s

1.2619 .2745 .2866 .2981 .3092 1.3199 .3303

1.2545

s

1.4987 .5150 .5309 .5465 .5617 1.5766

666 Appendix 2

Sat. 50 60 70 80 90 100 110 120

Temp. °F t

120 130 140 150 160 170 180 190 200 210 220 240 260 280 300

625.3

631.8 638.3 644.7 650.9 657.0 663.0 668.9

3.353 3.442 3.529 3.614 3.698 3.780 3.862

h

90 50.47

674.7 680.2 685.7 691.1 696.6 702.1 707.5 713.0 718.5 724.0 729.4 740.5 751.6 762.7 774.0

3.266

v

7.117 7.252 7.387 7.521 7.655 7.788 7.921 8.053 8.185 8.317 8.448 8.710 8.970 9.230 9.489

1.2571 .2695 .2814 .2928 1.3038 .3144 .3247

1.2445

s

.4009 .4103 .4195 1.4286 .4374 .4462 .4548 .4633 1.4716 .4799 .4880 .5040 .5197 1.5350 .5500

2.985 3.068 3.149 3.227 3.304 3.380 3.454

2.952

v

5.897 6.012 6.126 6.239 6.352 6.464 6.576 6.687 6.798 6.909 7.019 7.238 7.457 7.675 7.892

629.3 636.0 642.6 649.0 655.2 661.3 667.3

626.5

h

100 56.05

673.3 678.9 684.4 689.9 695.5 701.0 706.5 712.0 717.5 723.1 728.6 739.7 750.9 762.1 773.3

1.2409 .2539 .2661 .2778 1.2891 .2999 .3104

1.2356

s

.3778 .3873 .3966 1.4058 .4148 .4236 .4323 .4409 1.4493 .4576 .4658 .4819 .4976 1.5130 .5281

2.505 2.576 2.645 2.712 2.778 2.842

2.476

v

5.025 5.125 5.224 5.323 5.420 5.518 5.615 5.711 5.807 5.902 5.998 6.187 6.376 6.563 6.750

631.3 638.3 645.0 651.6 658.0 664.2

628.4

h

120 66.02

671.8 677.5 683.1 688.7 694.3 699.9 705.5 711.0 716.6 722.2 727.7 738.9 750.1 761.4 772.7

1.2255 .2386 .2510 1.2628 .2741 .2850

1.2201

s

.3579 .3676 .3770 1.3863 .3954 .4043 .4131 .4217 1.4302 .4386 .4469 .4631 .4789 1.4943 .5095

2.166 2.228 2.288 2.347 2.404

2.132

v

4.371 4.460 4.548 4.635 4.722 4.808 4.893 4.978 5.063 5.147 5.231 5.398 5.565 5.730 5.894

633.8 640.9 647.8 654.5 661.1

629.9

h

140 74.79

670.4 676.1 681.8 687.5 693.2 698 8 704.4 710.0 715.6 721.3 726.9 738.1 749.4 760.7 772.1

1.2140 .2272 1.2396 .2515 .2628 (continued)

1.2068

s

.3404 .3502 .3598 1.3692 .3784 3874 .3963 .4050 1.4136 .4220 .4304 .4467 .4626 1.4781 .4933

Appendix 2 667

Sat. 90 100 110 120

Temp. °F t

130 140 150 160 170 180 190 200 210 220 230 240 250 260 280 300

Temp. °F t

v

1.872 1.914 1.969 2.023 2.075

v

3.942 4.021 4 100 4.178 4.255 4.332 4.408 4.484 4.560 4.635 4.710 4.785 4.859 4.933 5.081 5.228

631.1 636.6 643.9 651.0 657.8

h

160 82.64

674.7 680.5 686.3 692.0 697.7 703.4 709.0 714.7 720.4 726.0 731.7 737.3 743.0 748.7 760.0 771.5

h

90 50.47

1.1952 1.2055 1.2186 .2311 .2429

s

.3347 .3444 1.3539 .3633 .3724 .3813 .3901 1.3988 .4073 .4157 .4239 .4321 1.4401 .4481 .4637 .4789

s

Ammonia: Properties of Superheated Vapor

TABLE A.8 (Continued)

v

1.667 1.668 1.720 1.770 1.818

v

3.527 3.600 3 672 3.743 3.813 3.883 3.952 4.021 4.090 4.158 4.226 4.294 4.361 4.428 4.562 4.695

632.0 632.2 639.9 647.3 654.4

h

180 89.78

673.3 679.2 685 0 690.8 696.6 702.3 708.0 713.7 719.4 725.1 730.8 736.5 742.2 747.9 759.4 770.8

h

100 56.05 s

1.1850 1.1853 1.1992 .2123 .2247

s

.3206 .3305 1.3401 .3495 .3588 .3678 .3767 1.3854 .3940 .4024 .4108 .4190 1.4271 .4350 .4507 .4660

v

h

632.7

643.4 650.9

1.567 1.612

h

200 96.34

670.4 676.5 682 5 688.4 694.3 700.2 706.0 711.8 717.6 723.4 729.2 734.9 740.7 746.5 758.0 769.6

1.502

v

2.905 2.967 3 029 3.089 3.149 3.209 3.268 3.326 3.385 3.442 3.500 3.557 3.614 3.671 3.783 3.895

120 66.02 s

1.1947 .2077

1.1756

s

.2956 .3058 1.3157 .3254 .3348 .3441 .3531 1.3620 .3707 .3793 .3877 .3960 1.4042 .4123 .4281 .4435

v

1.400 1.443

1.367

v

2.460 2.515 2 569 2.622 2.675 2.727 2.779 2.830 2.880 2.931 2.981 3.030 3.080 3.129 3.227 3.323

639.4 647.3

633.2

h

220 102.42

667.4 673.7 679.9 686.0 692.0 698.0 704.0 709.9 715.8 721.6 727.5 733.3 739.2 745.0 756.7 768.3

h

140 74.79 s

1.1781 .1917

1.1671

s

.2738 .2843 1.2945 .3045 .3141 .3236 .3328 1.3418 .3507 .3594 .3679 .3763 1.3846 .3928 .4088 .4243

668 Appendix 2

Sat. 110 120 130 140

Temp. °F t

130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 320 340 360 380

1.253 1.261 1.302 1.342 1.380

v

2.125 2.175 2.224 2.272 2.319 2.365 2.411 2.457 2.502 2.547 2 591 2.635 2.679 2.723 2.766 2.809 2.852 2.895 2.980 3.064

633.6 635.3 643.5 651.3 658.8

h

240 108.09

664.4 670.9 677.2 683.5 689.7 695.8 701.9 707.9 713.9 719.9 725.8 731.7 737.6 743.5 749.4 755.3 761.2 767.1 778.9 790.7

1.1592 1.1621 .1764 .1898 .2025

s

.2542 .2652 1.2757 .2859 .2958 .3054 .3148 1.3240 .3331 .3419 .3506 .3591 1.3675 .3757 .3838 .3919 .3998 1.4076 .4229 .4379

633.9 639.5 647.8 655.6

1.182 1.220 1.257

h

260 113.42

661.3 668.0 674.6 681.0 687.3 693.6 699.8 705.9 712.0 718.1 724 1 730.1 736.1 742.0 748.0 753.9 759.9 765.8 777.7 789.6

1.155

v

1.865 1.910 1.955 1.999 2.042 2.084 2.126 2.167 2.208 2.248 2 288 2.328 2.367 2.407 2.446 2.484 2.523 2.561 2.637 2.713

1.1617 .1757 .1889

1.1518

s

.2364 .2477 1.2586 .2691 .2792 .2891 .2987 1.3081 .3172 .3262 3350 .3436 1.3521 .3605 .3687 .3768 .3847 1.3926 .4081 .4231

1.078 1.115 1.151

1.072

v

1.656 1.698 1.740 1.780 1.820 1.859 1.897 1.935 1.972 2.009 2 046 2.082 2.118 2.154 2.189 2.225 2.260 2.295 2.364 2.432 2.500 2.568

635.4 644.0 652.2

634.0

h

280 118.45

658.1 665.0 671.8 678.4 684.9 691.3 697.7 703.9 710.1 716.3 722 4 728.4 734.5 740.5 746.5 752.5 758.5 764.5 776.5 788.5 800.5 812.5

1.1473 .1621 .1759

1.1449

s

.2200 .2317 1.2429 .2537 .2641 .2742 .2840 1.2935 .3029 .3120 3209 .3296 1.3382 .3467 .3550 .3631 .3712 1.3791 .3947 .4099 .4247 .4392

1.023 1.058

0.999

v

1.485 1.525 1.564 1.601 1.638 1.675 1.710 1.745 1.780 1.814 1 848 1.881 1.914 1.947 1.980 2.012 2.044 2.076 2.140 2.203 2.265 2.327

640.1 648.7

634.0

h

300 123.21

654.8 662.0 669.0 675.8 682.5 689.1 695.5 701.9 708.2 714.4 720 6 726.8 732.9 739.0 745.1 751.1 757.2 763.2 775.3 787.4 799.5 811.6

1.1487 .1632 (continued)

1.1383

s

.2045 .2167 1.2281 .2394 .2501 .2604 .2704 1.2801 .2896 .2989 .3079 .3168 1.3255 .3340 .3424 .3507 .3588 1.3668 .3825 .3978 .4127 .4273

Appendix 2 669

1.416 1.452 1.487 1.521 1.554 1.587 1.619 1.651 1.683 1.714 1.745 1.775 1.805 1.835 1.865 1.895 1.954 2.012 2.069 2.126

v

666.1 673.1 680.0 686.7 693.3 699.8 706.2 712.6 718.9 725.1 731.3 737.6 743.6 749.8 755.9 762.0 774.1 786.3 798.4 810.6

h

1.2145 .2259 .2369 .2475 .2577 1.2677 .2773 .2867 .2959 .3049 1.3137 .3224 .3308 .3392 .3474 1.3554 .3712 .3866 .4016 .4163

s 1.292 1.326 1.359 1.391 1.422 1.453 1.484 1.514 1.543 1.572 1.601 1.630 1.658 1.686 1.714 1.741 1.796 1.850 1.904 1.957 2.009

v 663.1 670.4 677.5 684.4 691.1 697.7 704.3 710.7 717.1 723.4 729.7 736.0 742.2 748.4 754.5 760.7 772.9 785.2 797.4 809.6 821.9

h

260 113.42

1.2014 .2132 .2245 .2354 .2458 1.2560 .2658 .2754 .2847 .2938 1.3027 .3115 .3200 .3285 .3367 1.3449 .3608 .3763 .3914 .4062 1.4206

s 1.184 1.217 1.249 1.279 1.309 1.339 1.367 1.396 1.424 1.451 1.478 1.505 1.532 1.558 1.584 1.610 1.661 1.712 1.762 1.811 1.861

v 660.1 667.6 674.9 681.9 688.9 695.6 702.3 708.8 715.3 721.8 728.1 734.4 740.7 747.0 753.2 759.4 771.7 784.0 796.3 808.7 821.0

h

280 118.45

1.1888 .2011 .2127 .2239 .2346 1.2449 .2550 .2647 .2742 .2834 1.2924 .3013 .3099 .3184 .3268 1.3350 .3511 .3667 .3819 .3967 1.4112

s 1.091 1.123 1.153 1.183 1.211 1.239 1.267 1.294 1.320 1.346 1.372 1.397 1.422 1.447 1.472 1.496 1.544 1.592 1.639 1.686 1.732

v

656.9 664.7 672.2 679.5 686.5 693.5 700.3 706.9 713.5 720.0 726.5 732.9 739.2 745.5 751.8 758.1 770.5 782.9 795.3 807.7 820.1

h

300 123.21

1.1767 .1894 .2014 .2129 .2239 1.2344 .2447 .2546 .2642 .2736 1.2827 .2917 .3004 .3090 .3175 1.3257 .3419 .3576 .3729 .3878 1.4024

s

Source: Abstracted from Tables of Thermodynamic Properties of Ammonia, U.S. Department of Commerce, Bureau of Standards Circular 142, 1945. With permission.

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 320 340 360 380 400

Temp. °F t

240 108.09

Ammonia: Properties of Superheated Vapor

TABLE A.8 (Continued)

670 Appendix 2

40 F

60 F

20

40

20 F

60

10.0

an

nst

0.3

Co

lu t vo

0.5

me

40

30

20

14

10

6

4

e t volum 3

60

n sta 1.6

n Co

1.8

1.7

5 1.6

py ro

5 1.7

nt te

300 F 250 F

200 F 150 F

100 F 80 F 60 F 40 F 20 F 0F 20 F 40 F

1.2 5

60 F

1.2

0.1

80 100 120 140 160 180 200 250 300 350 400 450 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 Enthalpy, Btu/lbm

6.0

3.0 4.0

2.0

1.5

1.0

0.6

n Consta

350 F

Source: Data from Tables of Thermodynamic Properties of Ammonia, Bureau of Standards, U.S. Department of Commerce.

20 0

nst

an

40 F

0.2

Co

me

lu t vo

100 F

0.2

400 F

6 5

8

10

15

20

30 25

60 50 40

80

100

150

n

200

0.9 1.3

300 250

Pressure (psia)

60 F

nt q

Co

20 F

S a tur ate d

80 F

l

ua

ity

0.3

0.4

0.6

0F

uid

liq

0.1

r

1

sta

0.2

0.4

ntropy

Consta nt e

0.3

Saturate d vapo

.35 1.4

0.2

0.4

0.6 1.0 ns

0.7 entropy Constant

0.5

0.7 1.1

0.7

5 tan Co

0.8

0.8 1.1 py tro te n

0.9

45

5

1.

1.

Pressure–Enthalpy Diagram for Ammonia

55

perature Constant tem

1.

TABLE A.9

Appendix 2 671

–152 –150 –145 –140 –135 –130 –125 –120 –115 –110 –105 –100 –95 –90 –85 –80 –75 –70 –65 –60 –55 –50 –45

t

Temp. °F 

0.13799 .15359 .19933 .25623 .32641 .41224 0.51641 .64190 .79200 .97034 1.1809 1.4280 1.7163 2.0509 2.4371 2.8807 3.3879 3.9651 4.6193 5.3575 6.1874 7.1168 8.1540

p

Abs. lb./ in.2

29.64024a 29.60849a 29.51537a 29.39951a 29.25663a 29.08186a 28.86978a 28.61429a 28.30869a 27.94558a 27.5169a 27.0138a 26.4268a 25.7456a 24.9593a 24.0560a 23.0234a 21.8482a 20.5164a 19.0133a 17.3237a 15.4313a 13.3196a

pd

Gauge lb./in.2

Pressure

0.0095673 .0095822 .0096198 .0096579 .0096966 .0097359 0.0097758 .0098163 .0098574 .0098992 .0099416 .0099847 .010029 .010073 .010118 .010164 0.010211 .010259 .010308 .010357 .010407 0.010459 .010511

vf

Liquid ft.3/lb.

197.58 178.65 139.83 110.46 88.023 70.730 57.283 46.741 38.410 31.777 26.458 22.164 18.674 15.821 13.474 11.533 9.9184 8.5687 7.4347 6.4774 5.6656 4.9742 4.3828

vs

Vapor ft.3/ lb.

Volume

104.52 104.36 103.95 103.54 103.13 102.71 102.29 101.87 101.45 101.02 100.59 100.15 99.715 99.274 98.830 98.382 97.930 97.475 97.016 96.553 96.086 95.616 95.141

1/vf

Liquid lb./ft.3

0.0050614 .0055976 .0071517 .0090533 .011361 .014138 0.017457 .021395 .026035 .031470 .037796 0.045119 .053550 .063207 .074216 .086708 0.10082 .11670 .13451 .15438 .17650 0.20104 .22816

l/vg

Vapor lb./ ft.3

Density

Dichlorodifluoromethane (Freon-12): Properties of Liquid and Saturated Vapor

TABLE A.10

–23.106 –22.697 –21.674 –20.652 –19.631 –18.609 –17.587 –16.565 –15.541 –14.518 –13.492 –12.466 –11.438 –10.409 –9.3782 –8.3451 –7.3101 –6.2730 –5.2336 –4.1919 –3.1477 –2.1011 –1.0519

hf

Liquid Btu/lb.

83.734 83.534 83.039 82.548 82.061 81.577 81.096 80.617 80.139 79.663 79.188 78.714 78.239 77.764 77.289 76.812 76.333 75.853 75.371 74.885 74.397 73.906 73.411

hfg

Latent Btu/lb.

60.628 60.837 61.365 61.896 62.430 62.968 63.509 64.052 64.598 65.145 65.696 66.248 66.801 67.355 67.911 68.467 69.023 69.580 70.137 70.693 71.249 71.805 72.359

hg

Vapor Btu/lb.

Enthalpy from –40°F

–0.063944 –0.062619 –0.059344 –0.056123 –0.052952 –0.049830 –0.046754 –0.043723 –0.040734 –0.037786 –0.034877 –0.032005 –0.029169 –0.026367 –0.023599 –0.020862 –0.018156 –0.015481 –0.012834 –0.010214 –0.007622 –0.005056 –0.002516

sf

Liquid Btu/ lbm·°R

0.20818 .20711 .20452 .20208 .19978 .19760 0.19554 .19359 .19176 .19002 .18838 0.18683 .18536 .18398 .18267 .18143 0.18027 .17916 .17812 .17714 .17621 0.17533 .17451

sg

Vapor Btu/ lbm·°R

Entropy from –40°F

672 Appendix 2

–40 –38 –36 –34 –32 –30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2 0 2 4 5 6 8 10 12 14

9.3076 9.8035 10.320 10.858 11.417 11.999 12.604 13.233 13.886 14.564 15.267 15.996 16.753 17.536 18.348 19.189 20.059 20.960 21.891 22.854 23.849 24.878 25.939 26.483 27.036 28.167 29.335 30.539 31.780

10.9709a 9.9611a 8.909a 7.814a 6.675a 5.490a 4.259a 2.979a 1.649a 0.270a 0.571 1.300 2.057 2.840 3.652 4.493 5.363 6.264 7.195 8.158 9.153 10.182 11.243 11.787 12.340 13.471 14.639 15.843 17.084

0.010564 .010586 .010607 .010629 .010651 0.010674 .010696 .010719 .010741 .010764 0.010788 .010811 .010834 .010858 .010882 0.010906 .010931 .010955 .010980 .011005 0.011030 .011056 .011082 .011094 .011107 .011134 0.011160 .011187 .011214

3.8750 3.6922 3.5198 3.3571 3.2035 3.0585 2.9214 2.7917 2.6691 2.5529 2.4429 2.3387 2.2399 2.1461 2.0572 1.9727 1.8924 1.8161 1.7436 1.6745 1.6089 1.5463 1.4867 1.4580 1.4299 1.3758 1.3241 1.2748 1.2278

94.661 94.469 94.275 94.081 93.886 93.690 93.493 93.296 93.098 92.899 92.699 92.499 92.298 92.096 91.893 91.689 91.485 91.280 91.074 90.867 90.659 90.450 90.240 90.135 90.030 89.818 89.606 89.392 89.178

0.25806 .27084 .28411 .29788 .31216 0.32696 0.34231 .35820 .37466 .39171 0.40934 .42758 .44645 .46595 .48611 0.50693 .52843 .55063 .57354 .59718 0.62156 .64670 .67263 .68588 .69934 .72687 0.75523 .78443 .81449

0 0.4215 .8434 1.2659 1.6887 2.1120 2.5358 2.9601 3.3848 3.8100 4.2357 4.6618 5.0885 5.5157 5.9434 6.3716 6.8003 7.2296 7.6594 8.0898 8.5207 8.9522 9.3843 9.6005 9.8169 10.250 10.684 11.118 11.554

72.913 72.712 72.511 72.309 72.106 71.903 71.698 71.494 71.288 71.081 70.874 70.666 70.456 70.246 70.036 69.824 69.611 69.397 69.183 68.967 68.750 68.533 68.314 68.204 68.094 67.873 67.651 67.428 67.203

72.913 73.134 73.354 73.575 73.795 74.015 74.234 74.454 74.673 74.891 75.110 75.328 75.545 75.762 75.979 76.196 76.411 76.627 76.842 77.057 77.271 77.485 77.698 77.805 77.911 78.123 78.335 78.546 78.757

0 0.001000 .001995 .002988 .003976 0.004961 .005942 .006919 .007894 .008864 0.009831 .010795 .011755 .012712 .013666 0.014617 .015564 .016508 .017449 .018388 0.019323 .020255 .021184 .021647 .022110 .023033 0.023954 .024871 .025786

0.17373 .17343 .17313 .17285 .17257 0.17229 .17203 .17177 .17151 .17126 0.17102 .17078 .17055 .17032 .17010 0.16989 .16967 .16947 .16927 .16907 0.16888 .16869 .16851 .16842 .16833 .16815 0.16798 .16782 .16765 (continued)

Appendix 2 673

16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62

t

Temp. °F

33.060 34.378 35.736 37.135 38.574 40.056 41.580 43.148 44.760 46.417 48.120 49.870 51.667 53.513 55.407 57.352 59.347 61.394 63.494 65.646 67.853 70.115 72.433 74.807

p

Abs. lb./in.2

18.364 19.682 21.040 22.439 23.878 25.360 26.884 28.452 30.064 31.721 33.424 35.174 36.971 38.817 40.711 42.656 44.651 46.698 48.798 50.950 53.157 55.419 57.737 60.111

pd

Gauge lb./in.2

Pressure

.011241 .011268 0.011296 .011324 .011352 .011380 .011409 0.011438 .011468 .011497 .011527 .011557 .011588 .011619 .011650 .011682 .011714 0.011746 .011779 .011811 .011845 .011879 0.011913 .011947

vf

Liquid ft.3/lb.

1.1828 1.1399 1.0988 1.0596 1.0220 0.98612 .95173 0.91880 .88725 .85702 .82803 .80023 0.77357 .74798 .72341 .69982 .67715 0.65537 .63444 .61431 .59495 .57632 0.55839 .54112

vs

Vapor ft.3/lb.

Volume

88.962 88.746 88.529 88.310 88.091 87.870 87.649 87.426 87.202 86.977 86.751 86.524 86.296 86.066 85.836 85.604 85.371 85.136 84.900 84.663 84.425 84.185 83.944 83.701

1/vf

Liquid lb./ft.3

.84544 .87729 0.91006 .94377 .97843 1.0141 1.0507 1.0884 1.1271 1.1668 1.2077 1.2496 1.2927 1.3369 1.3823 1.4289 1.4768 1.5258 1.5762 1.6278 1.6808 1.7352 1.7909 1.8480

l/vg

Vapor ​ lb./ft.3

Density

Dichlorodifluoromethane (Freon-12): Properties of Liquid and Saturated Vapor

TABLE A.10 (Continued)

11.989 12.426 12.863 13.300 13.739 14.178 14.618 15.058 15.500 15.942 16.384 16.828 17.273 17.718 18.164 18.611 19.059 19.507 19.957 20.408 20.859 21.312 21.766 22.221

hf

Liquid Btu/lb.

66.977 66.750 66.522 66.293 66.061 65.829 65.596 65.361 65.124 64.886 64.647 64.406 64.163 63.919 63.673 63.426 63.177 62.926 62.673 62.418 62.162 61.903 61.643 61.380

hfg

Latent Btu/lb.

78.966 79.176 79.385 79.593 79.800 80.007 80.214 80.419 80.624 80.828 81.031 81.234 81.436 81.637 81.837 82.037 82.236 82.433 82.630 82.826 83.021 83.215 83.409 83.601

hg

Vapor Btu/lb.

Enthalpy from –40°F

.026699 .027608 0.028515 .029420 .030322 .031221 .032118 0.033013 .033905 .034796 .035683 .036569 .037453 .038334 .039213 .040091 .040966 0.041839 .042711 .043581 .04449 .045316 0.046180 .047044

sƒ

Liquid Btu/ lbm·°R

.16750 .16734 0.16719 .16704 .16690 .16676 .16662 .16648 .16635 .16622 .16610 .16598 .16586 .16574 .16562 .16551 .16540 0.16530 .16519 .16509 .16499 .16489 0.16479 .16470

sg

Vapor Btu/ lbm·°R

Entropy from –40°F

674 Appendix 2

64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116

77.239 79.729 82.279 84.888 87.559 90.292 93.087 95.946 98.870 101.86 104.92 108.04 111.23 114.49 117.82 121.22 124.70 128.24 131.86 135.56 139.33 143.18 147.11 151.11 155.19 159.36 163.61

62.543 65.033 67.583 70.192 72.863 75.596 78.391 81.250 84.174 87.16 90.22 93.34 96.53 99.79 103.12 106.52 110.00 113.54 117.16 120.86 124.63 128.48 132.41 136.41 140.49 144.66 148.91

.011982 .012017 .012053 0.012089 .012126 .012163 .012201 .012239 0.012277 .012316 .012356 .012396 .012437 0.012478 .012520 .012562 .012605 .012649 0.012693 .012738 .012783 .012829 .012876 0.012924 .012972 .013022 .013072

.52450 .50848 .49305 0.47818 .46383 .45000 .43666 .42378 0.41135 .39935 .38776 .37657 .36575 0.35529 .34518 .33540 .32594 .31679 0.30794 .29937 .29106 .28303 .27524 0.26769 .26037 .25328 .24641

83.457 83.212 82.965 82.717 82.467 82.215 81.962 81.707 81.450 81.192 80.932 80.671 80.407 80.142 79.874 79.605 79.334 79.061 78.785 78.508 78.228 77.946 77.662 77.376 77.087 76.795 76.501

1.9066 1.9666 2.0282 2.0913 2.1559 2.2222 2.2901 2.3597 2.4310 2.5041 2.5789 2.6556 2.7341 2.8146 2.8970 2.9815 3.0680 3.1566 3.2474 3.3404 3.4357 3.5333 3.6332 3.7357 3.8406 3.9482 4.0584

22.676 23.133 23.591 24.050 24.511 24.973 25.435 25.899 26.365 26.832 27.300 27.769 28.241 28.713 29.187 29.663 30.140 30.619 31.100 31.583 32.067 32.553 33.041 33.531 34.023 34.517 35.014

61.116 60.849 60.580 60.309 60.035 59.759 59.481 59.201 58.917 58.631 58.343 58.052 57.757 57.461 57.161 56.858 56.551 56.242 55.929 55.613 55.293 54.970 54.643 54.313 53.978 53.639 53.296

83.792 83.982 84.171 84.359 84.546 84.732 84.916 85.100 85.282 85.463 85.643 85.821 85.998 86.174 86.348 86.521 86.691 86.861 87.029 87.196 87.360 87.523 87.684 87.844 88.001 88.156 88.310

.047905 .048765 .049624 0.050482 .051338 .052193 .053047 .053900 0.054751 .055602 .056452 .057301 .058149 0.058997 .059844 .06090 .061536 .062381 0.063227 .064072 .064916 .065761 .066606 0.067451 .068296 .069141 .069987

.16460 .16451 .16442 0.16434 .16425 .16417 .16408 .16400 0.16392 .16384 .16376 .16368 .16360 0.16353 .16345 .16338 .16330 .16323 0.16315 .16308 .16301 .16293 .16286 0.16279 .16271 .16264 .16256 (continued)

Appendix 2 675

167.94 172.35 176.85 181.43 186.10 190.86 195.71 200.64 205.67 210.79 216.01 221.32 226.72 232.22 237.82 243.51

p

Abs. lb./in.2

153.24 157.65 162.15 166.73 171.40 176.16 181.01 185.94 190.97 196.09 201.31 206.62 212.02 217.52 223.12 228.81

pd

Gauge lb./in.2

.013123 0.013174 .013227 .013280 .013335 .013390 0.013447 .013504 .013563 .013623 .013684 0.013746 .013810 .013874 .013941 .014008

vf

Liquid ft.3/lb.

.23974 0.23326 .22698 .22089 .21497 .20922 0.20364 .19821 .19294 .18782 .18283 0.17799 .17327 .16868 .16422 .15987

vs

Vapor ft.3/lb.

Volume

76.205 75.906 75.604 75.299 74.991 74.680 75.367 74.050 73.729 73.406 73.079 72.748 72.413 72.075 71.732 71.386

1/vf

Liquid lb./ft.3

4.1713 4.2870 4.4056 4.5272 4.6518 4.7796 4.9107 5.0451 5.1829 5.3244 5.4695 5.6184 5.7713 5.9283 6.0895 6.2551

l/vg

Vapor lb./ft.3

Density

35.512 36.013 36.516 37.021 37.529 38.040 38.553 39.069 39.588 40.110 40.634 41.162 41.693 42.227 42.765 43.306

hf

Liquid Btu/lb.

52.949 52.597 52.241 51.881 51.515 51.144 50.768 50.387 50.000 49.608 49.210 48.805 48.394 47.977 47.553 47.122

hfg

Latent Btu/lb.

88.461 88.610 88.757 88.902 89.044 89.184 89.321 89.456 89.588 89.718 89.844 89.967 90.087 90.204 90.318 90.428

hg

Vapor Btu/lb.

Enthalpy from –40°F

.070833 0.071680 .072528 .073376 .074225 .075075 0.075927 .076779 .077633 .078489 .079346 0.080205 .081065 .081928 .082794 .083661

sƒ

Liquid Btu/ lbm·°R

.16249 0.16241 .16234 .16226 .16218 .16210 0.16202 .16194 .16185 .16177 .16168 0.16159 .16150 .16140 .16130 .16120

sg

Vapor Btu/ lbm·°R

Entropy from –40°F

Source: R. C. Jordan and G.B. Priester, Refrigeration and Air Conditioning, 2nd ed., Prentice Hall, Inc., Upper Saddle River, N.J., 1956. Courtesy of E. I. Dupont de Nemours and Co. a Inches of mercury below one atmosphere.

118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148

t

Temp. °F

Pressure

Dichlorodifluoromethane (Freon-12): Properties of Liquid and Saturated Vapor

TABLE A.10 (Continued)

676 Appendix 2

t Sat. –150 –140 –130 –120 –110 –100 –90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90

s (0.20804) 0.20864 .21205 .21543 .21876 .22205 0.22530 .22851 .23169 .23482 .23793 0.24099 .24403 .24703 .25000 .25294 0.25585 .25873 .26158 .26440 .26719 0.26996 .27270 .27541 .27810 .28076

v (194.91) 196.01 202.37 208.73 215.09 221.44 227.80 234.15 240.50 246.85 253.20 259.54 265.89 272.23 278.58 284.92 291.27 297.61 303.95 310.30 316.64 322.98 329.32 335.66 342.01 348.35

Temp. °F

h (60.656) 60.840 61.916 63.012 64.127 65.261 66.414 67.585 68.774 69.981 71.206 72.447 73.706 74.980 76.271 77.578 78.901 80.239 81.591 82.959 84.341 85.737 87.147 88.570 90.007 91.457

Abs. Pressure 0.14 lb./in.3 Gauge Pressure 29.64 in. vac. (Sat. Temp. –151.7°F) h (61.372) 61.906 63.002 64.118 65.253 66.406 67.578 68.768 69.975 71.200 72.442 73.701 74.976 76.267 77.574 78.897 80.235 81.588 82.955 84.338 85.734 87.144 88.567 90.004 91.454

v (39.38) 141.58 146.04 150.50 154.95 159.40 163.85 168.30 172.75 177.19 181.64 186.09 190.53 194.97 199.42 203.86 208.30 212.74 217.18 221.62 226.07 230.51 234.95 239.39 243.82

0.20617 .20955 .21288 .21618 0.21943 .22264 .22582 .22896 .23206 0.23513 .23816 .24117 .24414 .24708 0.24998 .25286 .25571 .25854 .26133 0.26410 .26684 .26955 .27224 .27490

S (0.20449)

Abs. Pressure 0.20 lb./in.3 Gauge Pressure 29.51 in. vac. (Sat. Temp. –144.9°F)

Dichlorodifluoromethane (Freon-12): Properties of Superheated Vapor

TABLE A.11

72.903 75.139 77.374 79.607 81.839 84.070 86.299 88.527 90.755 92.982 95.207 97.433 99.657 101.88 104.11 106.33 108.55 110.77 113.00 115.22 117.44 119.66 121.88

v (72.756)

62.970 64.088 65.225 66.381 67.554 68.746 69.954 71.181 72.424 73.684 74.960 76.252 77.560 78.884 80.223 81.576 82.945 84.327 85.724 87.135 88.559 89.996 91.447

h (62.897)

0.19810 .20144 .20474 0.20799 .21121 .21439 .21753 .22064 0.22371 .22675 .22976 .23273 .23567 0.23858 .24146 .24431 .24714 .24993 0.25270 .25544 .25816 .26084 .26351

s (0.19788)

Abs. Pressure 0.40 lb./in.3 Gauge Pressure 29.11 in. vac. (Sat. Temp. –130.7°F)

50.020 51.515 53.009 54.502 55.993 57.483 58.972 60.460 61.947 63.433 64.919 66.404 67.889 69.373 70.857 72.340 73.823 75.306 76.789 78.271 79.753 81.235

v (49.786)

64.058 65.197 66.355 67.530 68.723 69.934 71.161 72.406 73.667 74.944 76.238 77.546 78.871 80.210 81.565 82.934 84.317 85.714 87.126 88.550 89.988 91.439

h (63.881)

0.19472 .19802 0.20128 .20451 .20769 .21084 .21395 0.21702 .22006 .22307 .22605 .22899 0.23190 .23479 .23764 .24046 .24326 0.24603 .24877 .25149 .25417 .25684 (continued)

s (0.19419)

Abs. Pressure 0.60 lb./in.3 Gauge Pressure 28.70 in. vac. (Sat. Temp. –121.6°F)

Appendix 2 677

Sat. –110 –100 –90 –80 –70 –60 –50 –40 –30 –20 –10 0 10

t

Temp. °F

t 100 110 120 130 140

(38.051) 38.586 39.710 40.833 41.954 43.074 44.194 45.312 46.429 47.546 48.662 49.778 50.893 52.007

v

(64.624) 65.170 66.329 67.506 68.701 69.913 71.142 72.388 73.650 74.928 76.223 77.533 78.858 80.198

h

(0.19167) 0.19324 0.19651 .19974 .20292 .20608 .20919 0.21227 .21531 .21832 .22130 .22424 0.22716 0.23004

s

Abs. Pressure 0.80 lb./in.2 Gauge Pressure 28.29 in. vac. (Sat. Temp. –114.8°F)

s 0.28340 .28601 .28860 .29116 .29370

v 354.69 361.03 367.37 373.71 380.05

Temp. °F

h 92.920 94.395 95.882 97.382 98.893

Abs. Pressure 0.14 lb./in.3 Gauge Pressure 29.64 in. vac. (Sat. Temp. –151.7°F) h 92.917 94.393 95.880 97.380 98.891

s 0.27754 .28015 .28274 .28530 .28784

(65.229) 66.303 67.482 68.679 68.892 71.123 72.370 73.633 74.913 76.208 77.519 78.845 80.186

31.730 32.631 33.531 34.429 35.327 36.223 37.119 38.014 38.908 39.802 40.695 41.587

h

(30.896)

v

0.19279 .19602 .19922 .20237 .20549 0.20857 .21162 .21463 .21761 .22056 0.22347 .22636

(0.18977)

s

Abs. Pressure 1.00 lb./in.2 Gauge Pressure 27.88 in. vac. (Sat. Temp. –109.3°F)

v 248.26 252.70 257.14 261.58 266.02

Abs. Pressure 0.20 lb./in.3 Gauge Pressure 29.51 in. vac. (Sat. Temp. –144.9°F)

Dichlorodifluoromethane (Freon-12): Properties of Superheated Vapor

TABLE A.11 (Continued)

h 92.910 94.386 95.874 97.374 98.885

s 0.26614 .26876 .27135 .27391 .27645

16.228 16.684 17.139 17.593 18.046 18.498 18.949 19.400 19.850 20.299 20.748

(16.195)

v

67.361 68.567 69.788 71.026 72.279 73.549 74.834 76.134 77.449 78.780 80.125

(67.276)

h

0.18440 .18762 .19079 .19393 0.19703 .20009 .20311 .20611 .20906 0.21199 .21488

(0.18417)

s

Abs. Pressure 2.0 lb./in.2 Gauge Pressure 25.85 in. vac. (Sat. Temp. –90.7°F)

v 124.10 126.32 128.54 130.77 132.99

Abs. Pressure 0.40 lb./in.3 Gauge Pressure 29.11 in. vac. (Sat. Temp. –130.7°F) h 92.902 94.378 95.867 97.367 98.879

s 0.25948 .26209 .26468 .26725 .26979

11.375 11.681 11.986 12.290 12.594 12.897 13.199 13.500 13.802

(11.106)

v

69.683 70.928 72.188 73.463 74.754 76.059 77.379 78.714 80.063

(68.604)

h

0.18394 .18709 0.19021 .19328 .19632 .19932 .20229 0.20523 .20813

(0.18114)

s

Abs. Pressure 3.0 lb./in.2 Gauge Pressure 23.81 in. vac. (Sat. Temp. –78.8°F)

v 82.716 84.197 85.679 87.160 88.641

Abs. Pressure 0.60 lb./in.3 Gauge Pressure 28.70 in. vac. (Sat. Temp. –121.6°F)

678 Appendix 2

Sat. –60 –50 –40 –30 –20 –10 0

t

Temp. °F

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

81.553 82.923 84.307 85.705 87.116 88.541 89.980 91.431 92.895 94.371 95.860 97.361 98.873 100.397 101.932 103.478 105.035

.23290 .23572 .23852 0.24129 .24403 .24675 .24944 .25210 0.25474 .25736 .25995 .26251 .26506 0.26758 .27007 .27255 .27500

(6.9069) 6.9509 7.1378 7.3239 7.5092 7.6938 7.8777 8.0611

v

(70.432) 70.729 72.003 73.291 74.593 75.909 77.239 78.582

h

(0.17759) 0.17834 0.18149 .18459 .18766 .19069 .19368 0.19663

s

Abs. Pressure 5.0 lb./in.2 Gauge Pressure 19.74 in. vac. (Sat. Temp. –62.4°F)

53.121 54.235 55.348 56.461 57.574 58.686 59.799 60.911 62.023 63.134 64.246 65.357 66.468 67.579 68.690 69.801 70.912

81.542 82.912 84.297 85.695 87.107 88.533 89.971 91.423 92.887 94.364 95.853 97.354 98.867 100.391 101.926 103.472 105.030

.22922 .23204 .23484 0.23761 .24036 .24307 .24576 .24843 0.25107 .25368 .25628 .25884 .26139 0.26391 .26640 .26888 .27133

(72.017)

73.073 74.390 75.719 77.061 78.415

4.8401 4.9664 5.0919 5.2169 5.3412

h

(4.7374)

v

0.17755 .18065 .18371 .18673 0.18971

(0.17501)

s

Abs. Pressure 7.5 lb./in.2 Gauge Pressure 14.65 in. vac. (Sat. Temp. –48.1°F)

42.480 43.372 44.263 45.154 46.045 46.936 47.826 48.716 49.606 50.496 51.386 52.275 53.165 54.054 54.943 55.832 56.721

81.484 82.858 84.245 85.646 87.061 88.489 89.930 91.384 92.850 94.329 95.819 97.322 98.836 100.361 101.898 103.445 105.003 106.572 108.151

.21775 .22058 .22339 0.22616 .22891 .23163 .23433 .23700 0.23964 .24226 .24485 .24742 .24997 0.25249 .25499 .25747 .25992 .26236 0.26477

3.6945 3.7906 3.8861 3.9809

(3.6246)

v

74.183 75.526 76.880 78.246

(73.219)

h

0.17557 .17866 .18171 0.18471

(0.17331)

s

Abs. Pressure 10.0 lb./in.2 Gauge Pressure 0.56 in. vac. (Sat. Temp. –37.2°F)

21.197 21.645 22.093 22.540 22.988 23.435 23.881 24.328 24.774 25.220 25.666 26.112 26.558 27.003 27.449 27.894 28.340 28.785 29.230

81.426 82.803 84.194 85.598 87.015 88.445 89.889 91.345 92.813 94.293 95.785 97.289 98.805 100.332 101.869 103.418 104.977 106.547 108.127

.21100 .21384 .21665 0.21944 .22219 .22492 .22762 .23029 0.23293 .23556 .23815 .24073 .24327 0.24580 .24830 .25078 .25324 .25567 0.25808

2.4885 2.5546 2.6201

(2.4835)

v

75.131 76.512 77.902

(75.208)

h

0.17134 .17445 0.17751 (continued)

(0.17111)

s

Abs. Pressure 15 lb./in.2 Gauge Pressure 0.3 lb./in.3 (Sat. Temp. –20.8°F)

14.102 14.403 14.703 15.002 15.302 15.601 15.900 16.198 16.497 16.795 17.093 17.391 17.689 17.987 18.284 18.582 18.879 19.176 19.473

Appendix 2 679

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

t

Temp. °F

8.2441 8.4265 8.6086 8.7903 8.9717 9.1528 9.3336 9.5142 9.6945 9.8747 10.055 10.234 10.414 10.594 10.773 10.952 11.131 11.311 11.489 11.668 11.847 12.026 12.205

v

79.939 81.309 82.693 84.090 85.500 86.922 88.358 89.806 91.266 92.738 94.222 95.717 97.224 98.743 100.272 101.812 103.363 104.925 106.497 108.079 109.670 111.272 112.883

h

.19955 .20244 .20529 .20812 0.21091 .21367 .21641 .21912 .22180 0.22445 .22708 .22968 .23226 .23481 0.23734 .23985 .24233 .24479 .24723 0.24964 .25204 .25441 .25677

s

Abs. Pressure 5.0 lb./in.2 Gauge Pressure 19.74 in. vac. (Sat. Temp. –62.4°F)

5.4650 5.5884 5.7114 5.8340 5.9562 6.0782 6.1999 6.3213 6.4425 6.5636 6.6844 6.8051 6.9256 7.0459 7.1662 7.2863 7.4063 7.5262 7.6461 7.7658 7.8855 8.0651 8.1246 8.2441

v 79.782 81.162 82.555 83.959 85.377 86.806 88.247 89.701 91.166 92.643 94.132 95.632 97.143 98.665 100.198 101.741 103.295 104.859 106.434 108.018 109.612 111.215 112.828 114.451

h .19265 .19556 .19843 .20127 0.20408 .20685 .20960 .21232 .21501 0.21767 .22031 .22292 .22550 .22806 0.23060 .23311 .23560 .23806 .24050 0.24292 .24532 .24770 .25005 .25239

s

Abs. Pressure 7.5 lb./in.2 Gauge Pressure 14.65 in. vac. (Sat. Temp. –48.1°F)

Dichlorodifluoromethane (Freon-12): Properties of Superheated Vapor

TABLE A.11 (Continued)

4.0753 4.1691 4.2626 4.3556 4.4484 4.5408 4.6329 4.7248 4.8165 4.9079 4.9992 5.0903 5.1812 5.2720 5.3627 5.4533 5.5437 5.6341 5.7243 5.8145 5.9046 5.9946 6.0846 6.1745 6.2643

v 79.624 81.014 82.415 83.828 85.252 86.689 88.136 89.596 91.067 92.548 94.042 95.546 97.061 98.586 100.123 101.669 103.226 104.793 106.370 107.957 109.553 111.159 112.774 114.398 116.031

h

.22830 .23080 .23326 .23571 0.23813 0.24054 .24291 .24527 .24761 0.24993

.18768 .19061 .19350 .19635 0.19918 .20197 .20473 .20746 .21016 0.21283 .21547 .21809 .22068 .22325

s

Abs. Pressure 10.0 lb./in.2 Gauge Pressure 0.56 in. vac. (Sat. Temp. –37.2°F)

2.6850 2.7494 2.8134 2.8770 2.9402 3.0031 3.0657 3.1281 3.1902 3.2521 3.3139 3.3754 3.4368 3.4981 3.5592 3.6202 3.6811 3.7419 3.8025 3.8632 3.9237 3.9841 4.0445 4.1049 4.1651

v 79.302 80.712 82.131 83.561 85.001 86.451 87.912 89.383 90.865 92.357 93.860 95.373 96.896 98.429 99.972 101.525 103.088 104.661 106.243 107.835 109.436 111.046 112.665 114.292 115.929

h

.18052 .18349 .18642 .18931 0.19216 .19498 .19776 .20051 .20324 0.20593 .20859 .21122 .21382 .21640 0.21895 .22148 .22398 .22646 .22891 0.23135 0.23375 .23614 .23850 .24085 0.24317

s

Abs. Pressure 15 lb./in.2 Gauge Pressure 0.3 lb./in.3 (Sat. Temp. –20.8°F)

680 Appendix 2

Sat. 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240

t

Temp. °F

(1.8977) 1.9390 1.9893 2.0391 2.0884 2.1373 2.1858 2.2340 2.2819 2.3295 2.3769 2.4241 2.4711 2.5179 2.5645 2.6110 2.6573 2.7036 2.7497 2.7957 2.8416 2.8874 2.9332 2.9789 3.0245 3.0700

v

(76.397) 77.550 78.973 80.403 81.842 83.289 84.745 86.210 87.684 89.168 90.661 92.164 93.676 95.198 96.729 98.270 99.820 101.380 102.949 104.528 106.115 107.712 109.317 110.932 112.555 114.186

h

(0.16969) 0.17222 .17528 .17829 .18126 .18419 0.18707 .18992 .19273 .19550 .19824 0.20095 .20363 .20628 .20890 .21149 0.21405 .21659 .21910 .22159 .22405 0.22649 0.22891 .23130 .23367 .23602

s

Abs. Pressure 20 lb./in.2 Gauge Pressure 5.3 lb./in.2 (Sat. Temp. –8.1°F)

(77.710) 78.566 80.024 81.487 82.956 84.432 85.916 87.407 88.906 90.413 91.929 93.453 94.986 96.527 98.078 99.637 101.204 102.781 104.367 105.961 107.563 109.174 110.794 112.422 114.058

1.5071 1.5468 1.5861 1.6248 1.6632 1.7013 1.7390 1.7765 1.8137 1.8507 1.8874 1.9240 1.9605 1.9967 2.0329 2.0689 2.1048 2.1406 2.1763 2.2119 2.2474 2.2828 2.3182 2.3535

h

(1.4835)

v

0.17033 .17340 .17642 .17939 0.18232 .18520 .18804 .19084 .19361 0.19634 .19904 .20171 .20435 .20695 0.20953 .21208 .21461 .21710 .21958 0.22202 0.22445 .22685 .22923 .23158

(0.16850)

s

Abs. Pressure 26 lb./in.2 Gauge Pressure 11.3 lb./in.2 (Sat. Temp. 4.1°F)

1.2387 1.2717 1.3042 1.3363 1.3681 1.3995 1.4306 1.4615 1.4921 1.5225 1.5528 1.5828 1.6127 1.6425 1.6721 1.7017 1.7311 1.7604 1.7896 1.8187 1.8478 1.8768 1.9057

(1.2198)

v

79.634 81.123 82.616 84.113 85.616 87.124 88.639 90.161 91.690 93.227 94.771 96.323 97.883 99.451 101.027 102.611 104.204 105.805 107.414 109.031 110.656 112.289 113.930

(78.793)

h

0.16939 .17246 .17548 0.17845 .18137 .18424 .18707 .18987 0.19263 .19535 .19803 .20069 .20331 0.20590 .20847 .21100 .21351 .21600 0.21845 0.22089 .22330 .22568 .22804

(0.16763)

s

Abs. Pressure 32 lb./in.2 Gauge Pressure 17.3 lb./in.2 (Sat. Temp. 14.4°F)

0.99865 1.0258 1.0526 1.0789 1.1049 1.1306 1.1560 1.1812 1.2061 1.2309 1.2554 1.2798 1.3041 1.3282 1.3522 1.3761 1.3999 1.4236 1.4472 1.4707 1.4942 1.5176

(0.98743)

v

80.622 82.148 83.676 85.206 86.739 88.277 89.819 91.367 92.920 94.480 96.047 97.620 99.200 100.788 102.383 103.985 105.595 107.212 108.837 110.469 112.109 113.757

(80.000)

h

0.16804 .17112 0.17415 .17712 .18005 .18292 .18575 0.18854 .19129 .19401 .19669 .19933 0.20195 .20453 .20708 .20961 .21210 0.21457 0.21702 .21944 .22183 .22420 (continued)

(0.16676)

s

Abs. Pressure 40 lb./in.2 Gauge Pressure 25.3 lb./in.2 (Sat. Temp. 25.9°F)

Appendix 2 681

v

h

s

Sat. 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

(0.79824) 0.80248 0.82502 .84713 .86886 .89025 .91134 0.93216 .95275 .97313 .99332 1.0133 1.0332 1.0529 1.0725 1.0920

(81.249) 81.540 83.109 84.676 86.243 87.811 89.380 90.953 92.529 94.110 95.695 97.286 98.882 100.485 102.093 103.708

h

(0.16597) 0.16655 0.16966 .17271 .17569 .17862 .18151 0.18434 .18713 .18988 .19259 .19527 0.19791 .20051 .20309 .20563

s

v

0.23835 .24065 .24294 .24520 .24745

t

115.826 117.475 119.131 120.796 122.469

Temp. °F

3.1155 3.1609 3.2063 3.2517 3.2970

Abs. Pressure 50 lb./in.2 Gauge Pressure 35.3 lb./in.2 (Sat. Temp. 38.2°F)

250 260 270 280 290

t

Temp. °F

Abs. Pressure 20 lb./in.2 Gauge Pressure 5.3 lb./in.2 (Sat. Temp. –8.1°F) h 115.703 117.355 119.016 120.684 122.360

s 0.23391 .23623 .23852 .24079 .24304

(82.299) 82.518 84.126 85.729 87.330 88.929 90.528 92.128 93.731 95.336 96.945 98.558 100.176 101.799 103.427

0.67272 .69210 .71105 .72964 .74790 0.76588 .78360 .80110 .81840 .83551 0.85247 .86928 .88596 .90252

h

(0.67005)

v

0.16580 .16892 .17198 .17497 .17791 0.18079 .18362 .18641 .18916 .19186 0.19453 .19716 .19976 .20233

(0.16537)

s

Abs. Pressure 60 lb./in.2 Gauge Pressure 45.3 lb./in.2 (Sat. Temp. 48.6°F)

2.3888 2.4240 2.4592 2.4943 2.5293

v

Abs. Pressure 26 lb./in.2 Gauge Pressure 11.3 lb./in.2 (Sat. Temp. 4.1°F)

Dichlorodifluoromethane (Freon-12): Properties of Superheated Vapor

TABLE A.11 (Continued)

h 115.579 117.235 118.900 120.572 122.251

s 0.23038 .23270 .23500 .23727 .23953

0.51269 .52795 .54281 0.55734 .57158 .58556 .59931 .61286 0.62623 .63943 .65250 .66543

(0.50680)

v

84.640 86.316 87.981 89.640 91.294 92.945 94.594 96.242 97.891 99.542 101.195 102.851

(84.003)

h

0.16571 .16885 .17190 0.17489 .17782 .18070 .18352 .18629 0.18902 .19170 .19435 .19696

(0.16450)

s

Abs. Pressure 80 lb./in.2 Gauge Pressure 65.3 lb./in.2 (Sat. Temp. 66.2°F)

1.9346 1.9634 1.9922 2.0209 2.0495

v

Abs. Pressure 32 lb./in.2 Gauge Pressure 17.3 lb./in.2 (Sat. Temp. 14.4°F) h 115.412 117.074 118.744 120.421 122.105

s 0.22655 .22888 .23118 .23347 .23573

0.41876 0.43138 .44365 .45562 .46733 .47881 0.49009 .50118 .51212 .52291

(0.40674)

v

86.964 88.694 90.410 92.116 93.814 95.507 97.197 98.884 100.571 102.257

(85.351)

h

0.16685 0.16996 .17300 .17597 .17888 .18172 0.18452 .18726 .18996 .19262

(0.16389)

s

Abs. Pressure 100 lb./in.2 Gauge Pressure 85.3 lb./in.2 (Sat. Temp. 80.8°F)

1.5409 1.5642 1.5874 1.6106 1.6337

v

Abs. Pressure 40 lb./in.2 Gauge Pressure 25.3 lb./in.2 (Sat. Temp. 25.9°F)

682 Appendix 2

Sat. 100 110 120 130 140 150 160 170 180

t

Temp. °F

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340

105.330 106.958 108.593 110.235 111.883 113.539 115.202 116.871 118.547 120.231 121.921 123.618 125.321 127.032 128.749

.20815 0.21064 .21310 .21553 .21794 .22032 0.22268 .22502 .22733 .22962 .23189 0.23414 .23637 .23857 .24076

(0.33886) 0.34655 .35766 .36841 .37884 .38901 0.39896 .40870 .41826 .42766

v

(86.459) 87.675 89.466 91.237 92.992 94.736 96.471 98.199 99.922 101.642

h

(0.16340) 0.16559 .16876 .17184 .17484 .17778 0.18065 .18346 .18622 .18892

s

Abs. Pressure 120 lb./in.2 Gauge Pressure 105.3 lb./in.2 (Sat. Temp. 93.3°F)

1.1114 1.1307 1.1499 1.1690 1.1880 1.2070 1.2259 1.2447 1.2636 1.2823 1.3010 1.3197 1.3383 1.3569 1.3754

105.060 106.700 108.345 109.997 111.655 113.319 114.989 116.666 118.350 120.039 121.736 123.438 125.147 126.863 128.585 130.313

.20486 0.20736 .20984 .21229 .21471 .21710 0.21947 .22182 .22414 .22644 .22872 0.23098 .23321 .23543 .23762 .23980

88.448 90.297 92.120 93.923 95.709 97.483 99.247 101.003

0.29548 .30549 .31513 .32445 0.33350 .34232 .35095 .35939

h (87.389)

(0.28964)

v

0.16486 .16808 .17120 .17423 0.17718 .18007 .18289 .18566

(0.16299)

s

Abs. Pressure 140 lb./in.2 Gauge Pressure 125.3 lb./in.2 (Sat. Temp. 104.4°F)

.91896 0.93531 .95157 .96775 .98385 .99988 1.0159 1.0318 1.0476 1.0634 1.0792 1.0949 1.1106 1.1262 1.1418 1.1574

104.511 106.174 107.841 109.513 111.190 112.872 114.559 116.251 117.949 119.652 121.361 123.075 124.795 126.521 128.253 129.990

.19953 0.20207 .20458 .20706 .20951 .21193 0.21432 .21669 .21903 .22135 .22364 0.22592 .22817 .23039 .23260 .23479

0.22863 .23710 0.24519 .25297 .26047 .26775

(0.22276)

v

90.179 92.136 94.053 95.940 97.803 99.647

(88.857)

h

0.16454 .16783 0.17100 .17407 .17705 .17995

(0.16228)

s

Abs. Pressure 180 lb./in.2 Gauge Pressure 165.3 lb./in.2 (Sat. Temp. 123.4°F)

.67824 0.69095 .70356 .71609 .72853 .74090 0.75320 .76544 .77762 .78975 .80183 0.81386 .82586 .83781 .84973 .86161

103.944 105.633 107.324 109.018 110.714 112.415 114.119 115.828 117.540 119.258 120.980 122.707 124.439 126.176 127.917 129.665

.19524 0.19782 .20036 .20287 .20535 .20780 0.21022 .21261 .21497 .21731 .21962 0.22191 .22417 .22641 .22863 .23083

0.17957 0.18746 .19487 .20190 .20861

(0.17917)

v

90.043 92.156 94.203 96.199 98.157

(89.937)

h

0.16179 0.16528 .16861 .17181 .17489 (continued)

(0.16161)

s

Abs. Pressure 220 lb./in.2 Gauge Pressure 205.3 lb./in.2 (Sat. Temp. 139.5°F)

.53358 0.54413 .55457 .56492 .57519 .58538 0.59549 .60554 .61553 .62546 .63534 0.64518 .65497 .66472 .67444 .68411

Appendix 2 683

.43692 0.44606 .45508 .46401 .47284 .48158 0.49025 .49885 .50739 .51587 .52429 0.53267 .54100 .54929 .55754 .56575 0.57393 .58208 .59019 .59829 .60635

v

103.359 105.076 106.792 108.509 110.227 111.948 113.670 115.396 117.125 118.857 120.593 122.333 124.077 125.825 127.578 129.335 131.097 132.863 134.634 136.410 138.191

h

.19159 0.19421 .19679 .19934 .20185 .20432 0.20677 .20918 .21157 .21393 .21626 0.21856 .22084 .22310 .22533 .22754 0.22973 .23190 .23405 .23618 .23829

s .36769 0.37584 .38387 .39179 .39961 .40734 0.41499 .42257 .43008 .43753 .44492 0.45226 .45955 .46680 .47400 .48117 0.48831 .49541 .50248 .50953 .51654

v 102.754 104.501 106.245 107.987 109.728 111.470 113.212 114.956 116.701 118.449 120.199 121.953 123.709 125.470 127.233 129.001 130.773 132.548 134.328 136.112 137.901

h .18838 0.19104 .19367 .19625 .19879 .20130 0.20377 .20621 .20862 .21100 .21335 0.21567 .21797 .22024 .22249 .22471 0.22692 .22910 .23125 .23339 .23551

s

Abs. Pressure 140 lb./in.2 Gauge Pressure 125.3 lb./in.2 (Sat. Temp. 104.4°F)

.27484 0.28176 .28852 .29516 .30168 .30810 0.31442 .32066 .32682 .33292 .33895 0.34492 .35084 .35672 .36255 .36834 0.37409 .37980 .38549 .39114 .39677 0.40237 .40794

v 101.475 103.291 105.098 106.896 108.689 110.478 112.263 114.046 115.828 117.610 119.392 121.174 122.958 124.744 126.531 128.321 130.113 131.909 133.707 135.509 137.314 139.122 140.934

h .18279 0.18556 .18828 .19095 .19357 .19614 0.19868 .20117 .20363 .20605 .20845 0.21081 .21314 .21545 .21772 .21998 0.22220 .22441 .22659 .22875 .23088 0.23300 .23509

s

Abs. Pressure 180 lb./in.2 Gauge Pressure 165.3 lb./in.2 (Sat. Temp. 123.4°F)

.21506 0.22130 .22735 .23324 .23900 .24463 0.25015 .25557 .26091 .26617 .27136 0.27648 .28155 .28657 .29153 .29645 0.30134 .30618 .31099 .31576 .32051 0.32523 .32992

v

100.084 101.986 103.869 105.735 107.589 109.432 111.267 113.095 114.919 116.738 118.555 120.369 122.183 123.996 125.809 127.623 129.438 131.255 133.073 134.893 136.715 138.540 140.368

h

.17788 0.18079 .18362 .18638 .18909 .19175 0.19435 .19691 .19942 .20190 .20434 0.20674 .20912 .21146 .21377 .21605 0.21830 .22053 .22274 .22492 .22708 0.22921 .23133

s

Abs. Pressure 220 lb./in.2 Gauge Pressure 205.3 lb./in.2 (Sat. Temp. 139.5°F)

Source: R. C. Jordan and G. B. Priester, Refrigeration and Air Conditioning, 2nd ed., Prentice Hall, Inc., Upper Saddle River, N.J. 1956. Courtesy of E. I. Dupont de Nemours and Co.

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410

t

Temp. °F

Abs. Pressure 120 lb./in.2 Gauge Pressure 105.3 lb./in.2 (Sat. Temp. 93.3°F)

Dichlorodifluoromethane (Freon-12): Properties of Superheated Vapor

TABLE A.11 (Continued)

684 Appendix 2

60 50

80

100

140

200

300

400

600 500

800

1000

1400

2000

3000

1.0

1.4

30

2

3

4

6 5

8

10

14

20

30

40

20

100

60

ENTROPY in Btu/(lb.)(oR)

10

80

60

0

10

40

20

10

20 30

0

20

40

40

80

20

60

120

100

140

160

30

50

200

40

60

100

80

40

70

60

SCALE CHANGE

50

60 70 80 90

180

220

WILMINGTON, DELAWARE 19898

“FREON” PRODUCTS DIVISION

E. I. DU PONT DE NEMOURS & COMPANY (INC.)

VOLUME in cu ft/lb

TEMPERATURE in oF.

70

20

20

80

40

60

40

80

100

60

120

80

90

140

160

180

220 200

100

90 100

120

140

160

100

180

110

PressureEnthalpy Diagram for Freon-12

200

110

220

240

280

120

260

120

300

130

8

340

360

130

380

1 0.019 0.

320

ENTHALPY (Btu/lb above Saturated Liquid at – 40oF)

0

0.13

233.6

80

0.14

SCALE CHANGE 50

“FREON” 12

UID

LIQ

UR A TED

SAT

AT E UR SAT

5000

PRESSURE (PSIA)

40

Y

T QU ALIT

STAN

CON

R DV AP O

30

5

20

6

10

0.2

5

0.1 0.2

0

7

10

0.2

7

9

0.1 6 CO EN NST TR A N OP T Y 8 0.2

0.1

0.2

4000

20

0 0.3

30

400

140

1 140

0.3

Pressure–Enthalpy Diagram for Freon-12

420

440

9

0.1

460

150

500

560

170

4 0.3

0.2

2

190

180

3000

300

400

80

100

1.4

2

3

6 5 4

1.0 190

70.0

5 0.3 50.0

30.0

20.0

8

14 10

10.0 14.0

20

7.0

30

40

60 50

5.0

3.0

2.0

1.4

1.000 100

0.700 140

0.500 200

0.300

0.100 1000 800 0.140 600 0.200 500

0.070 1400

0.050 2000

0.040

3 0.2 5000 0.025 4000 0.030

CONSTANT VOLUME

180

700 680 660 640 620 600 580

1 0.2

170

Copyright, 1955 and 1956, E. I. du Pont de Nemours & Company

160

3 0.3

540

160

520

0 0.2 0.021

480

150

2

NT TA RE NS TU CO PERA M TE 0.3

TABLE A.12

Appendix 2 685

Acetylene Air Ammonia Argon Butane Carbon dioxide Carbon monoxide Ethane Ethylene Helium Hydrogen Methane Nitrogen Octane Oxygen Propane Water vapor

Gas

NH3 Ar C4H10 CO2 CO C2H6 C2H4 He H2 CH4 N2 C8H18 O2 C3H8 H2O

C2H2

Chemical Formula

Gas Constant Values

TABLE A.13

26.02 28.97 17.024 39.94 58.12 44.01 28.01 30.07 28.052 4.003 2.016 16.04 28.016 114.14 32.000 44.094 18.016

Molecular Weight

R

59.39 53.34 90.7 38.68 26.58 35.10 55.16 51.38 55.07 386.0 766.4 96.35 55.15 13.53 48.28 35.04 85.76

ft. lb. lb.°R Btu at 77ϒF lb.ϒ ϒR 0.361 0.240 0.52 0.124 0.415 0.202 0.249 0.427 0.411 1.25 3.420 0.532 0.248 0.409 0.219 0.407 0.445

cp

English Units cp

0.285 0.171 0.404 0.075 0.381 0.157 0.178 0.361 0.340 0.753 2.434 0.403 0.177 0.392 0.157 0.362 0.335

Btu at 77ϒF lb.ϒ ϒR 1.27 1.40 1.29 1.667 1.09 1.29 1.40 1.18 1.21 1.667 1.405 1.32 1.40 1.044 1.39 1.124 1.33

cv

k,

cp 0.31955 0.28700 0.48802 0.20813 0.14304 0.18892 0.29683 0.27650 0.29637 2.07703 4.12418 0.51835 0.29680 0.07279 0.25983 0.18855 0.46152

1.5116 1.0052 2.1773 0.5207 1.7164 0.8464 1.0411 1.7662 1.5482 5.1926 14.3193 2.2537 1.0404 1.7113 0.9190 1.6794 1.8649

cp

kJ kg ⋅°K

R

kJ kg ⋅ °K

SI Units cv

1.1933 0.7180 1.6916 0.3124 1.5734 0.6573 0.7441 1.4897 1.2518 3.1156 10.1919 1.7354 0.7434 1.6385 0.6590 1.4909 1.4031

kJ kg ⋅ °K

686 Appendix 2

687

Appendix 2

TABLE A.14 Critical Constants Substance

Formula

Molecular Weight

Ammonia Argon Bromine Carbon dioxide Carbon monoxide Chlorine Deuterium (normal) Helium Helium3 Hydrogen (normal) Krypton Neon Nitrogen Nitrous oxide Oxygen Sulfur dioxide Water Xenon Benzene n-Butane Carbon tetrachloride Chloroform Dichlorodifluoromethane Dichlorofluoromethane Ethane Ethyl alcohol Ethylene n-Hexane Methane Methyl alcohol Methyl chloride Propane Propene Propyne Trichlorofluoromethane

NH3 A Br2 CO2 CO Cl2 D2 He He H2 Kr Ne N2 N2O O2 SO2 H2O Xe C6H6 C4H10 CCl4 CHCl3 CCl2F2 CHC12F C2H5 C2H5OH C2H4 C6H14 CH4 CH3OH CH3Cl C3H8 C3H6 C3H4 CCl3F

17.03 39.944 159.832 44.01 28.01 70.914 4.00 4.003 3.00 2.016 83.7 20.183 28.016 44.02 32.00 64.06 18.016 131.3 78.11 58.120 153.84 119.39 120.92 102.93 30.068 46.07 28.052 86.172 16.042 32.04 50.49 44.094 42.078 40.062 137.38

Temperature

Pressure

K

°R

atm

lbf/in.2

405.5 151 584 304.2 133 417 38.4 5.3 3.34 33.3 209.4 44.5 126.2 309.7 154.8 430.7 647.4 289.75 562 425.2 556.4 536.6 384.7 451.7 305.5 516.0 282.4 507.9 191.1 513.2 416.3 370.0 365.0 401 471.2

729.8 272 1052 547.5 240 751 69.1 9.5 6.01 59.9 376.9 80.1 227.1 557.4 278.6 775.2 1165.3 521.55 1012 765.2 1001.5 965.8 692.4 813.0 549.8 929.0 508.3 914.2 343.9 923.7 749.3 665.9 656.9 722 848.1

111.3 48.0 102 72.9 34.5 76.1 16.4 2.26 1.15 12.8 54.3 26.9 33.5 71.7 50.1 77.8 218.3 58.0 48.6 37.5 45.0 54.0 39.6 51.0 48.2 63.0 50.5 29.9 45.8 78.5 65.9 42.0 45.6 52.8 43.2

1636 705 1500 1071 507 1120 241 33.2 16.9 188.1 798 395 492 1054 736 1143 3208 852 714 551 661 794 582 749 708 926 742 439 673 1154 968 617 670 776 635

Volume ft.3/lb. mole 1.16 1.20 2.17 1.51 1.49 1.99 0.926 1.04 1.48 0.668 1.44 1.54 1.25 1.95 0.90 1.90 4.17 4.08 4.42 3.85 3.49 3.16 2.37 2.68 1.99 5.89 1.59 1.89 2.29 3.20 2.90 3.97

Source: G. J. Van Wylen and R. E. Sonntag, Fundamentals of Classical Thermodynamics, John Wiley & Sons, Inc., New York, 1965, p. 579, with permission.

psia

7.417 9.851 12.885 14.659 16.620 18.784 21.163 23.772 26.625 29.739 33.129 36.810 40.800 45.115 49.771 54.787 60.180 65.963 72.167

Temp. °F

–40 –30 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60

Pressure

0.0113 0.0115 0.0116 0.0117 0.0117 0.0118 0.0119 0.0119 0.0120 0.0121 0.0122 0.0123 0.0124 0.0124 0.0125 0.0126 0.0127 0.0128 0.0129

Liquid vf 5.7904 4.4366 3.4471 3.0525 2.7115 2.4155 2.1580 1.9327 1.7355 1.5620 1.4090 1.2737 1.1538 1.0472 0.9523 0.8675 0.7916 0.7234 0.6622

Vapor vg

Volume ft.3/lb.

88.31 87.31 86.30 85.79 85.28 84.76 84.23 83.70 83.17 82.63 82.08 81.52 80.96 80.40 79.82 79.24 78.64 78.04 77.43

Liquid 1/vf 0.1727 0.2254 0.2901 0.3276 0.3688 0.4140 0.4634 0.5174 0.5762 0.6402 0.7097 0.7851 0.8667 0.9549 1.0501 1.1527 1.2633 1.3823 1.5102

Vapor 1/vg

Density lb./ft.3

HFC-134a Saturation Properties—Temperature Table

TABLE A.15

0.0 3.0 6.0 7.5 9.0 10.6 12.1 13.7 15.2 16.8 18.4 20.0 21.6 23.2 24.8 26.4 28.0 29.7 31.4

Liquid hf 97.2 95.7 94.2 93.4 92.6 91.8 91.0 90.2 89.4 88.5 87.7 86.8 85.9 85.0 84.1 83.1 82.1 81.2 80.2

Latent hfg 97.2 98.7 100.2 100.9 101.7 102.4 103.1 103.9 104.6 105.3 106.0 106.7 107.4 108.1 108.8 109.5 110.2 110.9 111.5

Vapor hg

Enthalpy Btu/lb.

0.0000 0.0070 0.0139 0.0174 0.0208 0.0241 0.0275 0.0308 0.0342 0.0375 0.0408 0.0440 0.0473 0.0505 0.0538 0.0570 0.0602 0.0634 0.0666

Liquid sf

0.2316 0.2297 0.2281 0.2274 0.2267 0.2261 0.2255 0.2250 0.2244 0.2240 0.2235 0.2231 0.2227 0.2223 0.2220 0.2217 0.2214 0.2211 0.2208

Vapor sg

Entropy Btu/(lb.) (°R)

–40 –30 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60

Temp. °F

688 Appendix 2

78.803 85.890 93.447 101.494 110.050 119.138 128.782 138.996 149.804 161.227 173.298 186.023 213.572 244.068 277.721 314.800 355.547 400.280 449.384 503.361 563.037 582.316

0.0130 0.0131 0.0132 0.0134 0.0135 0.0136 0.0137 0.0139 0.0140 0.0142 0.0143 0.0145 0.0148 0.0152 0.0157 0.0162 0.0168 0.0176 0.0186 0.0201 0.0232 0.0259

0.6069 0.5570 0.5119 0.4709 0.4337 0.3999 0.3690 0.3408 0.3149 0.2912 0.2695 0.2494 0.2139 0.1835 0.1573 0.1344 0.1143 0.0964 0.0800 0.0645 0.0474 0.0394

76.81 76.18 75.54 74.89 74.22 73.54 72.84 72.13 71.40 70.66 69.89 69.10 67.46 65.70 63.81 61.74 59.45 56.83 53.73 49.73 43.19 38.65

1.6477 1.7952 1.9536 2.1234 2.3056 2.5009 2.7102 2.9347 3.1754 3.4337 3.7110 4.0089 4.6745 5.4491 6.3584 7.4390 8.7470 10.3750 12.4962 15.5155 21.1071 25.3583

33.0 34.7 36.4 38.1 39.9 41.6 43.4 45.1 46.9 48.7 50.5 52.4 56.2 60.0 64.0 68.1 72.4 76.9 81.8 87.3 94.4 98.4

79.1 78.1 77.0 75.9 74.8 73.6 72.4 71.2 69.9 68.6 67.3 65.9 63.0 59.9 56.5 52.7 48.5 43.7 38.0 30.7 18.9 11.1

112.2 112.8 113.4 114.0 114.6 115.2 115.8 116.3 116.9 117.4 117.9 118.3 119.2 119.9 120.5 120.8 120.9 120.7 119.8 118.0 113.4 109.5

Source: Thermodynamic Properties of HFC-134a. With permission of E. I. Du Pont de Nemours and Co.

65 70 75 80 85 90 95 100 105 110 115 120 130 140 150 160 170 180 190 200 210 213

0.0698 0.0729 0.0761 0.0792 0.0824 0.0855 0.0886 0.0918 0.0949 0.0981 0.1012 0.1043 0.1106 0.1170 0.1234 0.1299 0.1366 0.1435 0.1508 0.1589 0.1693 0.1750

0.2206 0.2203 0.2201 0.2199 0.2196 0.2194 0.2192 0.2190 0.2188 0.2185 0.2183 0.2181 0.2175 0.2168 0.2160 0.2150 0.2137 0.2119 0.2093 0.2054 0.1976 0.1915

65 70 75 80 85 90 95 100 105 110 115 120 130 140 150 160 170 180 190 200 210 213

Appendix 2 689

42.91845 44.05286 45.04505 46.08295 47.16981

48.30918 49.26108 50.25126 51.28205 52.35602

53.47594 54.64481 55.55556 56.81818 57.80347

58.82353 59.88024 60.97561

–50 –40 –30 –20 –10

0 10 20 30 40

50 60 70 80 90

100 110 120

v

0.01065 37.87879 38.61004 38.68254 40.81633 41.84100

–97.6 –97.6 –90 –80 –70 –60

Temp °F

h

124.3 126.4 128.4

114.4 116.3 118.3 120.2 122.3

105.0 106.8 108.7 110.5 112.4

96.3 98.0 99.7 101.4 103.2

–16.6 88.5 89.7 91.3 92.9 94.6

0.3259 0.3296 0.3332

0.3073 0.3111 0.3148 0.3186 0.3223

0.2880 0.2919 0.2958 0.2997 0.3035

0.2679 0.2720 0.2761 0.2801 0.2841

–0.0426 0.2478 0.2511 0.2554 0.2596 0.2638

s

0.2046 0.2069 0.2092

0.1930 0.1953 0.1977 0.2000 0.2023

0.1809 0.1834 0.1858 0.1882 0.1906

0.1686 0.1711 0.1736 0.1760 0.1785

0.2813 0.1570 0.1588 0.1612 0.1637 0.1662

Cp

Pressure = 1.00 psia

1.1059 1.1046 1.1033

1.1134 1.1118 1.1103 1.1088 1.1073

1.1226 1.1206 1.1187 1.1169 1.1151

1.1342 1.1317 1.1292 1.1269 1.1247

1.5295 1.1488 1.1462 1.1429 1.1398 1.1370

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16

vs

548.5 553.1 557.7

525.0 529.8 534.5 539.3 543.9

500.2 505.3 510.3 515.2 520.1

474.0 479.3 484.7 489.9 495.1

3163.1 447.2 451.6 457.3 463.0 468.5

SAT LIQ SAT VAP

150 160

100 110 120 130 140

50 60 70 80 90

0 10 20 30 40

–53 –53 –50 –40 –30 –20 –10

Temp °F

v

12.77139 12.98701

11.70960 11.91895 12.13592 12.34568 12.56281

10.62699 10.84599 11.06195 11.27396 11.49425

9.55110 9.76563 9.98004 10.20408 10.41667

0.01116 8.37521 8.44595 8.66551 8.88889 9.10747 9.32836

h

134.7 136.8

124.1 126.2 128.3 130.4 132.5

114.1 116.1 118.0 120.0 122.1

104.7 106.5 108.4 110.3 112.2

–3.8 95.2 95.7 97.5 99.2 101.0 102.8

0.3124 0.3159

0.2943 0.2980 0.3016 0.3052 0.3088

0.2756 0.2794 0.2832 0.2869 0.2906

0.2561 0.2601 0.2640 0.2679 0.2718

–0.0093 0.2343 0.2356 0.2398 0.2439 0.2480 0.2521

s

0.2166 0.2187

0.2056 0.2078 0.2100 0.2122 0.2144

0.1945 0.1968 0.1990 0.2012 0.2034

0.1835 0.1857 0.1879 0.1901 0.1923

0.2929 0.1726 0.1732 0.1752 0.1772 0.1793 0.1814

Cp

Pressure = 5.00 psia Cp/Cv

1.1013 1.1001

1.1084 1.1068 1.1054 1.1040 1.1026

1.1172 1.1152 1.1134 1.1116 1.1100

1.1289 1.1263 1.1238 1.1215 1.1193

1.5071 1.1471 1.1458 1.1418 1.1382 1.1349 1.1318

vs

569.5 574.0

546.5 551.2 555.9 560.5 565.0

522.3 527.3 532.2 537.0 541.8

496.5 501.8 507.0 512.2 517.3

2768.7 466.8 468.6 474.4 480.0 485.6 491.1

690 Appendix 2

h

v

0.01146 4.37445 – 4.48430 4.59770

4.71254 4.82393 4.93583 5.04796 5.15996

5.26870 5.37924 5.48847 5.59910

–29.5 –29.5 –30 –20 –10

0 10 20 30 40

50 60 70 80

Temp. °F

145.9 148.2 –

69.44444 70.42254 –

200 210 200

113.8 115.8 117.8 119.8

104.2 106.1 108.0 109.9 111.8

3.1 98.8 – 100.5 102.3

134.8 137.0 139.2 141.4 143.6

64.10256 64.93506 66.22517 67.11409 68.49315

150 160 170 180 190

130.5 132.7

62.11180 62.89308

130 140

0.2267 0.2288 –

0.2159 0.2181 0.2203 0.2224 0.2246

0.2114 0.2137

0.2616 0.2655 0.2693 0.2731

0.2419 0.2459 0.2499 0.2539 0.2578

0.0074 0.2297 – 0.2336 0.2378

s

0.1966 0.1986 0.2007 0.2027

0.1869 0.1888 0.1906 0.1926 0.1945

0.2996 0.1821 – 0.1836 0.1852

Cp

Pressure = 10.00 psia

0.3613 0.3648 –

0.3439 0.3474 0.3509 0.3544 0.3579

0.3368 0.3404

1.1222 1.1197 1.1175 1.1154

1.1374 1.1338 1.1306 1.1275 1.1247

1.5038 1.1503 – 1.1457 1.1414

Cp/Cv

1.0943 1.0934 –

1.0997 1.0985 1.0974 1.0964 1.0953

1.1020 1.1008

518.9 524.1 529.2 534.2

491.8 497.4 502.9 508.3 513.7

2567.0 474.4 – 480.1 486.0

vs

592.7 597.0 –

571.1 575.5 579.8 584.2 588.5

562.2 566.6

SAT LIQ SAT VAP

0.01167 2.98686 3.01932 3.09885 3.17662 3.25415 3.33111 3.40716 3.48189 3.55745 3.63240 3.70645 3.78072

0 10 20 30 40 50 60 70 80 90

v

14.90313 –

13.83126 14.04494 14.24501 14.47178 14.68429

13.19261 13.40483 13.62398

–14.1 –14.1 –10

Temp. °F

250 260

200 210 220 230 240

170 180 190

113.5 115.4 117.5 119.5 121.5

103.7 105.6 107.6 109.5 111.5

7.8 101.1 101.8

h

157.4 –

145.8 148.0 150.3 152.7 155.0

139.0 141.3 143.5

0.2374 –

0.2272 0.2293 0.2313 0.2334 0.2354

0.2209 0.2230 0.2251

0.2533 0.2571 0.2610 0.2648 0.2686

0.2332 0.2373 0.2414 0.2454 0.2494

0.0180 0.2273 0.2290

s

0.1987 0.2005 0.2024 0.2043 0.2063

0.1906 0.1920 0.1935 0.1952 0.1969

0.3043 0.1888 0.1893

Cp

Pressure = 15.00 psia

0.3468 –

0.3299 0.3333 0.3367 0.3401 0.3435

0.3194 0.3229 0.3264

1.1274 1.1245 1.1218 1.1193 1.1169

1.1467 1.1420 1.1378 1.1340 1.1306

1.5047 1.1543 1.1520

Cp/Cv

1.0907 –

1.0955 1.0945 1.0935 1.0925 1.0916

1.0989 1.0977 1.0966

(continued)

515.5 520.8 526.1 531.3 536.4

486.9 492.8 498.7 504.4 510.0

2437.1 478.1 480.7

vs

612.6 –

591.5 595.8 600.0 604.3 608.4

578.4 582.8 587.2

Appendix 2 691

5.81734 5.92417 6.03500 6.14251 6.25000

6.35728 6.46412 6.57030 6.68003 6.78887

6.89180 6.99790 7.10732 7.21501 7.32064

7.42942 7.53580 7.63942 7.74593

100 110 120 130 140

150 160 170 180 190

200 210 220 230 240

250 260 270 280

v

5.70776

Temp. °F

90

h

157.2 159.6 162.0 164.5

145.6 147.9 150.2 152.5 154.9

134.5 136.7 138.9 141.1 143.3

123.9 125.9 128.0 130.2 132.3

121.8

0.3332 0.3366 0.3399 0.3432

0.3162 0.3196 0.3231 0.3265 0.3298

0.2987 0.3022 0.3057 0.3093 0.3127

0.2805 0.2842 0.2879 0.2915 0.2951

0.2768

s

0.2379 0.2398 0.2418 0.2437

0.2278 0.2298 0.2319 0.2339 0.2359

0.2174 0.2195 0.2216 0.2237 0.2257

0.2069 0.2090 0.2111 0.2132 0.2153

0.2048

Cp

Pressure = 10.00 psia

1.0918 1.0908 1.0899 1.0890

1.0970 1.0959 1.0948 1.0938 1.0928

1.1034 1.1020 1.1007 1.0994 1.0982

1.1115 1.1097 1.1080 1.1064 1.1049

1.1134

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

vs

611.4 615.6 619.7 623.8

590.0 594.3 598.6 602.9 607.2

567.6 572.1 576.7 581.1 585.6

544.0 548.8 553.6 558.3 563.0

539.1

4.21941 4.29185 4.36300 4.43656 4.50857 4.58085 4.65333 4.72367 4.79616 4.86618 4.93827 5.01002 5.08130 5.15198 5.22466

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290

v 3.85356 3.92773 4.00160 4.07332 4.14594

100 110 120 130 140

Temp °F

h

157.1 159.5 161.9 164.4 166.8

145.5 147.7 150.1 152.4 154.7

134.3 136.5 138.7 140.9 143.2

123.6 125.7 127.8 130.0 132.1

0.3252 0.3285 0.3319 0.3352 0.3385

0.3081 0.3116 0.3150 0.3184 0.3218

0.2905 0.2941 0.2977 0.3012 0.3047

0.2723 0.2760 0.2797 0.2833 0.2869

s

0.2383 0.2403 0.2422 0.2441 0.2460

0.2284 0.2304 0.2324 0.2344 0.2363

0.2183 0.2203 0.2223 0.2244 0.2264

0.2082 0.2102 0.2122 0.2142 0.2163

Cp

Pressure = 15.00 psia Cp/Cv

1.0929 1.0919 1.0910 1.0900 1.0891

1.0986 1.0974 1.0962 1.0951 1.0940

1.1056 1.1041 1.1026 1.1012 1.0999

1.1147 1.1127 1.1108 1.1090 1.1072

vs

610.2 614.4 618.6 622.8 626.9

588.4 592.8 597.2 601.6 605.9

565.6 570.3 574.9 579.4 584.0

541.4 546.4 551.3 556.1 560.9

692 Appendix 2

2.58799 2.64550 2.70270 2.76014 2.81690

2.87274 2.92826 2.98418 3.03951 3.09502

3.14961 3.20513 3.26052 3.31455 3.36927

3.42349 3.47826 3.53232 3.58680

50 60 70 80 90

100 110 120 130 140

150 160 170 180 190

200 210 220 230

v

0.01184 2.27635 2.29095 2.35183 2.41196 2.47158 2.52972

–2.4 –2.4 0 10 20 30 40

Temp. °F

h

145.3 147.6 149.9 152.3

134.1 136.3 138.5 140.8 143.0

123.4 125.5 127.6 129.7 131.9

113.1 115.1 117.2 119.2 121.3

11.4 102.8 103.3 105.2 107.2 109.1 111.1

0.3024 0.3058 0.3093 0.3127

0.2847 0.2883 0.2918 0.2954 0.2989

0.2664 0.2701 0.2738 0.2775 0.2811

0.2472 0.2511 0.2550 0.2588 0.2626

0.0259 0.2258 0.2268 0.2310 0.2351 0.2392 0.2432

s

0.2290 0.2310 0.2329 0.2349

0.2192 0.2211 0.2231 0.2251 0.2270

0.2096 0.2115 0.2134 0.2153 0.2172

0.2009 0.2025 0.2042 0.2060 0.2078

0.3081 0.1943 0.1945 0.1955 0.1966 0.1979 0.1994

Cp

Pressure = 20.00 psia Cp/Cv

1.1002 1.0988 1.0976 1.0964

1.1078 1.1061 1.1045 1.1030 1.1015

1.1181 1.1158 1.1136 1.1116 1.1097

1.1329 1.1295 1.1263 1.1233 1.1206

1.5071 1.1585 1.1569 1.1510 1.1457 1.1410 1.1368

vs

586.9 591.4 595.8 600.2

563.6 568.4 573.1 577.7 582.3

538.8 543.9 549.0 553.9 558.8

511.9 517.5 523.0 528.4 533.6

2338.7 480.2 481.8 488.2 494.3 500.3 506.2

SAT LIQ SAT VAP

1.69319 1.73340 1.77336 1.81291 1.85185 1.89107 1.92938 1.96773 2.00562 2.04332 2.08117 2.11864 2.15610 2.19346 2.23015 2.26706 2.30415 2.34082 2.37756 2.41429

50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240

v 0.01211 1.54895 1.56863 1.61082 1.65235

15.4 15.4 20 30 40

Temp. °F

h

145.0 147.3 149.6 152.0 154.4

133.7 135.9 138.2 140.4 142.7

122.9 125.0 127.2 129.3 131.5

112.4 114.5 116.6 118.7 120.8

16.9 105.4 106.3 108.3 110.4

0.2941 0.2976 0.3011 0.3045 0.3079

0.2764 0.2800 0.2835 0.2871 0.2906

0.2578 0.2616 0.2653 0.2690 0.2727

0.2383 0.2423 0.2462 0.2501 0.2540

0.0377 0.2239 0.2259 0.2301 0.2342

s

0.2303 0.2321 0.2340 0.2359 0.2378

0.2210 0.2228 0.2247 0.2265 0.2284

0.2124 0.2141 0.2157 0.2175 0.2192

0.2056 0.2068 0.2080 0.2094 0.2109

0.3142 0.2032 0.2033 0.2039 0.2046

Cp

Pressure = 30.00 psia Cp/Cv

1.1034 1.1019 1.1004 1.0990 1.0977

1.1125 1.1105 1.1085 1.1067 1.1050

1.1253 1.1223 1.1196 1.1171 1.1147

1.1451 1.1403 1.1360 1.1321 1.1285

1.5132 1.1670 1.1635 1.1566 1.1505

vs

(continued)

583.7 588.4 593.0 597.5 602.0

559.6 564.6 569.5 574.3 579.0

533.5 538.9 544.2 549.4 554.6

504.6 510.7 516.6 522.4 528.0

2189.7 482.1 485.3 491.9 498.4

Appendix 2 693

0.01233 1.17606 1.17925 1.21242

1.24471 1.27665 1.30787 1.33887 1.36930

1.39958 1.42939 1.45900 1.48832 1.51745

29 29 30 40

50 60 70 80 90

100 110 120 130 140

122.4 124.5 126.7 128.9 131.1

111.7 113.8 116.0 118.1 120.2

21.2 107.3 107.5 109.6

h

v

Temp. °F

169.2

3.96354

300

154.6 157.0 159.4 161.8 164.2 166.7

h

3.64033 3.69413 3.74813 3.80228 2.85654 3.91083

v

240 250 260 270 280 290

Temp.°F

0.2482

0.2368 0.2387 0.2407 0.2426 0.2445 0.2464

Cp

0.2515 0.2554 0.2592 0.2629 0.2666

0.2316 0.2357 0.2398 0.2437 0.2477

0.0467 0.2228 0.2232 0.2275

s

0.2155 0.2168 0.2183 0.2198 0.2213

0.2108 0.2114 0.2122 0.2131 0.2142

0.3194 0.2106 0.2106 0.2105

Cp

Pressure = 40.00 psia

0.3360

0.3161 0.3195 0.3228 0.3261 0.3295 0.3328

s

Pressure = 20.00 psia

1.1331 1.1294 1.1260 1.1229 1.1201

1.1589 1.1525 1.1468 1.1417 1.1372

1.5200 1.1756 1.1748 1.1663

Cp/Cv

1.0891

1.0952 1.0941 1.0930 1.0920 1.0910 1.0901

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

528.1 533.8 539.4 544.9 550.3

497.0 503.6 510.0 516.2 522.2

2075.7 482.3 483.0 490.2

vs

630.0

604.6 608.9 613.2 617.5 621.7 625.9

vs

SAT LIQ SAT VAP

0.01253 0.94805 0.97494 1.00180 1.02807 1.05396 1.07933 1.10436 1.12905 1.15354 1.17772 1.20178 1.22534 1.24891 1.27226

40.2 40.2 50 60 70 80 90 100 110 120 130 140 150 160 170

v

2.63227 2.66809 2.70416

300 310 320

Temp. °F

2.52334 2.55951 2.59605

2.45038

250 270 280 290

v

Temp. °F

132.9 135.2 137.5

121.8 124.0 126.2 128.5 130.7

24.9 108.9 111.0 113.1 115.3 117.5 119.7

h

169.0 171.5 174.0

161.6 164.0 166.5

156.7

h

0.2489 0.2507 0.2526

0.2434 0.2452 0.2471

0.2396

Cp

0.2655 0.2691 0.2728

0.2465 0.2504 0.2542 0.2580 0.2617

0.0539 0.2220 0.2262 0.2304 0.2345 0.2386 0.2426

s

0.2250 0.2265 0.2280

0.2187 0.2197 0.2209 0.2222 0.2235

0.3239 0.2172 0.2166 0.2165 0.2167 0.2172 0.2178

Cp

Pressure = 50.00 psia

0.3279 0.3312 0.3344

0.3180 0.3213 0.3246

0.3113

s

Pressure = 30.00 psia

1.1226 1.1198 1.1171

1.1416 1.1370 1.1329 1.1292 1.1258

1.5271 1.1844 1.1748 1.1663 1.1589 1.1524 1.1467

Cp/Cv

1.0910 1.0900 1.0890

1.0941 1.0930 1.0920

1.0965

Cp/Cv

551.4 556.8 562.1

522.5 528.6 534.5 540.2 545.9

1981.8 481.7 489.0 496.2 503.1 509.8 516.3

vs

628.0 632.2 636.4

615.2 619.5 623.8

606.5

vs

694 Appendix 2

v

49.8 49.8 50 60 70

0.01271 0.79390 0.79428 0.81793 0.84104

h

1.96657 1.99362 2.02102 2.04834 –

300 310 320 330 340

Temp. °F

168.7 171.2 173.8 176.3 –

1.82849 1.85598 1.88359 1.91131 1.93911

250 260 270 280 290

28.0 110.2 110.2 112.4 114.6

156.5 158.9 161.3 163.8 166.2

144.7 147.0 149.3 151.7 154.1

1.68890 1.71674 1.74520 1.77305 1.80050

200 210 220 230 240

133.3 135.6 137.8 140.1 142.4

1.54655 1.57505 1.60359 1.63212 1.66058

150 160 170 180 190

0.2496 0.2514 0.2532 0.2550 –

0.2406 0.2424 0.2442 0.2460 0.2478

0.2316 0.2333 0.2351 0.2369 0.2388

0.2229 0.2246 0.2263 0.2280 0.2298

0.0601 0.2214 0.2215 0.2258 0.2300

s 0.3282 0.2232 0.2232 0.2222 0.2217

Cp

Pressure = 60.00 psia

0.3221 0.3254 0.3286 0.3319 –

0.3054 0.3088 0.3122 0.3155 0.3188

0.2882 0.2917 0.2952 0.2986 0.3020

0.2703 0.2739 0.2775 0.2811 0.2847

1.5343 1.1934 1.1932 1.1820 1.1725

Cp /Cv

1.0928 1.0917 1.0907 1.0897 –

1.0989 1.0976 1.0963 1.0951 1.0939

1.1068 1.1050 1.1034 1.1018 1.1003

1.1174 1.1150 1.1127 1.1106 1.1086

1901.3 480.5 480.6 488.5 496.0

vs

626.1 630.3 634.6 638.8 –

604.0 608.5 612.9 617.4 621.7

580.6 585.4 590.1 594.8 599.4

555.5 560.7 565.8 570.8 575.7

SAT LIQ SAT VAP

1.45518 1.47754 1.50015 1.52230 1.54440 1.56691 1.58907 1.61108 1.63292 1.65508 1.67701

250 260 270 280 290 300 310 320 330 340 350

58.3 58.3 60 70 80

0.01288 0.68236 0.68601 0.70691 0.72717

v

1.34174 1.36444 1.38735 1.41004 1.43266

200 210 220 230 240

Temp. °F

1.29550 1.31874

180 190

30.8 111.3 111.7 114.0 116.2

h

181.2

168.5 171.0 173.6 176.1 178.7

156.2 158.6 161.1 163.5 166.0

144.4 146.7 149.1 151.4 153.8

139.7 142.0

0.2590

0.2503 0.2521 0.2538 0.2555 0.2573

0.2415 0.2433 0.2450 0.2468 0.2485

0.2329 0.2346 0.2363 0.2380 0.2398

0.2296 0.2312

0.0655 0.2209 0.2217 0.2260 0.2302

s

0.3321 0.2288 0.2285 0.2272 0.2264

Cp

Pressure = 70.00 psia

0.3338

0.3176 0.3208 0.3241 0.3273 0.3306

0.3008 0.3042 0.3076 0.3109 0.3142

0.2835 0.2870 0.2905 0.2940 0.2974

0.2764 0.2799

1.5417 1.2026 1.2002 1.1880 1.1777

Cp/Cv

1.0893

1.0947 1.0935 1.0924 1.0913 1.0903

1.1014 1.0999 1.0985 1.0972 1.0959

1.1103 1.1083 1.1064 1.1046 1.1030

1.1147 1.1124

1830.2 478.9 480.3 488.5 496.3 (continued)

vs

645.5

624.1 628.4 632.8 637.0 641.3

601.5 606.1 610.7 615.2 619.6

577.4 582.3 587.2 592.0 596.8

567.3 572.4

Appendix 2 695

0.90728 0.92868 0.94967 0.97040 0.99098

1.01133 1.03135 1.05130 1.07101 1.09075

1.11012 1.12943 1.14903 1.16795 1.18723

1.20627 1.22519 1.24409 1.26295 1.28172

1.30039

100 110 120 130 140

150 160 170 180 190

200 210 220 230 240

250 260 270 280 290

300

v

0.86356 0.88566

80 90

Temp. °F

h

168.3

156.0 158.4 160.8 163.3 165.8

144.0 146.4 148.8 151.1 153.5

132.5 134.8 137.1 139.4 141.7

121.3 123.5 125.8 128.0 130.3

116.9 119.1

0.3138

0.2970 0.3004 0.3038 0.3071 0.3105

0.2796 0.2831 0.2866 0.2901 0.2936

0.2614 0.2651 0.2688 0.2724 0.2760

0.2422 0.2462 0.2500 0.2539 0.2577

0.2342 0.2382

s

0.2510

0.2425 0.2442 0.2459 0.2476 0.2493

0.2343 0.2359 0.2375 0.2391 0.2408

0.2271 0.2284 0.2298 0.2312 0.2327

0.2222 0.2229 0.2237 0.2247 0.2258

0.2215 0.2217

Cp

Pressure = 60.00 psia

1.0966

1.1040 1.1024 1.1008 1.0993 1.0979

1.1139 1.1117 1.1096 1.1076 1.1057

1.1282 1.1248 1.1218 1.1189 1.1163

1.1509 1.1453 1.1403 1.1359 1.1318

1.1643 1.1572

Cp /Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

vs

622.0

598.9 603.7 608.4 613.0 617.5

574.2 579.3 584.3 589.2 594.1

547.1 552.8 558.3 563.7 569.0

516.7 523.2 529.4 535.5 541.4

503.2 510.1 0.76628 0.78524 0.80386 0.82217 0.84034 0.85807 0.87573 0.89326 0.91058 0.92773 0.94473 0.96172 0.97847 0.99512 1.01184 1.02828 1.04482 1.06135 1.07747 1.09385 1.11012 1.12625

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310

v 0.74694

90

Temp. °F

h

168.1 170.6

155.7 158.1 160.6 163.1 165.6

143.7 146.1 148.5 150.9 153.3

132.1 134.4 136.7 139.0 141.4

120.7 123.0 125.3 127.5 129.8

118.5

0.3106 0.3139

0.2937 0.2971 0.3005 0.3039 0.3072

0.2762 0.2798 0.2833 0.2868 0.2903

0.2579 0.2617 0.2654 0.2690 0.2726

0.2385 0.2425 0.2464 0.2503 0.2541

0.2344

s

0.2517 0.2534

0.2435 0.2451 0.2467 0.2484 0.2501

0.2357 0.2372 0.2387 0.2403 0.2419

0.2293 0.2304 0.2316 0.2329 0.2343

0.2259 0.2262 0.2267 0.2274 0.2283

0.2260

Cp

Pressure = 70.00 psia Cp/Cv

1.0986 1.0972

1.1067 1.1049 1.1032 1.1015 1.1000

1.1177 1.1152 1.1128 1.1106 1.1086

1.1341 1.1302 1.1266 1.1234 1.1205

1.1611 1.1543 1.1484 1.1431 1.1383

1.1688

vs

620.0 624.6

596.4 601.2 606.0 610.8 615.4

570.9 576.2 581.4 586.4 591.5

542.8 548.7 554.4 560.0 565.5

510.8 517.6 524.2 530.6 536.8

503.7

696 Appendix 2

h

0.66020 0.67741 0.69430 0.71083 0.72711

0.74322 0.75896 0.77465 0.79020 0.80548

0.82068 0.83577 0.85063

100 110 120 130 140

150 160 170 180 190

200 210 220

143.4 145.8 148.2

131.7 134.0 136.3 138.7 141.0

120.2 122.5 124.8 127.1 129.4

33.3 112.3 113.2 115.6 117.9

v

0.01304 0.59787 0.60580 0.62445 0.64255

65.9 65.9 70 80 90

Temp. °F

181.1 –

1.39334 –

350 360

170.8 173.4 175.9 178.5

1.31891 1.33761 1.35630 1.37457

310 320 330 340 0.2595 –

0.2527 0.2544 0.2561 0.2578

0.2733 0.2768 0.2804

0.2548 0.2586 0.2623 0.2660 0.2696

0.2351 0.2392 0.2432 0.2471 0.2510

0.0703 0.2205 0.2224 0.2267 0.2309

s

0.2372 0.2386 0.2400

0.2316 0.2325 0.2335 0.2347 0.2359

0.2300 0.2298 0.2299 0.2303 0.2308

0.3359 0.2342 0.2333 0.2317 0.2306

Cp

Pressure = 80.00 psia

0.3301 –

0.3171 0.3204 0.3236 0.3268

1.1217 1.1188 1.1162

1.1403 1.1358 1.1318 1.1281 1.1248

1.1723 1.1642 1.1571 1.1508 1.1453

1.5492 1.2120 1.2058 1.1928 1.1818

Cp/Cv

1.0908 –

1.0953 1.0941 1.0930 1.0919

567.6 573.0 578.4

538.4 544.6 550.5 556.4 562.0

504.7 511.9 518.9 525.6 532.1

1766.4 477.0 480.7 489.1 497.1

vs

643.9 –

626.5 630.9 635.3 639.6

SAT LIQ SAT VAP

0.01319 0.53155 0.54416 0.56107 0.57743 0.59333 0.60887 0.62406 0.63906 0.65368 0.66814 0.68236 0.69643 0.71023 0.72401 0.73768 0.75126 0.76470

72.8 72.8 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230

v

1.19033 1.20642 –

350 360 370

Temp. °F

1.14233 1.15835 1.17426

320 330 340

143.1 145.5 147.9 150.3

131.3 133.6 136.0 138.3 140.7

119.6 121.9 124.3 126.6 128.9

35.7 113.1 114.9 117.2

h

180.9 183.5 –

173.1 175.7 178.3 0.2601 0.2618 –

0.2551 0.2567 0.2584

0.2706 0.2742 0.2778 0.2813

0.2520 0.2558 0.2596 0.2633 0.2670

0.2320 0.2361 0.2402 0.2442 0.2481

0.0747 0.2202 0.2234 0.2278

s

0.2387 0.2400 0.2413 0.2426

0.2341 0.2347 0.2355 0.2365 0.2376

0.2344 0.2337 0.2333 0.2333 0.2336

0.3396 0.2395 0.2376 0.2357

Cp

Pressure = 90.00 psia

0.3269 0.3301 –

0.3172 0.3204 0.3237

1.1258 1.1227 1.1197 1.1170

1.1470 1.1418 1.1372 1.1331 1.1293

1.1849 1.1751 1.1666 1.1592 1.1527

1.5568 1.2217 1.2100 1.1964

Cp/Cv

1.0923 1.0913 –

1.0959 1.0947 1.0935

564.2 569.9 575.4 580.8 (continued)

534.0 540.4 546.6 552.6 558.5

498.3 506.0 513.4 520.5 527.4

1708.1 475.0 481.6 490.2

vs

642.3 646.6 –

629.1 633.5 637.9

Appendix 2 697

h

1.03821 1.05230 1.06644

v

350 360 370

0.01333 0.47803 0.47952 0.49552

0.51093 0.52587

79.1 79.1 80 90

100 110

Temp. °F

180.7 183.3 185.9

0.96721 0.98155 0.99582 1.01010 1.02417

300 310 320 330 340

119.0 121.4

37.8 113.9 114.1 116.6

167.9 170.4 172.9 175.5 178.1

155.4 157.9 160.4 162.8 165.3

0.89501 0.90950 0.92404 0.93853 0.95302

250 260 270 280 290

150.6 153.0

h

0.86558 0.88020

v

230 240

Temp. °F

0.2606 0.2623 0.2639

0.2525 0.2541 0.2557 0.2574 0.2590

0.2445 0.2460 0.2476 0.2492 0.2508

0.2414 0.2429

Cp

0.2291 0.2333

0.0787 0.2199 0.2203 0.2248

s

0.2393 0.2379

0.3433 0.2446 0.2442 0.2413

Cp

Pressure = 100.00 psia

0.3241 0.3273 0.3305

0.3078 0.3111 0.3144 0.3176 0.3209

0.2908 0.2943 0.2977 0.3011 0.3044

0.2839 0.2874

s

Pressure = 80.00 psia

1.1989 1.1871

1.5646 1.2317 1.2300 1.2129

Cp/Cv

1.0939 1.0927 1.0916

1.1006 1.0991 1.0977 1.0964 1.0951

1.1094 1.1074 1.1056 1.1038 1.1021

1.1138 1.1115

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

491.7 499.9

1654.2 472.8 473.6 482.9

vs

640.7 645.0 649.4

618.0 622.6 627.2 631.8 636.2

593.8 598.8 603.7 608.5 613.3

583.6 588.8

vs

SAT LIQ SAT VAP

0.85616 0.86904 0.88191 0.89461 0.90728 0.91988 0.93257 0.94518 0.95767

300 310 320 330 340 350 360 370 380

90.5 90.5 100 110 120 130 140

0.01361 0.39689 0.41044 0.42402 0.43710 0.44976 0.46206

v

0.79108 0.80431 0.81746 0.83036 0.84331

250 260 270 280 290

Temp. °F

0.77791

v

240

Temp. °F

41.8 115.3 117.7 120.2 122.6 125.1 127.5

h

180.5 183.1 185.7 188.4

167.6 170.2 172.7 175.3 177.9

155.2 157.6 160.1 162.6 165.1

152.7

h

0.2612 0.2628 0.2644 0.2660

0.2532 0.2548 0.2564 0.2580 0.2596

0.2455 0.2470 0.2485 0.2501 0.2516

0.2441

Cp

0.0858 0.2194 0.2238 0.2282 0.2324 0.2366 0.2407

s

0.3504 0.2546 0.2506 0.2475 0.2453 0.2438 0.2428

Cp

Pressure = 120.00 psia

0.3216 0.3249 0.3280 0.3312

0.3052 0.3086 0.3119 0.3151 0.3184

0.2883 0.2917 0.2951 0.2985 0.3019

0.2848

s

Pressure = 90.00 psia

1.5808 1.2528 1.2326 1.2153 1.2010 1.1890 1.1788

Cp/Cv

1.0955 1.0942 1.0930 1.0919

1.1026 1.1010 1.0995 1.0981 1.0967

1.1122 1.1101 1.1080 1.1061 1.1043

1.1145

Cp/Cv

1557.1 467.9 477.6 487.1 496.0 504.4 512.4

vs

639.0 643.5 647.9 652.3

616.0 620.7 625.4 630.0 634.5

591.2 596.3 601.4 606.3 611.2

586.0

vs

698 Appendix 2

0.54037 0.55451 0.56838

0.58194 0.59527 0.60835 0.62135 0.63416

0.64675 0.65924 0.67155 0.68385 0.69604

0.70806 0.72015 0.73196 0.74388 0.75569

0.76740 0.77906 0.79064 0.80225 0.81387

0.82535 0.83675 0.84818 0.85955 –

120 130 140

150 160 170 180 190

200 210 220 230 240

250 260 270 280 290

300 310 320 330 340

350 360 370 380 390

180.3 182.9 185.6 188.2 –

167.4 170.0 172.5 175.1 177.7

154.9 157.4 159.9 162.4 164.9

142.7 145.1 147.6 150.0 152.4

130.8 133.2 135.6 137.9 140.3

123.7 126.1 128.5

0.3194 0.3226 0.3258 0.3290 –

0.3030 0.3063 0.3096 0.3129 0.3162

0.2859 0.2894 0.2928 0.2962 0.2996

0.2682 0.2718 0.2754 0.2789 0.2825

0.2494 0.2533 0.2570 0.2608 0.2645

0.2375 0.2415 0.2455

0.2618 0.2634 0.2649 0.2665 –

0.2540 0.2555 0.2571 0.2586 0.2602

0.2466 0.2480 0.2495 0.2509 0.2524

0.2403 0.2414 0.2426 0.2439 0.2452

0.2366 0.2370 0.2376 0.2384 0.2393

0.2370 0.2366 0.2365

1.0970 1.0957 1.0945 1.0933 –

1.1047 1.1030 1.1014 1.0999 1.0984

1.1151 1.1128 1.1106 1.1085 1.1066

1.1301 1.1266 1.1234 1.1204 1.1177

1.1541 1.1482 1.1430 1.1383 1.1340

1.1770 1.1683 1.1608

637.4 641.9 646.4 650.8 –

613.9 618.7 623.5 628.2 632.8

588.6 593.9 599.0 604.1 609.0

560.9 566.7 572.3 577.9 583.3

529.4 536.1 542.5 548.8 554.9

507.8 515.3 522.5 0.47405 0.48577 0.49724 0.50860 0.51967 0.53064 0.54139 0.55206 0.56268 0.57307 0.58350 0.59379 0.60394 0.61406 0.62414 0.63408 0.64404 0.65389 0.66375 0.67354 0.68329 0.69300 0.70264 0.71225 0.72192 0.73142

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400

193.3

179.9 182.6 185.2 187.9 190.6

167.0 169.5 172.1 174.7 177.3

154.4 156.8 159.4 161.9 164.4

142.0 144.5 146.9 149.4 151.9

129.9 132.3 134.8 137.2 139.6

0.3315

0.3155 0.3187 0.3220 0.3252 0.3283

0.2990 0.3023 0.3057 0.3090 0.3122

0.2818 0.2853 0.2888 0.2922 0.2956

0.2639 0.2675 0.2712 0.2747 0.2783

0.2447 0.2487 0.2525 0.2564 0.2601

0.2706

0.2629 0.2645 0.2660 0.2675 0.2690

0.2555 0.2570 0.2584 0.2599 0.2614

0.2488 0.2501 0.2514 0.2527 0.2541

0.2437 0.2445 0.2454 0.2465 0.2476

0.2423 0.2421 0.2422 0.2425 0.2430

1.0936

1.1003 1.0988 1.0974 1.0961 1.0948

1.1091 1.1071 1.1052 1.1035 1.1019

1.1212 1.1184 1.1158 1.1134 1.1112

1.1394 1.1351 1.1311 1.1275 1.1243

1.1700 1.1623 1.1555 1.1495 1.1442

656.9

634.1 638.8 643.4 648.0 652.5

609.8 614.8 619.8 624.6 629.4

583.4 588.9 594.2 599.5 604.7

554.0 560.1 566.2 572.0 577.8

520.0 527.3 534.3 541.1 547.6

Appendix 2 699

100.5 100.5 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Temp. °F

0.01388 0.33818 0.35042 0.36266 0.37438 0.38568 0.39662 0.40727 0.41764 0.42779 0.43777 0.44755 0.45714 0.46659 0.47596 0.48520 0.49432 0.50342 0.51235 0.52121 0.53011 0.53888 0.54750 0.55611 0.56478 0.57330 0.58184 0.59028

v

45.3 116.4 118.9 121.4 124.0 126.5 129.0 131.5 133.9 136.4 138.9 141.3 143.8 146.3 148.8 151.3 153.8 156.3 158.8 161.4 163.9 166.5 169.1 171.7 174.3 176.9 179.5 182.2

h

0.0921 0.2190 0.2234 0.2279 0.2322 0.2364 0.2406 0.2446 0.2486 0.2524 0.2563 0.2601 0.2638 0.2675 0.2711 0.2747 0.2782 0.2818 0.2853 0.2887 0.2921 0.2955 0.2989 0.3022 0.3056 0.3089 0.3121 0.3154

s 0.3576 0.2646 0.2593 0.2553 0.2523 0.2502 0.2487 0.2477 0.2472 0.2470 0.2470 0.2473 0.2478 0.2485 0.2492 0.2501 0.2511 0.2522 0.2534 0.2546 0.2558 0.2572 0.2585 0.2599 0.2613 0.2627 0.2641 0.2656

Cp

Pressure = 140.00 psia

1.5980 1.2757 1.2512 1.2307 1.2140 1.2001 1.1884 1.1784 1.1697 1.1622 1.1555 1.1496 1.1443 1.1395 1.1352 1.1313 1.1277 1.1244 1.1214 1.1186 1.1160 1.1136 1.1113 1.1092 1.1073 1.1054 1.1036 1.1020

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

1470.8 462.7 473.2 483.3 492.8 501.7 510.1 518.1 525.7 533.0 540.1 546.9 553.5 559.9 566.1 572.1 578.0 583.8 589.4 594.9 600.3 605.6 610.9 616.0 621.0 626.0 630.9 635.7

vs SAT LIQ SAT VAP

109.5 109.5 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Temp. °F 0.01414 0.29362 0.29426 0.30608 0.31726 0.32792 0.33817 0.34806 0.35767 0.36700 0.37611 0.38504 0.39378 0.40238 0.41085 0.41916 0.42746 0.43554 0.44364 0.45165 0.45954 0.46729 0.47508 0.48281 0.49053 0.49816 0.50566 0.51324

v 48.5 117.3 117.5 120.2 122.8 125.4 128.0 130.5 133.1 135.6 138.1 140.6 143.1 145.7 148.2 150.7 153.2 155.8 158.3 160.9 163.5 166.0 168.6 171.2 173.9 176.5 179.1 181.8

h 0.0977 0.2186 0.2188 0.2235 0.2281 0.2324 0.2367 0.2409 0.2449 0.2489 0.2528 0.2566 0.2604 0.2641 0.2678 0.2715 0.2751 0.2786 0.2821 0.2856 0.2891 0.2925 0.2959 0.2992 0.3026 0.3059 0.3092 0.3124

s 0.3648 0.2748 0.2744 0.2675 0.2624 0.2588 0.2561 0.2541 0.2528 0.2519 0.2515 0.2513 0.2514 0.2517 0.2522 0.2528 0.2536 0.2545 0.2555 0.2565 0.2577 0.2588 0.2601 0.2613 0.2627 0.2640 0.2654 0.2667

Cp

Pressure = 160.00 psia

1.6163 1.3006 1.2988 1.2685 1.2448 1.2258 1.2101 1.1970 1.1859 1.1764 1.1681 1.1608 1.1544 1.1486 1.1435 1.1388 1.1346 1.1308 1.1273 1.1241 1.1211 1.1183 1.1158 1.1134 1.1112 1.1091 1.1071 1.1053

Cp/Cv

1392.4 457.2 457.9 469.6 480.4 490.4 499.7 508.5 516.8 524.7 532.3 539.6 546.7 553.4 560.0 566.4 572.6 578.6 584.5 590.3 595.9 601.4 606.9 612.2 617.4 622.5 627.6 632.5

vs

700 Appendix 2

0.29231 0.30170 0.31073 0.31948 0.32803

0.33629 0.34438 0.35227 0.36006 0.36776

0.37536 0.38278 0.39014 0.39739

150 160 170 180 190

200 210 220 230 240

250 260 270 280

h

152.7 155.2 157.8 160.4

139.9 142.4 145.0 147.5 150.1

126.9 129.6 132.2 134.8 137.3

51.5 118.1 118.8 121.6 124.3

v

0.01439 0.25856 0.26125 0.27221 0.28251

184.8 187.5 190.2 192.9 195.6

0.59866 0.60716 0.61542 0.62375 0.63203

117.7 117.7 120 130 140

Temp. °F

370 380 390 400 410

0.2670 0.2685 0.2700 0.2715 0.2730

1.2722 0.2757 0.2793 0.2828

0.2535 0.2573 0.2611 0.2648 0.2685

0.2331 0.2374 0.2415 0.2456 0.2496

0.1029 0.2182 0.2193 0.2241 0.2287

s

0.2562 0.2569 0.2577 0.2586

0.2556 0.2553 0.2552 0.2554 0.2557

0.2647 0.2615 0.2591 0.2575 0.2563

0.3723 0.2854 0.2831 0.2749 0.2690

Cp

Pressure = 180.00 psia

0.3186 0.3218 0.3250 0.3282 0.3313

1.1420 1.1376 1.1335 1.1298

1.1732 1.1654 1.1586 1.1524 1.1470

1.2361 1.2189 1.2046 1.1925 1.1822

1.6360 1.3280 1.3184 1.2838 1.2572

Cp/Cv

1.1004 1.0989 1.0975 1.0962 1.0949

567.1 573.4 579.6 585.6

532.2 539.7 546.9 553.8 560.6

488.7 498.4 507.5 516.1 524.3

1320.2 451.5 454.6 467.0 478.3

vs

640.4 645.1 649.7 654.3 658.8

SAT LIQ SAT VAP

0.01465 0.23026 0.23544 0.24565 0.25521 0.26428 0.27294 0.28129 0.28930 0.29712 0.30477 0.31217 0.31946 0.32658 0.33360 0.34046 0.34727 0.35398 0.36063

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290

v

0.52067 0.52818 0.53565 0.54301 0.55030 –

125.2 125.2 130 140

Temp. °F

370 380 390 400 410 420

152.1 154.7 157.3 159.9 162.5

139.1 141.7 144.3 146.9 149.5

125.8 128.5 131.2 133.9 136.5

54.3 118.8 120.2 123.0

h

184.5 187.2 189.9 192.6 195.3 –

0.2681 0.2696 0.2710 0.2724 0.2738 –

0.2695 0.2731 0.2767 0.2802 0.2837

0.2505 0.2545 0.2583 0.2621 0.2658

0.2296 0.2340 0.2383 0.2425 0.2466

0.1076 0.2178 0.2202 0.2250

s

0.2590 0.2594 0.2600 0.2607 0.2615

0.2604 0.2595 0.2590 0.2587 0.2588

0.2749 0.2700 0.2664 0.2637 0.2618

0.3801 0.2966 0.2908 0.2816

Cp

Pressure = 200.00 psia

0.3157 0.3189 0.3221 0.3253 0.3284 –

1.1500 1.1448 1.1401 1.1359 1.1320

1.1872 1.1777 1.1694 1.1622 1.1557

1.2678 1.2449 1.2263 1.2110 1.1981

1.6574 1.3582 1.3352 1.2969

Cp/Cv

1.1035 1.1019 1.1003 1.0988 1.0974 –

561.5 568.1 574.6 580.9 587.0 (continued)

524.5 532.5 540.2 547.5 554.6

477.0 487.8 497.8 507.2 516.1

1253.0 445.6 452.3 465.3

vs

637.4 642.2 647.0 651.7 656.3 –

Appendix 2 701

h

0.48015 0.48681 0.49336 –

v

400 410 420 430

0.01517 0.18715 0.18846

0.19819 0.20712 0.21545

138.7 138.7 140

150 160 170

Temp. °F

192.2 195.0 197.7 –

0.44645 0.45325 0.46007 0.46677 0.47344

350 360 370 380 390

123.3 126.3 129.2

59.5 119.8 120.2

178.7 181.4 184.1 186.8 189.5

165.6 168.2 170.8 173.4 176.1

0.41168 0.41873 0.42577 0.43269 0.43964

300 310 320 330 340

163.0

h

0.40461

v

290

Temp. °F

0.2734 0.2748 0.2762 –

0.2666 0.2679 0.2693 0.2706 0.2720

0.2606 0.2617 0.2629 0.2641 0.2653

0.2596

Cp

0.2227 0.2276 0.2322

0.1162 0.2169 0.2176

s

0.3032 0.2924 0.2846

0.3972 0.3214 0.3189

Cp

Pressure = 240.00 psia

0.3227 0.3259 0.3290 –

0.3065 0.3098 0.3131 0.3163 0.3195

0.2897 0.2931 0.2965 0.2999 0.3032

0.2863

s

Pressure = 180.00 psia

1.3589 1.3154 1.2829

1.7064 1.4297 1.4201

Cp/Cv

1.1016 1.1000 1.0986 –

1.1107 1.1086 1.1067 1.1049 1.1032

1.1233 1.1204 1.1177 1.1152 1.1129

1.1264

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

450.9 464.6 476.9

1130.0 433.3 435.4

vs

649.0 653.8 658.5 –

624.2 629.3 634.4 639.3 644.2

597.2 602.8 608.3 613.7 619.0

591.5

vs

SAT LIQ SAT VAP

0.42989 0.43590 0.44191 0.44791 –

400 410 420 430 440

150.6 150.6 160 170 180 190

0.01570 0.15571 0.16463 0.17318 0.18101 0.18832

v

0.39909 0.40532 0.41151 0.41762 0.42375

350 360 370 380 390

Temp. °F

0.36716 0.37365 0.38008 0.38646 0.39282

v

300 310 320 330 340

Temp. °F

64.3 120.5 123.7 126.8 129.9 132.9

h

191.9 194.7 197.4 200.2 –

178.3 181.0 183.7 186.4 189.2

165.1 167.7 170.4 173.0 175.7

h

0.2743 0.2757 0.2770 0.2784 –

0.2679 0.2692 0.2704 0.2717 0.2730

0.2624 0.2634 0.2645 0.2656 0.2667

Cp

0.1238 0.2160 0.2211 0.2262 0.2310 0.2356

s

0.4172 0.3512 0.3275 0.3111 0.2998 0.2916

Cp

Pressure = 280.00 psia

0.3203 0.3235 0.3267 0.3298 –

0.3041 0.3074 0.3107 0.3139 0.3171

0.2872 0.2906 0.2941 0.2974 0.3008

s

Pressure = 200.00 psia

1.7668 1.5212 1.4317 1.3684 1.3235 1.2899

Cp/Cv

1.1044 1.1027 1.1011 1.0996 –

1.1144 1.1121 1.1100 1.1080 1.1061

1.1285 1.1252 1.1222 1.1194 1.1168

Cp/Cv

1018.2 420.5 437.5 453.2 467.1 479.6

vs

646.4 651.3 656.1 660.8 –

620.9 626.2 631.3 636.4 641.5

593.0 598.8 604.5 610.1 615.5

vs

702 Appendix 2

0.22330 0.23083

0.23799 0.24495 0.25165 0.25818 0.26457

0.27079 0.27685 0.28289 0.28878 0.29459

0.30028 0.30593 0.31156 0.31709 0.32253

0.32794 0.33332 0.33866 0.34395 0.34921

0.35443 0.35962 0.36478 0.36990 0.37501 –

180 190

200 210 220 230 240

250 260 270 280 290

300 310 320 330 340

350 360 370 380 390

400 410 420 430 440 450

191.2 194.0 196.8 199.6 202.4 –

177.5 180.3 183.0 185.7 188.5

164.1 166.8 169.5 172.2 174.8

150.9 153.5 156.2 158.8 161.5

137.5 140.2 142.9 145.6 148.2

132.0 134.8

0.3162 0.3194 0.3226 0.3257 0.3289 –

0.2998 0.3031 0.3064 0.3097 0.3130

0.2827 0.2862 0.2896 0.2931 0.2965

0.2646 0.2683 0.2720 0.2756 0.2792

0.2451 0.2492 0.2531 0.2570 0.2609

0.2366 0.2409

0.2764 0.2776 0.2788 0.2801 0.2814 –

0.2706 0.2717 0.2728 0.2740 0.2751

0.2663 0.2670 0.2678 0.2687 0.2696

0.2652 0.2650 0.2651 0.2653 0.2658

0.2716 0.2692 0.2675 0.2664 0.2656

0.2789 0.2747

1.1101 1.1081 1.1063 1.1045 1.1028 –

1.1222 1.1194 1.1169 1.1145 1.1122

1.1396 1.1355 1.1318 1.1283 1.1251

1.1677 1.1608 1.1546 1.1491 1.1441

1.2204 1.2064 1.1945 1.1843 1.1754

1.2575 1.2371

641.1 646.2 651.2 656.2 661.0 –

614.2 619.8 625.3 630.6 635.9

584.3 590.6 596.7 602.7 608.5

550.1 557.4 564.4 571.3 577.9

508.3 517.5 526.2 534.5 542.5

488.1 498.6

0.19519 0.20178 0.20809 0.21413 0.22001 0.22573 0.23127 0.23672 0.24208 0.24728 0.25246 0.25753 0.26250 0.26744 0.27230 0.27712 0.28188 0.28661 0.29128 0.29592 0.30053 0.30509 0.30964 0.31414 0.31862 0.32308 0.32751

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460

204.6 207.4

190.5 193.3 196.1 198.9 201.8

176.7 179.5 182.2 185.0 187.7

163.1 165.9 168.6 171.3 174.0

149.6 152.3 155.0 157.7 160.4

135.7 138.6 141.4 144.1 146.9

0.3285 0.3316

0.3126 0.3158 0.3190 0.3222 0.3253

0.2960 0.2994 0.3027 0.3060 0.3093

0.2787 0.2823 0.2858 0.2892 0.2927

0.2603 0.2641 0.2678 0.2715 0.2751

0.2400 0.2443 0.2484 0.2525 0.2564

0.2843 0.2855

0.2785 0.2796 0.2807 0.2819 0.2831

0.2735 0.2744 0.2753 0.2763 0.2774

0.2706 0.2709 0.2714 0.2720 0.2727

0.2722 0.2713 0.2707 0.2704 0.2704

0.2857 0.2812 0.2778 0.2753 0.2735

1.1059 1.1042

1.1162 1.1138 1.1117 1.1096 1.1077

1.1305 1.1272 1.1241 1.1213 1.1186

1.1519 1.1468 1.1422 1.1379 1.1340

1.1882 1.1791 1.1711 1.1639 1.1576

1.2637 1.2427 1.2254 1.2110 1.1988

661.7 666.6

635.8 641.2 646.4 651.6 656.7

607.5 613.4 619.2 624.8 630.4

575.6 582.3 588.9 595.2 601.4

538.3 546.3 554.0 561.5 568.6

491.1 501.7 511.7 521.0 529.8

Appendix 2 703

0.01627 0.13160 0.13984 0.14815 0.15562

0.16251 0.16893 0.17500 0.18080 0.18638

0.19175 0.19694 0.20198 0.20692 0.21174

0.21648 0.22111 0.22567 0.23016 0.23459

0.23895 0.24327 0.24754 0.25176

200 210 220 230 240

250 260 270 280 290

300 310 320 330 340

350 360 370 380

v

161.3 161.3 170 180 190

Temp. °F

175.9 178.7 181.5 184.2

162.1 164.9 167.6 170.4 173.1

148.3 151.1 153.8 156.6 159.4

133.8 136.8 139.7 142.6 145.5

68.7 120.9 124.1 127.5 130.7

h

0.2927 0.2961 0.2994 0.3028

0.2751 0.2787 0.2823 0.2858 0.2892

0.2563 0.2602 0.2640 0.2678 0.2715

0.2351 0.2396 0.2439 0.2482 0.2523

0.1308 0.2148 0.2200 0.2254 0.2304

s

0.2766 0.2772 0.2780 0.2788

0.2753 0.2752 0.2753 0.2756 0.2760

0.2803 0.2784 0.2771 0.2762 0.2756

0.3043 0.2964 0.2905 0.2861 0.2828

0.4415 0.3889 0.3548 0.3308 0.3152

Cp

Pressure = 320.00 psia

1.1393 1.1354 1.1318 1.1285

1.1655 1.1592 1.1535 1.1483 1.1436

1.2125 1.2003 1.1898 1.1807 1.1727

1.3225 1.2899 1.2644 1.2438 1.2267

1.8437 1.6421 1.5153 1.4254 1.3655

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

600.7 607.0 613.1 619.0

566.8 574.0 581.0 587.7 594.3

526.1 535.0 543.4 551.5 559.3

472.5 484.9 496.3 506.8 516.8

914.5 407.2 425.6 443.4 458.8

vs SAT LIQ SAT VAP

0.01689 0.11237 0.12101 0.12915 0.13633 0.14285 0.14888 0.15458 0.15998 0.16513 0.17007 0.17486 0.17950 0.18402 0.18843 0.19275 0.19698 0.20113 0.20522 0.20925 0.21322 0.21713 0.22100 0.22483

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390

v

171 171 180 190

Temp. °F

175.1 177.9 180.7 183.5 186.3

161.1 163.9 166.7 169.5 172.3

146.9 149.8 152.6 155.5 158.3

131.6 134.9 138.0 141.0 144.0

72.9 120.9 124.6 128.2

h

0.2896 0.2930 0.2964 0.2998 0.3031

0.2718 0.2754 0.2790 0.2826 0.2861

0.2524 0.2565 0.2604 0.2643 0.2680

0.2301 0.2350 0.2396 0.2440 0.2483

0.1373 0.2135 0.2193 0.2249

s

0.2798 0.2803 0.2808 0.2814 0.2821

0.2804 0.2798 0.2795 0.2794 0.2796

0.2898 0.2867 0.2843 0.2825 0.2813

0.3303 0.3164 0.3066 0.2993 0.2939

0.4727 0.4391 0.3841 0.3508

Cp

Pressure = 360.00 psia

1.1488 1.1442 1.1399 1.1360 1.1324

1.1806 1.1728 1.1658 1.1596 1.1539

1.2413 1.2251 1.2114 1.1997 1.1895

1.4071 1.3540 1.3149 1.2847 1.2608

1.9458 1.8089 1.6069 1.4840

Cp/Cv

594.0 600.6 607.0 613.2 619.3

557.9 565.6 573.1 580.3 587.2

513.6 523.4 532.6 541.4 549.8

452.1 466.8 480.0 492.1 503.2

816.6 393.7 415.6 435.3

vs

704 Appendix 2

h

v

0.01759 0.09649 0.09655 0.10650 0.11446

0.12136 0.12755 0.13325 0.13858

0.14362 0.14842 0.15302 0.15746 0.16176

0.16594

179.9 179.9 180 190 200

210 220 230 240

250 260 270 280 290

300

Temp. °F

204.0 206.9 209.7

0.28032 0.28428 0.28823

450 460 470

160.0

145.4 148.4 151.3 154.3 157.1

132.7 136.0 139.3 142.4

76.9 120.7 120.7 125.2 129.1

189.8 192.6 195.5 198.3 201.1

0.26008 0.26419 0.26827 0.27232 0.27633

400 410 420 430 440

187.0

0.25594

390

0.2860 0.2871 0.2883

0.2806 0.2816 0.2827 0.2837 0.2848

0.2797

0.2686

0.2487 0.2529 0.2570 0.2609 0.2648

0.2303 0.2352 0.2399 0.2444

0.1435 0.2119 0.2119 0.2190 0.2249

s

0.2860

0.3011 0.2963 0.2926 0.2898 0.2876

0.3445 0.3278 0.3160 0.3075

0.5155 0.5106 0.5097 0.4139 0.3701

Cp

Pressure = 400.00 psia

0.3254 0.3285 0.3316

0.3094 0.3126 0.3158 0.3190 0.3222

0.3061

1.1974

1.2762 1.2544 1.2364 1.2214 1.2085

1.4457 1.3828 1.3375 1.3031

2.0897 2.0521 2.0487 1.6998 1.5401

Cp/Cv

1.1107 1.1087 1.1069

1.1225 1.1198 1.1173 1.1150 1.1127

1.1254

548.9

500.8 511.6 521.7 531.2 540.3

447.2 462.7 476.6 489.2

722.7 380.0 380.2 408.0 429.3

vs

657.5 662.6 667.6

630.5 636.1 641.6 647.0 652.3

624.8

SAT LIQ SAT VAP

0.02000 0.06538 0.06646 0.07860 0.08669 0.09326 0.09896 0.10410 0.10883 0.11326 0.11744 0.12142 0.12523 0.12891 0.13248 0.13594

199.4 199.4 200 210 220 230 240 250 260 270 280 290 300 310 320 330

v

0.24707 0.25066 0.25425 0.25781

450 460 470 480

Temp. °F

0.22862 0.23237 0.23609 0.23978 0.24343

400 410 420 430 440

157.2 160.2 163.2 166.1

141.3 144.6 147.9 151.0 154.1

86.9 118.1 118.7 125.3 130.0 134.1 137.8

h

203.4 206.3 209.2 212.1

189.1 192.0 194.8 197.7 200.5 0.2877 0.2887 0.2898 0.2909

0.2829 0.2838 0.2847 0.2856 0.2866

0.2614 0.2653 0.2692 0.2730

0.2397 0.2444 0.2489 0.2532 0.2573

0.1584 0.2057 0.2065 0.2164 0.2234 0.2294 0.2348

s

0.3030 0.2998 0.2974 0.2955

0.3416 0.3289 0.3195 0.3125 0.3072

0.7816 0.9822 0.9106 0.5274 0.4325 0.3868 0.3596

Cp

Pressure = 500.00 psia

0.3226 0.3257 0.3288 0.3319

0.3064 0.3097 0.3130 0.3162 0.3194

1.2486 1.2325 1.2188 1.2070

1.4041 1.3561 1.3196 1.2909 1.2677

3.0254 3.6942 3.4381 2.0697 1.7319 1.5687 1.4704

Cp/Cv

1.1156 1.1134 1.1113 1.1093

1.1291 1.1260 1.1231 1.1205 1.1180

526.7 536.4 545.6 554.4 (continued)

467.2 481.1 493.8 505.5 516.4

496.6 345.3 348.6 387.4 413.4 434.1 451.7

vs

653.4 658.7 663.9 669.0

625.3 631.1 636.9 642.5 648.0

Appendix 2 705

0.18546 0.18916 0.19280 0.19639 0.19994

0.20345 0.20692 0.21034 0.21375 0.21712

0.22046 0.22377 0.22706 0.23033 –

350 360 370 380 390

400 410 420 430 440

450 460 470 480 490

202.8 205.7 208.6 211.5 –

188.4 191.3 194.1 197.0 199.9

174.2 177.0 179.9 182.7 185.6

162.9 165.7 168.5 171.4

h

0.3200 0.3232 0.3263 0.3294 –

0.3038 0.3071 0.3103 0.3136 0.3168

0.2867 0.2902 0.2937 0.2971 0.3004

0.2724 0.2760 0.2796 0.2832

s

0.2894 0.2904 0.2914 0.2924 –

0.2853 0.2860 0.2868 0.2876 0.2885

0.2833 0.2834 0.2837 0.2842 0.2847

0.2849 0.2841 0.2836 0.2833

Cp

1.1207 1.1182 1.1159 1.1137 –

1.1360 1.1325 1.1292 1.1262 1.1233

1.1590 1.1535 1.1485 1.1440 1.1399

1.1878 1.1793 1.1717 1.1650

Cp/Cv

649.3 654.8 660.2 665.5 –

620.1 626.2 632.2 638.0 643.7

587.3 594.3 601.0 607.5 613.9

557.2 565.1 572.8 580.2

vs 0.13930 0.14260 0.14582 0.14898 0.15208 0.15513 0.15813 0.16110 0.16402 0.16691 0.16976 0.17259 0.17538 0.17815 0.18090 0.18362 0.18632

350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500

v

340

Temp. °F

216.0

201.2 204.2 207.1 210.1 213.1

186.6 189.5 192.5 195.4 198.3

172.0 174.9 177.9 180.8 183.7

169.1

h

0.3302

0.3143 0.3176 0.3208 0.3239 0.3271

0.2978 0.3012 0.3045 0.3078 0.3111

0.2803 0.2839 0.2874 0.2909 0.2944

0.2767

s

0.2981

0.2940 0.2947 0.2955 0.2963 0.2971

0.2917 0.2920 0.2923 0.2928 0.2934

0.2930 0.2923 0.2918 0.2916 0.2916

0.2940

Cp

Pressure = 500.00 psia

1.1198

1.1341 1.1308 1.1278 1.1249 1.1223

1.1547 1.1499 1.1454 1.1413 1.1376

1.1876 1.1795 1.1723 1.1659 1.1600

1.1966

Cp/Cv

668.0

639.4 645.4 651.2 656.9 662.5

607.6 614.3 620.8 627.1 633.4

571.0 578.8 586.3 593.6 600.7

562.9

vs

Source: Thermodynamic Properties of HFC-134a. With permission of E. I. Du Pont de Nemours and Co. Note: Cp = heat capacity at constant pressure in Btu/(lb.) (°F); Cp/Cv = heat capacity ratio (dimensionless); h = enthalpy in Btu/lb.; s = entropy in Btu/(lb.) (°R); v = volume in ft.3/lb.; vs = velocity of sound in ft./s.

0.17001 0.17399 0.17788 0.18171

v

310 320 330 340

Temp. °F

Pressure = 400.00 psia

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (Continued)

706 Appendix 2

707

Appendix 2

TABLE A.15 (SI) HFC-134a Saturation Properties—Temperature Table Pressure Temp. °C –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 101

Volume m3/kg

Density kg/m3

Enthalpy kJ/kg

Entropy kJ/(kg)(°K)

kPa (abs)

Liquid vf

Vapor. vg

Liquid 1/vf

Vapor. 1/vg

Liquid hf

Latent hfg

Vapor. hg

Liquid sf

Vapor sg

Temp. °C

51.14 66.07 84.29 106.32 132.67 163.90 200.60 243.39 292.93 349.87 414.92 488.78 572.25 666.06 771.02 887.91 1017.61 1161.01 1319.00 1492.59 1682.76 1890.54 2117.34 2364.31 2632.97 2925.11 3242.87 3589.44 3969.94 4051.35

0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0010 0.0010 0.0010 0.0010 0.0011 0.0011 0.0012 0.0013 0.0015 0.0018

0.3614 0.2843 0.2260 0.1817 0.1474 0.1207 0.0996 0.0828 0.0693 0.0583 0.0494 0.0421 0.0360 0.0309 0.0266 0.0230 0.0200 0.0174 0.0151 0.0132 0.0115 0.0100 0.0087 0.0075 0.0065 0.0055 0.0046 0.0037 0.0027 0.0022

1414.6 1400.2 1385.7 1371.0 1356.0 1340.8 1325.3 1309.4 1293.3 1276.7 1259.8 1242.3 1224.4 1205.9 1186.7 1166.8 1146.1 1124.5 1101.8 1077.9 1052.5 1025.3 995.9 963.7 927.8 886.7 837.3 772.3 651.4 566.4

2.767 3.518 4.424 5.504 6.784 8.288 10.044 12.082 14.435 17.140 20.236 23.770 27.791 32.359 37.540 43.413 50.072 57.630 66.225 76.035 87.287 100.283 115.442 133.373 155.010 181.929 217.162 268.255 375.503 457.594

148.4 154.6 160.9 167.3 173.7 180.2 186.7 193.3 200.0 206.8 213.6 220.5 227.5 234.6 241.8 249.2 256.6 264.2 271.9 279.8 287.9 296.2 304.8 313.7 322.9 332.8 343.4 355.6 373.2 383.0

225.9 222.8 219.6 216.4 213.1 209.7 206.2 202.5 198.8 194.9 190.9 186.8 182.5 178.0 173.3 168.3 163.2 157.7 151.9 145.8 139.2 132.1 124.4 115.8 106.3 95.3 82.1 64.9 33.8 13.0

374.3 377.4 380.6 383.7 386.8 389.8 392.9 395.9 398.8 401.7 404.5 407.3 410.0 412.6 415.1 417.5 419.8 421.9 423.8 425.6 427.1 428.3 429.1 429.5 429.2 428.1 425.5 420.5 407.0 396.0

0.7967 0.8231 0.8492 0.8750 0.9005 0.9257 0.9507 0.9755 1.0000 1.0244 1.0485 1.0726 1.0964 1.1202 1.1439 1.1676 1.1912 1.2148 1.2384 1.2622 1.2861 1.3102 1.3347 1.3597 1.3854 1.4121 1.4406 1.4727 1.5187 1.5447

1.7655 1.7586 1.7525 1.747 1.7422 1.7379 1.7341 1.7308 1.7278 1.7252 1.7229 1.7208 1.7189 1.7171 1.7155 1.7138 1.7122 1.7105 1.7086 1.7064 1.7039 1.7009 1.6971 1.6924 1.6863 1.6782 1.6668 1.6489 1.6092 1.5794

–40 –35 –30 –25 –15 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 101

Source: Thermodynamic Properties of HFC-134a. With permission of E. I. Du Pont de Nemours and Co.

v

0.00070 0.45496 – 0.46490 0.47574 0.48662

0.49727 0.50787 0.51867 0.52910 0.53967

0.55036 0.56085 0.57110 0.58173 0.59207

0.60241 0.61312 0.62344 0.63371 0.64392

0.65445 0.66489 0.67522

Temp. °C

–44.57 –44.57 –45 –40 –35 –30

–25 –20 –15 –10 –5

0 5 10 15 20

25 30 35 40 45

50 55 60

447.4 451.9 456.3

425.9 430.1 434.4 438.7 443.0

405.4 409.4 413.5 417.6 421.7

386.0 389.8 393.6 397.5 401.5

142.8 371.4 – 374.8 378.5 382.2

h

2.0494 2.0630 2.0765

1.9801 1.9941 2.0081 2.0219 2.0357

1.9083 1.9229 1.9374 1.9517 1.9659

1.8336 1.8489 1.8639 1.8789 1.8937

0.7722 1.7725 – 1.7871 1.8028 1.8183

s

0.8813 0.8895 0.8977

0.8401 0.8484 0.8566 0.8649 0.8731

0.7988 0.8070 0.8152 0.8235 0.8318

0.7587 0.7665 0.7745 0.7825 0.7906

1.2311 0.7301 – 0.7364 0.7437 0.7511

Cp

Pressure = 40.00 kPa (abs)

1.1055 1.1042 1.1030

1.1128 1.1112 1.1097 1.1082 1.1068

1.1219 1.1199 1.1180 1.1161 1.1144

1.1342 1.1314 1.1288 1.1264 1.1241

1.5059 1.1475 – 1.1440 1.1404 1.1372

Cp/Cv

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI)

169.6 170.9 172.1

163.1 164.4 165.7 167.0 168.3

156.2 157.7 159.0 160.4 161.8

148.9 150.4 151.9 153.4 154.8

831.3 142.8 – 144.3 145.9 147.4

vs SAT LIQ SAT VAP

0.00072 0.23747 0.23872 0.24438 0.24994 0.25549 0.26103 0.26645 0.27196 0.27732 0.28273 0.28810 0.29343 0.29878 0.30404 0.30941 0.31466 0.32000 0.32520 0.33047 0.33568 0.34095 0.34614

–25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

v

–31.09 –31.09 –30

Temp. °C

446.9 451.3 455.8 460.3 464.9

425.2 429.4 433.7 438.1 442.4

404.5 408.5 412.6 416.8 421.0

384.6 388.5 392.4 396.4 400.4

159.5 379.9 380.7

h

1.9916 2.0053 2.0188 2.0323 2.0457

1.9218 1.9359 1.9500 1.9640 1.9778

1.8492 1.8640 1.8786 1.8931 1.9075

1.7730 1.7886 1.8040 1.8192 1.8343

0.8435 1.7538 1.7572

s

0.8865 0.8944 0.9022 0.9100 0.9178

0.8478 0.8555 0.8632 0.8709 0.8787

0.8107 0.8179 0.8252 0.8326 0.8402

0.7783 0.7842 0.7904 0.7969 0.8037

1.2606 0.7718 0.7729

Cp

Cp/Cv

1.1085 1.1071 1.1056 1.1043 1.1030

1.1172 1.1153 1.1135 1.1118 1.1101

1.1290 1.1263 1.1238 1.1215 1.1193

1.1460 1.1420 1.1383 1.1349 1.1318

1.5038 1.1515 1.1505

Pressure = 80.00 kPa (abs)

168.8 170.1 171.4 172.7 173.9

162.1 163.5 164.8 166.2 167.5

154.9 156.4 157.8 159.3 160.7

147.1 148.7 150.3 151.9 153.4

768.3 145.0 145.4

vs

708 Appendix 2

v

0.00073 0.19246 0.19372 0.19829 0.20284 0.20734 0.21182

0.21626 0.22065 0.22502 0.22941 0.23370

0.23804 0.24231

0 5 10 15 20

25 30

0.75758 0.76805 0.77821

100 105 110

–26.34 –26.34 –25 –20 –15 –10 –5

0.70621 0.71633 0.72674 0.73692 0.74738

75 80 85 90 95

Temp. °C

0.68540 0.69589

65 70

424.8 429.1

404.0 408.1 412.2 416.4 420.6

165.6 382.8 383.9 387.9 391.8 395.8 399.9

h

2.1818 2.1947 2.2074

2.1165 2.1297 2.1429 2.1559 2.1689

2.0899 2.1033

0.9613 0.9691 0.9768

0.9219 0.9299 0.9378 0.9457 0.9535

0.9058 0.9138

s

1.9027 1.9169

1.8297 1.8445 1.8593 1.8739 1.8883

0.8681 1.7484 1.7527 1.7685 1.7840 1.7994 1.8146

Cp

0.8517 0.8591

0.8169 0.8235 0.8304 0.8373 0.8445

1.2715 0.7876 0.7888 0.7935 0.7988 0.8045 0.8106

1.1196 1.1175

1.1327 1.1296 1.1269 1.1243 1.1218

1.5046 1.1539 1.1525 1.1477 1.1434 1.1395 1.1359

Cp/Cv

1.0945 1.0936 1.0927

1.0995 1.0985 1.0974 1.0964 1.0954

1.1018 1.1006

Pressure = 100.00 kPa (abs)

493.5 498.3 503.2

470.0 474.6 479.3 484.0 488.7

460.8 465.4

161.6 163.0

154.2 155.7 157.2 158.7 160.1

746.2 145.7 146.1 147.8 149.5 151.1 152.7

vs

181.8 183.0 184.1

175.8 177.0 178.2 179.4 180.6

173.4 174.6

SAT LIQ SAT VAP

0.00074 0.13123 0.13259 0.13576 0.13889 0.14196 0.14503 0.14806 0.15106 0.15404 0.15701 0.15995 0.16289 0.16581

–17.12 –17.12 –15 –10 –5 0 5 10 15 20 25 30 35 40

v

0.37736 0.38256 0.38775 0.39293 0.39809

100 105 110 115 120

Temp. °C

0.35137 0.35663 0.36179 0.36697 0.37216

75 80 85 90 95

423.9 428.2 432.5 436.9

402.7 406.9 411.1 415.3 419.6

177.4 388.5 390.3 394.4 398.5

h

2.1246 2.1375 2.1503 2.1630 2.1757

2.0591 2.0723 2.0855 2.0986 2.1116 0.9640 0.9716 0.9792 0.9867 0.9941

0.9255 0.9333 0.9410 0.9487 0.9564 1.0961 1.0951 1.0942 1.0932 1.0923

1.1017 1.1005 1.0994 1.0982 1.0972

1.8673 1.8817 1.8959 1.9101

1.7931 1.8083 1.8233 1.8381 1.8528

0.9150 1.7397 1.7464 1.7622 1.7778

s

0.8620 0.8685 0.8752 0.8820

0.8333 0.8384 0.8438 0.8496 0.8557

1.2939 0.8201 0.8213 0.8247 0.8287

Cp

1.1257 1.1231 1.1206 1.1183

1.1426 1.1386 1.1350 1.1316 1.1285

1.5081 1.1599 1.1574 1.1519 1.1470

Cp/Cv

Pressure = 150.00 kPa (abs)

493.1 498.0 502.8 507.8 512.7

469.5 474.2 478.8 483.6 488.3

160.2 161.7 163.2 164.6 (continued)

152.4 154.1 155.7 157.2 158.7

703.7 146.5 147.3 149.1 150.8

vs

181.3 182.5 183.6 184.8 186.0

175.2 176.4 177.6 178.9 180.1

Appendix 2 709

0.32216

125

v

0.30139 0.30553 0.30969 0.31387 0.31797

100 105 110 115 120

0.00075 0.09985

0.28043 0.28466 0.28885 0.29300 0.29718

75 80 85 90 95

–10.08 –10.08

0.25940 0.26364 0.26788 0.27203 0.27624

50 55 60 65 70

Temp. °C

0.24661 0.25088 0.25517

v

35 40 45

Temp. °C

186.6 392.8

h

2.1698

2.1060 2.1189 2.1318 2.1445 2.1572

2.0404 2.0537 2.0669 2.0800 2.0930

1.9727 1.9864 2.0001 2.0136 2.0270

1.9310 1.9450 1.9589

s

1.0026

0.9654 0.9729 0.9804 0.9878 0.9952

0.9274 0.9350 0.9427 0.9503 0.9578

0.8892 0.8968 0.9045 0.9121 0.9198

0.8665 0.8741 0.8816

Cp

s

0.9503 1.7342

Cp 1.3124 0.8468

Cp/Cv

1.5125 1.1661

Cp/Cv

1.0921

1.0970 1.0959 1.0949 1.0940 1.0930

1.1028 1.1016 1.1004 1.0992 1.0981

1.1101 1.1085 1.1070 1.1055 1.1042

1.1155 1.1136 1.1118

Pressure = 200.00 kPa (abs)

517.5

492.9 497.8 502.7 507.6 512.5

469.3 473.9 478.6 483.4 488.1

446.6 451.0 455.5 460.1 464.7

433.4 437.7 442.1

h

Pressure = 100.00 kPa (abs)

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

671.3 146.9

vs

186.9

181.0 182.2 183.4 184.6 185.8

174.9 176.1 177.4 178.6 179.8

168.4 169.7 171.0 172.3 173.6

164.3 165.7 167.1

vs

SAT LIQ SAT VAP

0.18587 0.18875 0.19157 0.19440 0.19720 0.20000 0.20284 0.20563 0.20846 0.21124 0.21404 0.21683 0.21964

75 80 85 90 95 100 105 110 115 120 125 130 135

–5.37 –5.37

0.00076 0.08389

v

0.17156 0.17449 0.17734 0.18018 0.18305

50 55 60 65 70

Temp. °C

0.16869

v

45

Temp. °C

198.2 395.6

h

2.1360 2.1486 2.1611

2.0720 2.0850 2.0978 2.1106 2.1234

2.0061 2.0195 2.0327 2.0459 2.0590

1.9380 1.9518 1.9656 1.9792 1.9927

1.9241

s

1.0052 1.0123 1.0195

0.9688 0.9761 0.9834 0.9907 0.9979

0.9322 0.9395 0.9468 0.9541 0.9615

0.8960 0.9032 0.9103 0.9176 0.9249

0.8890

Cp

1.0937 1.0928 1.0919

1.0991 1.0979 1.0968 1.0958 1.0947

1.1057 1.1043 1.1029 1.1016 1.1003

1.1142 1.1123 1.1105 1.1088 1.1072

1.1162

Cp/Cv

0.9736 1.7310

s

1.3254 0.8656

Cp

1.5164 1.1711

Cp/Cv

Pressure = 240.00 kPa (abs)

517.1 522.2 527.2

492.4 497.3 502.2 507.1 512.1

468.7 473.4 478.1 482.8 487.6

445.8 450.3 454.9 459.4 464.0

441.4

h

Pressure = 150.00 kPa (abs)

649.7 147.0

vs

186.4 187.6 188.7

180.4 181.6 182.8 184.0 185.2

174.1 175.3 176.6 177.9 179.1

167.4 168.7 170.1 171.4 172.8

166.0

vs

710 Appendix 2

0.09989 0.10235

0.10478 0.10717 0.10953 0.11186 0.11417

0.11647 0.11874 0.12099 0.12324 0.12547

0.12767 0.12989 0.13207 0.13425 0.13643

0.13860 0.14075 0.14290 0.14505 0.14719

0.14932 0.15145 0.15359 0.15571 0.15783

–10 –5

0 5 10 15 20

25 30 35 40 45

50 55 60 65 70

75 80 85 90 95

100 105 110 115 120

491.9 496.8 501.7 506.7 511.7

468.1 472.8 477.5 482.3 487.1

445.1 449.6 454.2 458.8 463.4

422.9 427.3 431.7 436.1 440.6

401.4 405.6 409.9 414.2 418.5

392.9 397.1

2.0476 2.0606 2.0735 2.0864 2.0991

1.9814 1.9948 2.0082 2.0214 2.0345

1.9129 1.9268 1.9406 1.9543 1.9679

1.8414 1.8560 1.8704 1.8847 1.8989

1.7661 1.7815 1.7968 1.8118 1.8267

1.7344 1.7504

0.9723 0.9794 0.9865 0.9936 1.0007

0.9370 0.9440 0.9511 0.9581 0.9652

0.9031 0.9097 0.9164 0.9232 0.9301

0.8729 0.8784 0.8843 0.8904 0.8967

0.8510 0.8543 0.8583 0.8627 0.8676

0.8468 0.8485

1.1013 1.1000 1.0988 1.0976 1.0965

1.1087 1.1070 1.1055 1.1040 1.1026

1.1185 1.1163 1.1142 1.1122 1.1104

1.1323 1.1291 1.1261 1.1234 1.1208

1.1537 1.1485 1.1438 1.1396 1.1358

1.1660 1.1595

179.7 181.0 182.2 183.4 184.7

173.2 174.6 175.9 177.2 178.4

166.3 167.8 169.2 170.5 171.9

158.9 160.4 162.0 163.4 164.9

150.6 152.3 154.0 155.7 157.3

146.9 148.8

0.08405 0.08615 0.08821 0.09024 0.09224 0.09422 0.09618 0.09812 0.10004 0.10194 0.10383 0.10571 0.10757 0.10942 0.11127 0.11311 0.11494 0.11675 0.11857 0.12038 0.12219 0.12398 0.12577 0.12755 0.12935 0.13111

–5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

491.5 496.4 501.4 506.3 511.3

467.6 472.3 477.1 481.9 486.7

444.5 449.0 453.6 458.3 462.9

422.1 426.5 431.0 435.4 439.9

400.3 404.6 409.0 413.3 417.7

396.0

2.0320 2.0450 2.0579 2.0708 2.0836

1.9656 1.9790 1.9924 2.0057 2.0189

1.8967 1.9107 1.9245 1.9383 1.9520

1.8246 1.8393 1.8539 1.8683 1.8825

1.7482 1.7639 1.7794 1.7947 1.8097

1.7322

0.9752 0.9821 0.9891 0.9960 1.0030

0.9410 0.9478 0.9546 0.9614 0.9683

0.9090 0.9151 0.9214 0.9278 0.9344

0.8820 0.8867 0.8919 0.8973 0.9030

0.8663 0.8680 0.8705 0.8738 0.8776

0.8657

1.1030 1.1017 1.1004 1.0991 1.0979

1.1111 1.1093 1.1076 1.1060 1.1045

1.1220 1.1196 1.1172 1.1151 1.1130

1.1379 1.1341 1.1307 1.1276 1.1247

1.1634 1.1571 1.1515 1.1465 1.1420

1.1706

(continued)

179.2 180.5 181.7 183.0 184.2

172.6 173.9 175.3 176.6 177.9

165.5 167.0 168.4 169.8 171.2

157.8 159.4 161.0 162.5 164.0

149.1 150.9 152.7 154.4 156.1

147.2

Appendix 2 711

v

0.00077 0.07235 0.07281 0.07464 0.07645 0.07822 0.07996

0.08168 0.08338 0.08506 0.08672 0.08837

0.09001 0.09163 0.09325 0.09485 0.09645

–1.24 –1.24 0 5 10 15 20

25 30 35 40 45

50 55 60 65 70

0.15995 0.16207 0.16418 0.16628 –

v

Temp. °C

125 130 135 140 145

Temp. °C

443.9 448.5 453.1 457.7 462.4

421.3 425.8 430.3 434.8 439.3

198.3 398.1 399.2 403.6 408.0 412.4 416.9

h

2.1118 2.1244 2.1370 2.1495 –

s 1.0078 1.0148 1.0218 1.0288 –

Cp

s

1.8827 1.8968 1.9108 1.9246 1.9383

1.8100 1.8249 1.8396 1.8541 1.8685

0.9939 1.7285 1.7325 1.7485 1.7643 1.7797 1.7950

Cp

0.9150 0.9207 0.9266 0.9326 0.9388

0.8915 0.8954 0.8998 0.9045 0.9096

1.3374 0.8830 0.8827 0.8826 0.8835 0.8854 0.8881

Cp/Cv

1.1258 1.1230 1.1204 1.1180 1.1158

1.1438 1.1395 1.1356 1.1320 1.1288

1.5204 1.1762 1.1741 1.1665 1.1598 1.1539 1.1486

Cp/Cv

1.0954 1.0944 1.0934 1.0924 –

Pressure = 280.00 kPa (abs)

516.7 521.8 526.8 532.0 –

h

Pressure = 200.00 kPa (abs)

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

164.7 166.2 167.6 169.1 170.5

156.7 158.3 160.0 161.6 163.1

630.8 147.0 147.5 149.5 151.3 153.2 154.9

vs

185.9 187.1 188.2 189.4 –

vs

SAT LIQ SAT VAP

0.00077 0.06770 0.06921 0.07092 0.07260 0.07424 0.07587 0.07748 0.07906 0.08063 0.08219 0.08372 0.08525 0.08678 0.08829 0.08978

0.66 0.66 5 10 15 20 25 30 35 40 45 50 55 60 65 70

v

0.13291 0.13466 0.13646 0.13824 0.13998 –

125 130 135 140 145 150

Temp. °C

v

Temp. °C

443.6 448.2 452.8 457.5 462.1

420.9 425.4 429.9 434.4 439.0

200.9 399.2 403.1 407.5 412.0 416.4

h

2.0963 2.1090 2.1216 2.1341 2.1465 –

s 1.0099 1.0168 1.0237 1.0306 1.0375 –

Cp 1.0967 1.0956 1.0946 1.0936 1.0926 –

Cp/Cv

1.8764 1.8905 1.9045 1.9184 1.9322

1.8034 1.8183 1.8331 1.8477 1.8621

1.0032 1.7275 1.7415 1.7573 1.7729 1.7883

s

0.9181 0.9236 0.9292 0.9350 0.9411

0.8964 0.8998 0.9038 0.9082 0.9130

1.3431 0.8912 0.8902 0.8904 0.8915 0.8936

Cp

1.1277 1.1247 1.1220 1.1195 1.1171

1.1469 1.1423 1.1381 1.1343 1.1309

1.5225 1.1787 1.1715 1.1642 1.1578 1.1521

Cp/Cv

Pressure = 300.00 kPa (abs)

516.4 521.4 526.5 531.7 536.8 –

h

Pressure = 240.00 kPa (abs)

164.2 165.8 167.3 168.7 170.2

156.1 157.8 159.5 161.1 162.7

622.1 147.0 148.7 150.7 152.5 154.3

vs

185.4 186.7 187.9 189.0 190.2 –

vs

712 Appendix 2

0.11358 0.11511 0.11665 0.11818 0.11969

0.12121

125 130 135 140 145

150

0.00078 0.05998 0.06024 0.06180 0.06333 0.06483

0.06630

4.18 4.18 5 10 15 20

25

v

0.10588 0.10743 0.10897 0.11052 0.11206

100 105 110 115 120

Temp. °C

0.09804 0.09962 0.10118 0.10275 0.10432

75 80 85 90 95

420.1

205.6 401.2 402.0 406.5 411.0 415.5

h

2.1458

2.0831 2.0958 2.1084 2.1209 2.1334

2.0186 2.0317 2.0447 2.0576 2.0704

1.9520 1.9655 1.9789 1.9922 2.0055

1.0460

1.0120 1.0189 1.0257 1.0325 1.0392

0.9781 0.9848 0.9916 0.9984 1.0052

0.9451 0.9516 0.9581 0.9647 0.9714

1.7911

1.0204 1.7256 1.7283 1.7444 1.7602 1.7758

s

0.9066

1.3541 0.9069 0.9064 0.9047 0.9043 0.9050

Cp

1.1535

1.5266 1.1838 1.1823 1.1736 1.1660 1.1594

Cp/Cv

1.0927

1.0981 1.0969 1.0958 1.0947 1.0937

1.1049 1.1034 1.1020 1.1006 1.0993

1.1137 1.1117 1.1098 1.1081 1.1064

Pressure = 340.00 kPa (abs)

541.7

516.0 521.1 526.2 531.4 536.5

491.1 496.1 501.0 506.0 511.0

467.1 471.8 476.6 481.4 486.3

154.9

605.9 146.8 147.2 149.2 151.2 153.1

vs

191.0

185.0 186.2 187.5 188.7 189.9

178.7 180.0 181.2 182.5 183.8

171.9 173.3 174.7 176.0 177.3

SAT LIQ SAT VAP

0.10585 0.10730 0.10873 0.11017 0.11158 0.11301 0.11442

125 130 135 140 145 150 155

0.00079 0.05384 0.05459 0.05600 0.05738 0.05874 0.06007

7.4 7.4 10 15 20 25 30

v

0.09863 0.10009 0.10153 0.10299 0.10444

100 105 110 115 120

Temp. °C

0.09128 0.09276 0.09424 0.09571 0.09718

75 80 85 90 95

419.2 423.8

210.0 403.1 405.5 410.1 414.6

h

2.1399 2.1523

2.0772 2.0899 2.1025 2.1151 2.1275

2.0126 2.0257 2.0387 2.0516 2.0645

1.9458 1.9594 1.9728 1.9862 1.9994

1.0468 1.0535

1.0131 1.0199 1.0266 1.0334 1.0401

0.9796 0.9862 0.9929 0.9996 1.0064

0.9472 0.9535 0.9599 0.9664 0.9730

1.0932 1.0922

1.0988 1.0976 1.0964 1.0953 1.0943

1.1058 1.1042 1.1028 1.1014 1.1001

1.1149 1.1129 1.1110 1.1091 1.1074

1.7799 1.7952

1.0360 1.7240 1.7325 1.7486 1.7644

s

0.9174 0.9188

1.3645 0.9218 0.9200 0.9178 0.9170

Cp

1.1604 1.1544

1.5308 1.1890 1.1838 1.1750 1.1672

Cp/Cv

Pressure = 380.00 kPa (abs)

541.6 546.9

515.9 520.9 526.1 531.2 536.4

490.9 495.9 500.8 505.8 510.8

466.9 471.6 476.4 481.2 486.1

153.7 155.6 (continued)

591.1 146.6 147.8 149.8 151.8

vs

190.9 192.1

184.8 186.0 187.3 188.5 189.7

178.4 179.7 181.0 182.3 183.5

171.6 173.0 174.4 175.7 177.1

Appendix 2 713

0.06776 0.06919 0.07060 0.07200

0.07339 0.07476 0.07612 0.07747 0.07880

0.08013 0.08146 0.08280 0.08410 0.08540

0.08669 0.08800 0.08929 0.09058 0.09184

0.09314 0.09440 0.09568 0.09696 0.09822

50 55 60 65 70

75 80 85 90 95

100 105 110 115 120

125 130 135 140 145

v

30 35 40 45

Temp. °C

515.5 520.6 525.7 530.9 536.1

490.5 495.5 500.4 505.4 510.4

466.4 471.1 475.9 480.8 485.6

442.9 447.6 452.2 456.9 461.6

424.6 429.2 433.7 438.3

h

2.0664 2.0791 2.0917 2.1043 2.1168

2.0016 2.0147 2.0278 2.0407 2.0536

1.9346 1.9482 1.9617 1.9751 1.9884

1.8648 1.8790 1.8931 1.9070 1.9209

1.8062 1.8211 1.8358 1.8504

s

1.0153 1.0220 1.0286 1.0352 1.0419

0.9826 0.9890 0.9955 1.0021 1.0087

0.9515 0.9575 0.9636 0.9698 0.9761

0.9245 0.9294 0.9346 0.9400 0.9456

0.9091 0.9122 0.9158 0.9200

Cp

Cp/Cv

1.1002 1.0989 1.0977 1.0965 1.0954

1.1077 1.1060 1.1044 1.1030 1.1015

1.1176 1.1153 1.1132 1.1113 1.1094

1.1316 1.1284 1.1254 1.1226 1.1200

1.1482 1.1434 1.1391 1.1352

Pressure = 340.00 kPa (abs)

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

184.4 185.6 186.9 188.1 189.3

177.9 179.2 180.5 181.8 183.1

170.9 172.3 173.8 175.1 176.5

163.4 164.9 166.5 168.0 169.5

156.7 158.4 160.1 161.8

vs 0.06138 0.06267 0.06395 0.06521 0.06645 0.06769 0.06892 0.07014 0.07135 0.07254 0.07374 0.07492 0.07611 0.07729 0.07846 0.07962 0.08078 0.08193 0.08308 0.08423 0.08538 0.08653 0.08767

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145

v

35 40 45

Temp. °C

515.2 520.3 525.4 530.6 535.8

490.1 495.1 500.1 505.1 510.1

465.9 470.7 475.5 480.3 485.2

442.3 447.0 451.7 456.4 461.1

428.4 433.0 437.7

h

2.0567 2.0694 2.0821 2.0947 2.1072

1.9918 2.0049 2.0180 2.0310 2.0439

1.9245 1.9381 1.9517 1.9652 1.9785

1.8542 1.8686 1.8827 1.8968 1.9107

1.8102 1.8251 1.8397

s

1.0175 1.0241 1.0306 1.0371 1.0437

0.9856 0.9919 0.9982 1.0046 1.0111

0.9558 0.9615 0.9673 0.9733 0.9794

0.9311 0.9354 0.9401 0.9451 0.9503

0.9209 0.9238 0.9272

Cp

1.1016 1.1003 1.0990 1.0977 1.0966

1.1096 1.1078 1.1061 1.1046 1.1031

1.1203 1.1179 1.1156 1.1135 1.1115

1.1358 1.1321 1.1288 1.1258 1.1229

1.1490 1.1441 1.1398

Cp/Cv

Pressure = 380.00 kPa (abs)

183.9 185.2 186.5 187.7 189.0

177.3 178.7 180.0 181.3 182.6

170.2 171.7 173.1 174.6 176.0

162.5 164.1 165.7 167.2 168.8

157.4 159.1 160.8

vs

714 Appendix 2

0.00079 0.05122 0.05152 0.05288 0.05421

0.05552 0.05680 0.05806 0.05930 0.06052

0.06172 0.06293 0.06411 0.06529 0.06645

0.06761 0.06876 0.06989 0.07102 0.07215

25 30 35 40 45

50 55 60 65 70

75 80 85 90 95

v

0.09948 0.10074 –

8.91 8.91 10 15 20

Temp. °C

150 155 160

465.6 470.4 475.3 480.1 485.0

442.0 446.7 451.4 456.1 460.8

418.8 423.4 428.0 432.7 437.3

212.1 403.9 404.9 409.6 414.2

h

2.1292 2.1416 –

1.0485 1.0551 –

1.9198 1.9335 1.9471 1.9605 1.9739

1.8493 1.8637 1.8779 1.8920 1.9059

1.7747 1.7900 1.8051 1.8201 1.8348

1.0433 1.7234 1.7269 1.7432 1.7590

s

0.9580 0.9635 0.9692 0.9751 0.9810

0.9345 0.9385 0.9429 0.9477 0.9527

0.9230 0.9238 0.9254 0.9278 0.9309

1.3695 0.9290 0.9281 0.9249 0.9233

Cp

1.1217 1.1192 1.1168 1.1146 1.1125

1.1379 1.1341 1.1306 1.1274 1.1244

1.1641 1.1576 1.1519 1.1467 1.1421

1.5329 1.1916 1.1893 1.1797 1.1714

Cp/Cv

1.0943 1.0933 –

Pressure = 400.00 kPa (abs)

541.3 546.6 –

169.9 171.4 172.8 174.3 175.7

162.0 163.7 165.3 166.9 168.4

153.1 155.0 156.9 158.6 160.4

584.1 146.5 147.0 149.1 151.2

vs

190.5 191.7 –

SAT LIQ SAT VAP

0.00081 0.04114 0.04213 0.04325 0.04434 0.04541 0.04646 0.04749 0.04851 0.04951 0.05050 0.05147 0.05244 0.05339 0.05434 0.05528 0.05621 0.05713 0.05806 0.05898

25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

v

0.08881 0.08994 0.09107

15.71 15.71 20

Temp. °C

150 155 160

488.9 493.9

464.3 469.2 474.1 479.0 483.9

440.4 445.1 449.9 454.7 459.5

416.6 421.3 426.1 430.8 435.6

221.5 407.7 411.8

h

2.1196 2.1320 2.1443

1.0502 1.0567 1.0632

1.0954 1.0943 1.0933

1.9670 1.9803

1.8989 1.9128 1.9265 1.9401 1.9536

1.8274 1.8420 1.8565 1.8708 1.8849

1.7508 1.7667 1.7822 1.7975 1.8125

1.0759 1.7205 1.7347

s

0.9950 1.0007

0.9695 0.9741 0.9791 0.9842 0.9895

0.9523 0.9547 0.9577 0.9612 0.9652

0.9535 0.9509 0.9496 0.9496 0.9505

1.3937 0.9633 0.9578

Cp

1.1156 1.1134

1.1290 1.1259 1.1230 1.1204 1.1179

1.1493 1.1444 1.1400 1.1360 1.1323

1.1844 1.1755 1.1677 1.1609 1.1548

1.5436 1.2049 1.1947

Cp/Cv

Pressure = 500.00 kPa (abs)

541.0 546.3 551.6

175.7 177.1 (continued)

168.2 169.7 171.3 172.8 174.2

159.8 161.5 163.3 164.9 166.6

150.0 152.1 154.1 156.1 158.0

552.8 145.8 147.8

vs

190.2 191.4 192.6

Appendix 2 715

0.00082 0.03432 0.03502 0.03600 0.03695 0.03787 0.03878

0.03967

21.54 21.54 25 30 35 40 45

50

0.08426 0.08535 0.08642 –

150 155 160 165

v

0.07881 0.07991 0.08101 0.08210 0.08318

125 130 135 140 145

Temp. °C

0.07328 0.07440 0.07551 0.07661 0.07772

v

100 105 110 115 120

Temp. °C

438.7

229.7 410.8 414.2 419.2 424.1 428.9 433.8

h

2.1152 2.1276 2.1399 –

2.0522 2.0649 2.0776 2.0902 2.1028

1.9872 2.0004 2.0134 2.0264 2.0394

s

1.0510 1.0575 1.0640 –

1.0187 1.0251 1.0316 1.0381 1.0445

0.9871 0.9933 0.9996 1.0059 1.0123

Cp

1.8086

1.1038 1.7183 1.7299 1.7463 1.7623 1.7780 1.7934

s

0.9718

1.4165 0.9954 0.9890 0.9819 0.9771 0.9740 0.9723

Cp

Cp/Cv

1.1622

1.5545 1.2187 1.2090 1.1967 1.1862 1.1771 1.1692

Cp/Cv

1.0960 1.0949 1.0938 –

1.1023 1.1009 1.0996 1.0983 1.0971

1.1106 1.1087 1.1070 1.1054 1.1038

Pressure = 600.00 kPa (abs)

540.9 546.1 551.4 –

515.0 520.1 525.2 530.4 535.6

489.9 494.9 499.9 504.9 509.9

h

Pressure = 400.00 kPa (abs)

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

157.4

525.8 145.0 146.7 149.0 151.3 153.4 155.5

vs

190.0 191.2 192.4 –

183.7 185.0 186.3 187.5 188.8

177.1 178.4 179.8 181.1 182.4

vs

SAT LIQ SAT VAP

0.06702 0.06790 0.06877 0.06964 0.07052

150 155 160 165 170

0.00083 0.02939 0.02999 0.03086 0.03171 0.03253 0.03333 0.03412

26.68 26.68 30 35 40 45 50 55

v

0.06258 0.06348 0.06437 0.06526 0.06613

125 130 135 140 145

Temp. °C

0.05989 0.06078 0.06169

v

110 115 120

Temp. °C

436.9 441.9

237.0 413.5 416.8 421.9 426.9 431.9

h

2.0957 2.1082 2.1205 2.1328 2.1450

2.0324 2.0452 2.0580 2.0707 2.0832

1.9934 2.0065 2.0195

s

1.0554 1.0616 1.0679 1.0742 1.0804

1.0244 1.0305 1.0367 1.0429 1.0491

1.0065 1.0124 1.0183

Cp

1.0988 1.0975 1.0964 1.0952 1.0941

1.1060 1.1044 1.1029 1.1015 1.1001

1.1114 1.1095 1.1077

Cp/Cv

1.7919 1.8071

1.1282 1.7166 1.7278 1.7444 1.7606 1.7764

s

0.9935 0.9918

1.4385 1.0265 1.0182 1.0085 1.0015 0.9967

Cp

1.1768 1.1689

1.5658 1.2332 1.2223 1.2081 1.1960 1.1857

Cp/Cv

Pressure = 700.00 kPa (abs)

540.1 545.4 550.7 556.1 561.5

514.1 519.3 524.4 529.6 534.9

498.9 503.9 509.0

h

Pressure = 500.00 kPa (abs)

155.0 157.0

501.8 144.0 145.7 148.2 150.6 152.8

vs

189.1 190.4 191.6 192.8 194.0

182.6 184.0 185.3 186.6 187.8

178.5 179.9 181.3

vs

716 Appendix 2

0.04054 0.04140 0.04224 0.04308

0.04390 0.04472 0.04552 0.04633 0.04712

0.04790 0.04868 0.04945 0.05023 0.05100

0.05175 0.05252 0.05327 0.05402 0.05477

0.05552 0.05626 0.05700 0.05774 0.05848

0.05921

55 60 65 70

75 80 85 90 95

100 105 110 115 120

125 130 135 140 145

150 155 160 165 170

175

566.3

539.4 544.7 550.0 555.4 560.8

513.3 518.4 523.6 528.8 534.1

487.8 492.9 497.9 503.0 508.1

463.0 468.0 472.9 477.9 482.8

443.5 448.4 453.3 458.1

2.1413

2.0796 2.0921 2.1045 2.1168 2.1291

2.0159 2.0288 2.0417 2.0544 2.0670

1.9500 1.9634 1.9767 1.9899 2.0030

1.8813 1.8953 1.9092 1.9229 1.9365

1.8235 1.8382 1.8527 1.8671

1.0901

1.0598 1.0658 1.0719 1.0780 1.0840

1.0303 1.0361 1.0419 1.0478 1.0538

1.0033 1.0084 1.0137 1.0191 1.0247

0.9818 0.9854 0.9895 0.9938 0.9985

0.9724 0.9738 0.9759 0.9786

1.0954

1.1017 1.1003 1.0990 1.0977 1.0965

1.1099 1.1081 1.1063 1.1047 1.1032

1.1209 1.1184 1.1161 1.1139 1.1118

1.1369 1.1331 1.1297 1.1265 1.1236

1.1560 1.1505 1.1455 1.1410

194.5

188.2 189.5 190.8 192.0 193.3

181.5 182.9 184.3 185.6 186.9

174.3 175.8 177.3 178.7 180.1

166.4 168.1 169.7 171.3 172.8

159.3 161.2 163.0 164.7

0.03488 0.03564 0.03638 0.03711 0.03784 0.03855 0.03925 0.03995 0.04064 0.04133 0.04201 0.04269 0.04336 0.04402 0.04468 0.04535 0.04600 0.04665 0.04730 0.04795 0.04859 0.04923 0.04987 0.05051 0.05114

60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180

565.6 571.1

538.6 544.0 549.3 554.7 560.2

512.4 517.6 522.8 528.0 533.3

486.8 491.9 496.9 502.1 507.2

461.7 466.7 471.7 476.7 481.7

446.8 451.8 456.7

2.1276 2.1398

2.0657 2.0782 2.0907 2.1031 2.1154

2.0018 2.0147 2.0276 2.0404 2.0531

1.9354 1.9489 1.9622 1.9755 1.9887

1.8658 1.8801 1.8941 1.9080 1.9217

1.8221 1.8369 1.8515

1.0936 1.0996

1.0643 1.0701 1.0760 1.0818 1.0877

1.0365 1.0419 1.0473 1.0529 1.0586

1.0120 1.0165 1.0212 1.0261 1.0312

0.9949 0.9974 1.0005 1.0040 1.0078

0.9913 0.9917 0.9929

1.0977 1.0965

1.1047 1.1032 1.1017 1.1003 1.0990

1.1139 1.1118 1.1099 1.1081 1.1063

1.1266 1.1236 1.1209 1.1184 1.1161

1.1454 1.1409 1.1369 1.1331 1.1297

1.1620 1.1559 1.1504

193.8 195.0

187.3 188.7 190.0 191.3 192.5

180.4 181.8 183.2 184.6 186.0

172.9 174.5 176.0 177.5 179.0

164.6 166.3 168.0 169.7 171.3

159.0 160.9 162.8

Appendix 2 717

v

0.00085 0.02565 – 0.02626 0.02705 0.02782

0.02856 0.02928 0.02998 0.03067 0.03135

0.03202 0.03267 0.03331 0.03395 0.03457

0.03520 0.03581 0.03642 0.03703 0.03763

0.03822 0.03881 0.03940 0.03998

Temp. °C

31.29 31.29 30 35 40 45

50 55 60 65 70

75 80 85 90 95

100 105 110 115 120

125 130 135 140

511.5 516.7 522.0 527.2

485.7 490.8 495.9 501.1 506.3

460.4 465.4 470.5 475.5 480.6

435.1 440.2 445.2 450.3 455.3

243.7 415.7 – 419.6 424.8 430.0

h

1.9892 2.0023 2.0152 2.0281

1.9223 1.9360 1.9494 1.9628 1.9761

1.8520 1.8664 1.8806 1.8947 1.9086

1.7767 1.7923 1.8076 1.8226 1.8374

1.1500 1.7150 – 1.7278 1.7445 1.7608

s

1.0428 1.0478 1.0529 1.0582

1.0212 1.0250 1.0291 1.0334 1.0380

1.0090 1.0103 1.0122 1.0147 1.0177

1.0178 1.0133 1.0105 1.0089 1.0085

1.4602 1.0569 – 1.0453 1.0332 1.0243

Cp

Cp/Cv

1.1181 1.1157 1.1136 1.1115

1.1325 1.1292 1.1261 1.1232 1.1205

1.1548 1.1494 1.1446 1.1402 1.1362

1.1935 1.1836 1.1750 1.1674 1.1607

1.5775 1.2485 – 1.2344 1.2184 1.2049

Pressure = 800.00 kPa (abs)

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

179.3 180.8 182.2 183.6

171.5 173.1 174.7 176.3 177.8

162.7 164.6 166.4 168.1 169.8

152.4 154.7 156.8 158.8 160.8

480.2 142.9 – 145.0 147.6 150.1

vs SAT LIQ SAT VAP

0.00087 0.02034 0.02044 0.02114 0.02181 0.02246 0.02308 0.02368 0.02427 0.02485 0.02541 0.02596 0.02650 0.02703 0.02756 0.02807 0.02859 0.02909 0.02959 0.03008 0.03058 0.03106 0.03155 0.03203

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145

v

39.35 39.35 40 45

Temp. °C

509.7 515.0 520.3 525.6 531.0

483.5 488.7 493.9 499.1 504.4

457.5 462.7 467.9 473.1 478.3

431.2 436.5 441.8 447.1 452.3

255.6 419.5 420.2 425.7

h

1.9676 1.9809 1.9940 2.0070 2.0198

1.8997 1.9136 1.9273 1.9409 1.9543

1.8277 1.8425 1.8571 1.8715 1.8857

1.7491 1.7655 1.7816 1.7972 1.8126

1.1881 1.7124 1.7147 1.7322

s

1.0563 1.0604 1.0647 1.0692 1.0739

1.0409 1.0432 1.0459 1.0490 1.0525

1.0406 1.0388 1.0381 1.0383 1.0393

1.0766 1.0644 1.0552 1.0485 1.0438

1.5035 1.1177 1.1144 1.0928

Cp

1.1270 1.1241 1.1214 1.1189 1.1165

1.1457 1.1413 1.1372 1.1335 1.1301

1.1762 1.1687 1.1619 1.1559 1.1506

1.2354 1.2195 1.2061 1.1947 1.1848

1.6025 1.2817 1.2782 1.2546

Cp/Cv

Pressure = 1000.00 kPa (abs)

177.0 178.6 180.1 181.7 183.1

168.6 170.4 172.1 173.8 175.4

158.9 160.9 162.9 164.9 166.8

146.9 149.6 152.1 154.4 156.7

442.1 140.6 141.0 144.1

vs

718 Appendix 2

0.04398 0.04455 0.04511

175 180 185

0.00093 0.01308 0.01363 0.01417 0.01468

0.01516 0.01562 0.01606 0.01649 0.01690

0.01731 0.01770 0.01809 0.01847 0.01885

55.2 55.2 60 65 70

75 80 85 90 95

100 105 110 115 120

v

0.04114 0.04171 0.04229 0.04285 0.04342

150 155 160 165 170

Temp. °C

0.04056

145

2.1157 2.1279 2.1400

2.0535 2.0661 2.0786 2.0910 2.1034

2.0408

1.0972 1.1030 1.1087

1.0690 1.0745 1.0801 1.0858 1.0915

1.0636

1.1001 1.0988 1.0975

1.1078 1.1061 1.1045 1.1029 1.1015

1.1096

477.5 483.0 488.5 494.0 499.4

449.5 455.2 460.9 466.4 472.0

280.1 425.7 431.7 437.8 443.7

h

1.8546 1.8692 1.8837 1.8978 1.9119

1.7769 1.7932 1.8090 1.8245 1.8397

1.2632 1.7063 1.7246 1.7427 1.7601

s

1.1016 1.0982 1.0959 1.0948 1.0945

1.1507 1.1349 1.1228 1.1136 1.1067

1.6205 1.2844 1.2358 1.1989 1.1715

Cp

1.1875 1.1790 1.1714 1.1647 1.1587

1.2552 1.2368 1.2214 1.2084 1.1972

1.6778 1.3876 1.3416 1.3056 1.2776

Cp/Cv

Pressure = 1500.00 kPa (abs)

565.0 570.5 576.0

537.9 543.2 548.6 554.0 559.5

532.5

160.8 163.0 165.2 167.2 169.2

148.0 150.9 153.6 156.1 158.5

365.0 134.2 138.0 141.7 145.0

vs

193.1 194.3 195.6

186.4 187.8 189.1 190.5 191.8

185.0

SAT LIQ SAT VAP

0.00099 0.00931 0.00959 0.01009 0.01055 0.01097 0.01137 0.01175 0.01211 0.01246 0.01279 0.01312 0.01344 0.01374 0.01405

67.47 67.47 70 75 80 85 90 95 100 105 110 115 120 125 130

v

0.03485 0.03531 0.03577 0.03623

175 180 185 190

Temp. °C

0.03250 0.03298 0.03345 0.03392 0.03438

150 155 160 165 170

499.8 505.5

470.8 476.7 482.6 488.4 494.1

439.5 446.1 452.5 458.8 464.8

300.4 428.8 432.5

h

2.0953 2.1076 2.1198 2.1319

2.0326 2.0453 2.0579 2.0705 2.0829 1.1046 1.1100 1.1154 1.1209

1.0787 1.0837 1.0888 1.0940 1.0993 1.1050 1.1035 1.1020 1.1006

1.1143 1.1122 1.1103 1.1084 1.1067

1.8925 1.9068

1.8173 1.8330 1.8483 1.8633 1.8781

1.7303 1.7493 1.7673 1.7845 1.8011

1.3223 1.6991 1.7101

s

1.1433 1.1401

1.1874 1.1733 1.1625 1.1542 1.1479

1.3600 1.3019 1.2601 1.2291 1.2055

1.7690 1.5055 1.4452

Cp

1.1869 1.1789

1.2493 1.2327 1.2186 1.2066 1.1961

1.4173 1.3638 1.3242 1.2936 1.2692

1.7844 1.5484 1.4943

Cp/Cv

Pressure 2000.00 kPa (abs)

563.6 569.2 574.7 580.3

536.3 541.8 547.2 552.6 558.1

164.9 167.1 (continued)

152.3 155.1 157.7 160.2 162.6

134.7 138.9 142.7 146.2 149.3

302.2 127.2 129.9

vs

191.6 192.9 194.2 195.6

184.6 186.0 187.5 188.9 190.2

Appendix 2 719

0.01921 0.01958 0.01993 0.02028 0.02063

0.02098 0.02132 0.02166 0.02199 0.02233

0.02265 0.02298 0.02331 0.02363 0.02395

0.02427 0.02459 0.02491

150 155 160 165 170

175 180 185 190 195

200 205 210

v

125 130 135 140 145

Temp. °C

588.7 594.4 600.2

560.3 565.9 571.6 577.2 582.9

532.4 537.9 543.5 549.1 554.7

504.9 510.4 515.9 521.4 526.9

h

2.1183 2.1303 2.1424

2.0566 2.0691 2.0815 2.0939 2.1061

1.9926 2.0056 2.0185 2.0313 2.0440

1.9257 1.9394 1.9529 1.9663 1.9795

s

1.1472 1.1520 1.1569

1.1244 1.1288 1.1332 1.1378 1.1425

1.1057 1.1090 1.1125 1.1163 1.1203

1.0950 1.0962 1.0979 1.1001 1.1027

Cp

1.1084 1.1067 1.1050

1.1185 1.1162 1.1141 1.1121 1.1102

1.1325 1.1293 1.1263 1.1235 1.1209

1.1532 1.1483 1.1438 1.1397 1.1360

Cp/Cv

Pressure = 1500.00 kPa (abs)

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

195.1 196.5 197.8

187.9 189.3 190.8 192.3 193.7

180.0 181.6 183.2 184.8 186.3

171.1 173.0 174.8 176.6 178.3

vs 0.01434 0.01463 0.01492 0.01520 0.01547 0.01575 0.01602 0.01629 0.01655 0.01681 0.01707 0.01733 0.01758 0.01784 0.01809 0.01834 0.01858 0.01883

150 155 160 165 170 175 180 185 190 195 200 205 210 215 220

v

135 140 145

Temp. °C

585.7 591.5 597.4 603.2 609.1

556.8 562.6 568.3 574.1 579.9

528.3 534.0 539.7 545.4 551.1

511.2 516.9 522.6

h

2.0900 2.1023 2.1145 2.1265 2.1386

2.0274 2.0401 2.0527 2.0653 2.0777

1.9619 1.9752 1.9884 2.0015 2.0145

1.9208 1.9347 1.9483

s

1.1638 1.1678 1.1719 1.1761 1.1804

1.1466 1.1496 1.1528 1.1563 1.1599

1.1370 1.1380 1.1395 1.1415 1.1439

1.1380 1.1369 1.1366

Cp

1.1198 1.1175 1.1153 1.1133 1.1114

1.1337 1.1305 1.1276 1.1248 1.1222

1.1541 1.1493 1.1449 1.1409 1.1372

1.1717 1.1652 1.1594

Cp/Cv

Pressure 2000.00 kPa (abs)

192.1 193.6 195.0 196.5 197.9

184.1 185.7 187.4 189.0 190.5

175.2 177.1 178.9 180.7 182.4

169.2 171.3 173.3

vs

720 Appendix 2

v

0.00114 0.00528 0.00575 0.00624

0.00665 0.00701 0.00733 0.00764 0.00792

0.00819 0.00845 0.00869 0.00893 0.00916

0.00939 0.00960 0.00982 0.01003 0.01023

0.01043 0.01063 0.01083

Temp. °C

86.22 86.22 90 95

100 105 110 115 120

125 130 135 140 145

150 155 160 165 170

175 180 185

549.6 555.6 561.6

519.4 525.5 531.6 537.6 543.6

488.3 494.7 501.0 507.2 513.3

453.5 461.1 468.2 475.1 481.8

335.3 427.6 436.1 445.3

h

1.9820 1.9953 2.0085

1.9128 1.9271 1.9411 1.9549 1.9686

1.8369 1.8528 1.8683 1.8835 1.8983

1.7466 1.7667 1.7855 1.8034 1.8204

1.4188 1.6758 1.6992 1.7245

s

1.1992 1.1984 1.1983

1.2179 1.2116 1.2068 1.2032 1.2007

1.2884 1.2669 1.2500 1.2366 1.2262

1.5654 1.4676 1.4007 1.3523 1.3161

2.3843 2.5300 2.0156 1.7214

Cp

1.1705 1.1646 1.1593

1.2113 1.2011 1.1921 1.1841 1.1770

1.2926 1.2704 1.2520 1.2363 1.2229

1.5427 1.4573 1.3977 1.3537 1.3197

2.2770 2.3769 1.9317 1.6778

Cp/Cv

Pressure = 3000.00 kPa (abs) vs

176.6 178.6 180.5

165.5 167.9 170.2 172.4 174.5

151.7 154.7 157.6 160.4 163.0

131.7 136.6 140.9 144.8 148.4

195.8 112.1 119.1 126.1

SAT LIQ SAT VAP

0.00530 0.00556 0.00580 0.00603 0.00624 0.00645 0.00664 0.00683 0.00702 0.00719 0.00737 0.00753 0.00770 0.00786 0.00802

125 130 135 140 145 150 155 160 165 170 175 180 185 190 195

v 0.00158 0.00254 – 0.00376 0.00429 0.00468 0.00501

100.37 100.37 100 105 110 115 120

Temp. °C h

541.9 548.2 554.5 560.8 567.0

509.5 516.2 522.7 529.2 535.6

473.8 481.5 488.8 495.9 502.8

375.6 404.4 – 433.7 446.7 456.8 465.7

1.9454 1.9594 1.9732 1.9867 2.0001

1.8710 1.8866 1.9018 1.9166 1.9311

1.7840 1.8031 1.8212 1.8385 1.8550

1.5250 1.6022 – 1.6804 1.7143 1.7406 1.7634

s

1.2658 1.2591 1.2539 1.2499 1.2470

1.3354 1.3146 1.2981 1.2849 1.2743

1.5762 1.4963 1.4384 1.3950 1.3615

28.1470 42.1018 – 3.1309 2.2216 1.8780 1.6927

Cp

1.2177 1.2076 1.1985 1.1904 1.1831

1.2965 1.2755 1.2577 1.2424 1.2293

1.5117 1.4429 1.3921 1.3530 1.3219

vs

169.4 171.8 174.1 176.3 178.4

155.9 158.9 161.7 164.4 167.0

137.5 141.8 145.8 149.4 152.8

95.7 95.0 – 111.6 120.4 127.1 132.7

(continued)

24.2211 35.2394 – 2.8151 2.0540 1.7663 1.6106

Cp/Cv

Pressure = 4000.00 kPa (abs)

Appendix 2 721

0.01230 0.01248 0.01265 0.01283

225 230 235 240

609.7 615.8 621.9 628.0

579.6 585.6 591.6 597.6 603.7

567.6 573.6

h

2.1092 2.1214 2.1334 2.1454

2.0471 2.0598 2.0723 2.0847 2.0970

2.0215 2.0344

s

1.2130 1.2161 1.2194 1.2227

1.2012 1.2030 1.2051 1.2075 1.2102

1.1988 1.1998

Cp

1.1291 1.1264 1.1239 1.1215

1.1458 1.1420 1.1384 1.1351 1.1320

1.1544 1.1499

Cp/Cv

Pressure = 3000.00 kPa (abs) vs

194.5 196.1 197.7 199.2

186.1 187.8 189.6 191.3 192.9

182.4 184.3

0.00892 0.00906 0.00920 0.00934 0.00948 0.00962

225 230 235 240 245 250

v 0.00817 0.00833 0.00848 0.00863 0.00877

200 205 210 215 220

Temp. °C h

635.5

604.3 610.5 616.8 623.0 629.3

573.2 579.4 585.7 591.9 598.1

2.1386

2.0774 2.0898 2.1022 2.1144 2.1265

2.0134 2.0265 2.0394 2.0522 2.0649

s

1.2539

1.2445 1.2458 1.2475 1.2494 1.2515

1.2450 1.2438 1.2432 1.2431 1.2436

Cp

1.1337

1.1511 1.1471 1.1434 1.1400 1.1368

1.1765 1.1705 1.1650 1.1600 1.1554

Cp/Cv

Pressure = 4000.00 kPa (abs) vs

198.6

190.1 191.9 193.6 195.3 197.0

180.5 182.5 184.5 186.4 188.3

Source: Thermodynamic Properties of HFC-134a. With permission of E. I. Du Pont de Nemours and Co. Note: Cp = heat capacity at constant pressure in kJ/(kg) (°C); Cp/Cv = heat capacity ratio (dimensionless); h = enthalpy in kJ/kg; s = entropy in kJ/(kg) (°K); v = volume in m3/kg ; vs = velocity of sound in m/s.

0.01139 0.01158 0.01176 0.01194 0.01212

200 205 210 215 220

v

0.01102 0.01121

190 195

Temp. °C

HFC-134a Superheated Vapor–Constant Pressure Tables

TABLE A.16 (SI) (Continued)

722 Appendix 2

40

40

60

60

40

20

Temperature = 0 oF

20

80 16

60

80

40

60

80

100

160 140 120

c.p.

180

120 20 .022 .024 0 0

0.0

100 0

0.03

20

0

20

40

80

60

100

Enthalpy (BTU/lb)

80

120

Source: Thermodynamic Properties of HFC-134a. With permission of E. I. Du Pont de Nemours and Co.

1.

2.

4.

10. 8. 6.

20.

40.

60.

100. 80.

200.

id

400.

(Engineering Units)

40

600.

HFC-134a

0.012

20

0.2

1000. 800.

Pressure (psia)

Pressure–Enthalpy Diagram

60

0.0

20

100

0.5

Temperature = 20 oF

liqu

Sat ura ted

80

0.4

uali ty

0.3

14 120

0.0 140

0.6

0

0.1

160

0.7

0

0.9

180

0.

200

0.8

01

8 apor Satura ted v

0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0 . 3 1 0.3 2

20 140 0.040

160

140

py

2000.

0.3 3 0.3 4 0.3 5 0.3 6 0.3 7

tro

180 = Volume

160

=0 .3

lb . o F

180

200

4.0

3.0

2.0

1.5

0.80 1.0

0.60

0.40

0.30

0.20

0.15

3

/lb 0.060 ft 0 8 .0 0 0.10

200

40.

30.

20.

15.

8.0 10.

6.0

440

Pressure–Enthalpy Diagram for HCF-134a

8

BT U/

9

Q

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 En

360 380 0.3

400 oF

Temperature 0 1 0.4

0.4

420

0.4 2

TABLE A.17

1. 220

2.

4.

10. 8. 6.

20.

40.

100. 80. 60.

200.

400.

600.

1000. 800.

220 2000.

Appendix 2 723

0.01 100

0.02

0.04

0.1 0.08 0.06

0.2

0.4

1. 0.8 0.6

2. 30

50 50

40

30

20

10

Temperature = 0 oC

10

0 0.0 20

30

40

50

60

90 80 70

c.p.

1

01

0.0

150

200

250

60

300

350

2 3 01 .001 0.0014 0

0.0

16 .0018 0.0020 0

0.00

500

Enthalpy (kJ/kg)

400

450

500

Source: Thermodynamic Properties of HFC-134a. With permission of E. I. Du Pont de Nemours and Co.

Pressure (MPa)

4.

0

(SI Units)

20

0.00080

10

0.2

6.

liq

Sat ura ted

60

0.5

HFC-134a

60 50 0.00070 40 30 Temperature = 20 oC 10

uid

0.1

40

=0 .4

Qua lity

0.3

00 0.0

70

0.6

01

100

90

80 0.7

10. 8.

2.05

90

0.8

450

2. 1 0 2.1 5

Pressure–Enthalpy Diagram

Satura ted va por

0.9

400

5

350

2.2 0

300

2.2

250

0

200

2.3

150 550

5

100 20.

1.95 2.00

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90

3 g 40 m /k

650

0.20

0.15

0.080 0.10

0.060

0.040

0.030

0.020

0.015

0.0060 0.0080 0.010

0.0030

600

= 0.00 Volume

550

g .K

600

5 2.4

Pressure–Enthalpy Diagram for HCF-134a

2.3

py

0 5 2.5

J/k 0k =2 .4 tro En

2.5

650

2.0

1.5

0.80 1.0

0.60

0.40

0.30

20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 Temperature =220 oC 230 240

TABLE A.17 (SI)

0.1 700

0.2

0.4

0.6

1. 0.8

2.

4.

6.

10. 8.

20.

40.

100. 80. 60.

700 200.

724 Appendix 2

Pressure (bar)

–150 –149 –148 –147 –146 –145 –144 –143 –142 –141 –140 –139 –138 –137 –136 –135 –134 –133 –132 –131 –130 –129 –128 –127 –126 –125

Temp. °F

0.49 0.52 0.55 0.58 0.60 0.64 0.67 0.70 0.74 0.77 0.81 0.85 0.89 0.93 0.98 1.02 1.07 1.12 1.17 1.23 1.28 1.34 1.40 1.46 1.52 1.59

Liquid pf

0.49 0.51 0.54 0.57 0.60 0.63 0.66 0.69 0.73 0.76 0.80 0.84 0.88 0.92 0.97 1.01 1.06 1.11 1.16 1.21 1.27 1.33 1.39 1.45 1.51 1.58

Vapor pg

Pressure, psia

0.0106 0.0106 0.0106 0.0106 0.0106 0.0106 0.0107 0.0107 0.0107 0.0107 0.0107 0.0107 0.0107 0.0107 0.0107 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.0109 0.0109 0.0109

Liquid vf 94.0107 89.5452 85.3254 81.3361 77.5632 73.9935 70.6147 67.4151 64.3842 61.5119 58.7888 56.2061 53.7558 51.4301 49.2219 47.1244 45.1314 43.2370 41.4356 39.7222 38.0917 36.5397 35.0619 33.6542 32.3129 31.0344

Vapor vg

Volume, ft.3/lb.

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18

94.39 94.30 94.20 94.10 94.01 93.91 93.81 93.72 93.62 93.52 93.42 93.33 93.23 93.13 93.03 92.93 92.84 92.74 92.64 92.54 92.44 92.34 92.24 92.14 92.04 91.94

Liquid 1/vf 0.0106 0.0112 0.0117 0.0123 0.0129 0.0135 0.0142 0.0148 0.0155 0.0163 0.0170 0.0178 0.0186 0.0194 0.0203 0.0212 0.0222 0.0231 0.0241 0.0252 0.0263 0.0274 0.0285 0.0297 0.0309 0.0322

Vapor 1/vg

Density, lb./ft.3

–34.1 –33.8 –33.5 –33.2 –32.9 –32.6 –32.4 –32.1 –31.8 –31.5 –31.2 –30.9 –30.6 –30.3 –30.0 –29.7 –29.5 –29.2 –28.9 –28.6 –28.3 –28.0 –27.7 –27.4 –27.1 –26.8

Liquid hf 134.3 134.1 134.0 133.8 133.7 133.5 133.4 133.2 133.1 132.9 132.8 132.6 132.5 132.3 132.2 132.0 131.9 131.7 131.5 131.4 131.2 131.1 130.9 130.8 130.6 130.4

Latent hfg 100.2 100.3 100.5 100.6 100.7 100.9 101.0 101.2 101.3 101.4 101.6 101.7 101.8 102.0 102.1 102.3 102.4 102.5 102.7 102.8 102.9 103.1 103.2 103.4 103.5 103.6

Vapor hg

Enthalpy, Btu/lb.

–0.0946 –0.0937 –0.0928 –0.0919 –0.0910 –0.0900 –0.0891 –0.0882 –0.0873 –0.0864 –0.0855 –0.0846 –0.0838 –0.0829 –0.0820 –0.0811 –0.0802 –0.0793 –0.0784 –0.0775 –0.0766 –0.0757 –0.0748 –0.0739 –0.0730 –0.0721

Liquid sf 0.3390 0.3380 0.3371 0.3361 0.3352 0.3343 0.3334 0.3325 0.3316 0.3307 0.3298 0.3289 0.3281 0.3272 0.3264 0.3255 0.3247 0.3239 0.3231 0.3223 0.3215 0.3207 0.3199 0.3191 0.3184 0.3176

Vapor sg

Entropy, Btu/(lb.)(°R)

–150 –149 –148 –147 –146 –145 –144 –143 –142 –141 –140 –139 –138 –137 –136 –135 –134 –133 –132 –131 –130 –129 –128 –127 –126 –125 (continued)

Temp. °F

Appendix 2 725

–124 –123 –122 –121 –120 –119 –118 –117 –116 –115 –114 –113 –112 –111 –110 –109 –108 –107 –106 –105 –104 –103 –102 –101 –100 –99 –98 –97

Temp. °F

1.66 1.73 1.81 1.88 1.96 2.04 2.13 2.22 2.31 2.40 2.50 2.60 2.70 2.81 2.92 3.03 3.15 3.27 3.40 3.53 3.66 3.80 3.94 4.08 4.23 4.39 4.54 4.71

Liquid pf

1.65 1.72 1.79 1.87 1.95 2.03 2.12 2.20 2.29 2.39 2.48 2.58 2.69 2.79 2.91 3.02 3.14 3.26 3.38 3.51 3.64 3.78 3.92 4.07 4.22 4.37 4.53 4.69

Vapor pg

Pressure, psia

0.0109 0.0109 0.0109 0.0109 0.0109 0.0109 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0110 0.0111 0.0111 0.0111 0.0111 0.0111 0.0111 0.0111 0.0111 0.0112 0.0112 0.0112 0.0112 0.0112 0.0112

Liquid vf 29.8154 28.6527 27.5434 26.4846 25.4738 24.5085 23.5863 22.7051 21.8628 21.0573 20.2870 19.5499 18.8446 18.1694 17.5228 16.9035 16.3101 15.7415 15.1963 14.6736 14.1722 13.6912 13.2296 12.7865 12.3611 11.9525 11.5599 11.1828

Vapor vg

Volume, ft.3/lb.

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (Continued)

91.84 91.74 91.64 91.54 91.44 91.34 91.24 91.14 91.04 90.93 90.83 90.73 90.63 90.53 90.42 90.32 90.22 90.11 90.01 89.91 89.81 89.70 89.60 89.49 89.39 89.29 89.18 89.08

Liquid 1/vf 0.0335 0.0349 0.0363 0.0378 0.0393 0.0408 0.0424 0.0440 0.0457 0.0475 0.0493 0.0512 0.0531 0.0550 0.0571 0.0592 0.0613 0.0635 0.0658 0.0681 0.0706 0.0730 0.0756 0.0782 0.0809 0.0837 0.0865 0.0894

Vapor 1/vg

Density, lb./ft.3

–26.5 –26.2 –25.9 –25.6 –25.3 –25.0 –24.7 –24.4 –24.1 –23.8 –23.5 –23.2 –22.9 –22.6 –22.3 –22.0 –21.7 –21.4 –21.1 –20.8 –20.5 –20.2 –19.9 –19.6 –19.3 –19.0 –18.6 –18.3

Liquid hf 130.3 130.1 130.0 129.8 129.6 129.5 129.3 129.1 129.0 128.8 128.6 128.5 128.3 128.1 128.0 127.8 127.6 127.5 127.3 127.1 127.0 126.8 126.6 126.4 126.3 126.1 125.9 125.7

Latent hfg 103.8 103.9 104.0 104.2 104.3 104.5 104.6 104.7 104.9 105.0 105.1 105.3 105.4 105.5 105.7 105.8 105.9 106.1 106.2 106.3 106.5 106.6 106.7 106.9 107.0 107.1 107.3 107.4

Vapor hg

Enthalpy, Btu/lb.

–0.0713 –0.0704 –0.0695 –0.0686 –0.0677 –0.0668 –0.0660 –0.0651 –0.0642 –0.0633 –0.0624 –0.0616 –0.0607 –0.0598 –0.0589 –0.0580 –0.0572 –0.0563 –0.0554 –0.0546 –0.0537 –0.0528 –0.0520 –0.0511 –0.0502 –0.0494 –0.0485 –0.0476

Liquid sf 0.3169 0.3161 0.3154 0.3147 0.3139 0.3132 0.3125 0.3118 0.3111 0.3104 0.3097 0.3091 0.3084 0.3077 0.3071 0.3064 0.3058 0.3051 0.3045 0.3039 0.3033 0.3027 0.3020 0.3014 0.3008 0.3002 0.2997 0.2991

Vapor sg

Entropy, Btu/(lb.)(°R)

–124 –123 –122 –121 –120 –119 –118 –117 –116 –115 –114 –113 –112 –111 –110 –109 –108 –107 –106 –105 –104 –103 –102 –101 –100 –99 –98 –97

Temp. °F

726 Appendix 2

–96 –95 –94 –93 –92 –91 –90 –89 –88 –87 –86 –85 –84 –83 –82 –81 –80 –79 –78 –77 –76 –75 –74 –73 –72 –71 –70 –69 –68 –67 –66

4.88 5.05 5.23 5.41 5.60 5.79 5.99 6.19 6.40 6.62 6.84 7.07 7.30 7.54 7.79 8.04 8.30 8.56 8.84 9.12 9.40 9.70 10.00 10.30 10.62 10.94 11.28 11.61 11.96 12.32 12.68

4.86 5.03 5.21 5.39 5.58 5.77 5.97 6.18 6.39 6.60 6.82 7.05 7.28 7.52 7.77 8.02 8.28 8.54 8.82 9.09 9.38 9.67 9.97 10.28 10.60 10.92 11.25 11.59 11.93 12.29 12.65

0.0112 0.0113 0.0113 0.0113 0.0113 0.0113 0.0113 0.0113 0.0113 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0116 0.0116 0.0116 0.0116 0.0116 0.0116 0.0116 0.0117

10.8203 10.4718 10.1367 9.8144 9.5043 9.2059 8.9187 8.6422 8.3760 8.1196 7.8725 7.6345 7.4050 7.1839 6.9706 6.7649 6.5665 6.3750 6.1903 6.0120 5.8398 5.6736 5.5130 5.3579 5.2080 5.0632 4.9232 4.7878 4.6570 4.5304 4.4080

88.97 88.87 88.76 88.66 88.55 88.44 88.34 88.23 88.12 88.02 87.91 87.80 87.70 87.59 87.48 87.37 87.27 87.16 87.05 86.94 86.83 86.72 86.61 86.50 86.39 86.28 86.17 86.06 85.95 85.84 85.73

0.0924 0.0955 0.0987 0.1019 0.1052 0.1086 0.1121 0.1157 0.1194 0.1232 0.1270 0.1310 0.1350 0.1392 0.1435 0.1478 0.1523 0.1569 0.1615 0.1663 0.1712 0.1763 0.1814 0.1866 0.1920 0.1975 0.2031 0.2089 0.2147 0.2207 0.2269

–18.0 –17.7 –17.4 –17.1 –16.8 –16.5 –16.2 –15.9 –15.5 –15.2 –14.9 –14.6 –14.3 –14.0 –13.7 –13.3 –13.0 –12.7 –12.4 –12.1 –11.8 –11.4 –11.1 –10.8 –10.5 –10.2 –9.8 –9.5 –9.2 –8.9 –8.5

125.6 125.4 125.2 125.0 124.8 124.7 124.5 124.3 124.1 123.9 123.7 123.6 123.4 123.2 123.0 122.8 122.6 122.4 122.2 122.1 121.9 121.7 121.5 121.3 121.1 120.9 120.7 120.5 120.3 120.1 119.9

107.5 107.7 107.8 107.9 108.1 108.2 108.3 108.4 108.6 108.7 108.8 109.0 109.1 109.2 109.4 109.5 109.6 109.7 109.9 110.0 110.1 110.2 110.4 110.5 110.6 110.7 110.9 111.0 111.1 111.2 111.4

–0.0468 –0.0459 –0.0450 –0.0442 –0.0433 –0.0425 –0.0416 –0.0408 –0.0399 –0.0390 –0.0382 –0.0373 –0.0365 –0.0356 –0.0348 –0.0339 –0.0331 –0.0323 –0.0314 –0.0306 –0.0297 –0.0289 –0.0280 –0.0272 –0.0264 –0.0255 –0.0247 –0.0238 –0.0230 –0.0222 –0.0213

0.2985 0.2979 0.2974 0.2968 0.2962 0.2957 0.2951 0.2946 0.2940 0.2935 0.2930 0.2925 0.2919 0.2914 0.2909 0.2904 0.2899 0.2894 0.2889 0.2884 0.2879 0.2874 0.2869 0.2865 0.2860 0.2855 0.2851 0.2846 0.2841 0.2837 0.2832

–96 –95 –94 –93 –92 –91 –90 –89 –88 –87 –86 –85 –84 –83 –82 –81 –80 –79 –78 –77 –76 –75 –74 –73 –72 –71 –70 –69 –68 –67 –66 (continued)

Appendix 2 727

–65 –64 –63 –62 –61 –60 –59 –58 –57 –56 –55 –54 –53 –52 –51 –50 –49 –48 –47 –46 –45 –44 –43 –42 –41 –40 –39

Temp. °F

13.05 13.43 13.82 14.22 14.63 15.05 15.47 15.91 16.35 16.81 17.28 17.75 18.24 18.73 19.24 19.76 20.29 20.82 21.38 21.94 22.51 23.10 23.69 24.30 24.92 25.56 26.20

Liquid pf

13.02 13.40 13.79 14.19 14.60 15.01 15.44 15.87 16.32 16.77 17.24 17.71 18.19 18.69 19.19 19.71 20.24 20.78 21.32 21.88 22.46 23.04 23.64 24.24 24.86 25.49 26.14

Vapor pg

Pressure, psia

0.0117 0.0117 0.0117 0.0117 0.0117 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0119 0.0119 0.0119 0.0119 0.0119 0.0119 0.0119 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120 0.0121 0.0121 0.0121

Liquid vf 4.2895 4.1749 4.0639 3.9565 3.8526 3.7519 3.6543 3.5599 3.4683 3.3796 3.2937 3.2103 3.1295 3.0512 2.9752 2.9015 2.8300 2.7606 2.6933 2.6279 2.5645 2.5029 2.4430 2.3849 2.3285 2.2737 2.2204

Vapor vg

Volume, ft.3/lb.

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (Continued)

85.62 85.51 85.40 85.29 85.17 85.06 84.95 84.84 84.72 84.61 84.50 84.38 84.27 84.15 84.04 83.92 83.81 83.69 83.58 83.46 83.35 83.23 83.11 83.00 82.88 82.76 82.65

Liquid 1/vf 0.2331 0.2395 0.2461 0.2527 0.2596 0.2665 0.2736 0.2809 0.2883 0.2959 0.3036 0.3115 0.3195 0.3277 0.3361 0.3447 0.3534 0.3622 0.3713 0.3805 0.3899 0.3995 0.4093 0.4193 0.4295 0.4398 0.4504

Vapor 1/vg

Density, lb./ft.3

–8.2 –7.9 –7.6 –7.3 –6.9 –6.6 –6.3 –6.0 –5.6 –5.3 –5.0 –4.6 –4.3 –4.0 –3.7 –3.3 –3.0 –2.7 –2.3 –2.0 –1.7 –1.3 –1.0 –0.7 –0.3 0.0 0.3

Liquid hf 119.7 119.5 119.3 119.1 118.9 118.7 118.5 118.3 118.1 117.9 117.7 117.4 117.2 117.0 116.8 116.6 116.4 116.2 115.9 115.7 115.5 115.3 115.1 114.9 114.6 114.4 114.2

Latent hfg 111.5 111.6 111.7 111.8 112.0 112.1 112.2 112.3 112.4 112.6 112.7 112.8 112.9 113.0 113.2 113.3 113.4 113.5 113.6 113.7 113.8 114.0 114.1 114.2 114.3 114.4 114.5

Vapor hg

Enthalpy, Btu/lb.

–0.0205 –0.0197 –0.0189 –0.0180 –0.0172 –0.0164 –0.0155 –0.0147 –0.0139 –0.0131 –0.0122 –0.0114 –0.0106 –0.0098 –0.0090 –0.0082 –0.0073 –0.0065 –0.0057 –0.0049 –0.0041 –0.0033 –0.0025 –0.0017 –0.0008 0.0000 0.0008

Liquid sf 0.2828 0.2823 0.2819 0.2815 0.2810 0.2806 0.2802 0.2797 0.2793 0.2789 0.2785 0.2781 0.2777 0.2773 0.2768 0.2764 0.2761 0.2757 0.2753 0.2749 0.2745 0.2741 0.2737 0.2733 0.2730 0.2726 0.2722

Vapor sg

Entropy, Btu/(lb.)(°R)

–65 –64 –63 –62 –61 –60 –59 –58 –57 –56 –55 –54 –53 –52 –51 –50 –49 –48 –47 –46 –45 –44 –43 –42 –41 –40 –39

Temp. °F

728 Appendix 2

–38 –37 –36 –35 –34 –33 –32 –31 –30 –29 –28 –27 –26 –25 –24 –23 –22 –21 –20 –19 –18 –17 –16 –15 –14 –13 –12 –11 –10 –9 –8 –7

26.86 27.53 28.22 28.92 29.63 30.35 31.09 31.85 32.61 33.39 34.19 35.00 35.83 36.67 37.52 38.39 39.28 40.18 41.10 42.03 42.98 43.95 44.93 45.94 46.95 47.99 49.04 50.11 51.20 52.31 53.43 54.57

26.80 27.47 28.15 28.84 29.55 30.28 31.01 31.76 32.53 33.31 34.10 34.91 35.73 36.57 37.42 38.29 39.17 40.07 40.99 41.92 42.86 43.83 44.81 45.81 46.82 47.85 48.90 49.97 51.05 52.16 53.28 54.42

0.0121 0.0121 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0123 0.0123 0.0123 0.0123 0.0123 0.0124 0.0124 0.0124 0.0124 0.0124 0.0124 0.0125 0.0125 0.0125 0.0125 0.0125 0.0126 0.0126 0.0126 0.0126 0.0126 0.0127 0.0127 0.0127

2.1687 2.1183 2.0694 2.0219 1.9757 1.9307 1.8870 1.8444 1.8030 1.7628 1.7236 1.6854 1.6483 1.6122 1.5770 1.5427 1.5093 1.4768 1.4452 1.4143 1.3843 1.3550 1.3264 1.2986 1.2715 1.2450 1.2192 1.1941 1.1695 1.1456 1.1222 1.0995

82.53 82.41 82.29 82.17 82.05 81.93 81.81 81.70 81.58 81.45 81.33 81.21 81.09 80.97 80.85 80.73 80.60 80.48 80.36 80.23 80.11 79.99 79.86 79.74 79.61 79.49 79.36 79.24 79.11 78.98 78.86 78.73

0.4611 0.4721 0.4832 0.4946 0.5062 0.5179 0.5300 0.5422 0.5546 0.5673 0.5802 0.5933 0.6067 0.6203 0.6341 0.6482 0.6625 0.6771 0.6920 0.7071 0.7224 0.7380 0.7539 0.7701 0.7865 0.8032 0.8202 0.8375 0.8551 0.8729 0.8911 0.9095

0.7 1.0 1.3 1.7 2.0 2.3 2.7 3.0 3.4 3.7 4.0 4.4 4.7 5.1 5.4 5.7 6.1 6.4 6.8 7.1 7.5 7.8 8.2 8.5 8.8 9.2 9.5 9.9 10.2 10.6 10.9 11.3

114.0 113.7 113.5 113.3 113.1 112.8 112.6 112.4 112.1 111.9 111.7 111.4 111.2 111.0 110.7 110.5 110.3 110.0 109.8 109.5 109.3 109.1 108.8 108.6 108.3 108.1 107.8 107.6 107.3 107.1 106.8 106.6

114.6 114.7 114.9 115.0 115.1 115.2 115.3 115.4 115.5 115.6 115.7 115.8 115.9 116.0 116.1 116.2 116.3 116.5 116.6 116.7 116.8 116.9 117.0 117.1 117.2 117.3 117.4 117.5 117.6 117.6 117.7 117.8

0.0016 0.0024 0.0032 0.0040 0.0048 0.0056 0.0064 0.0072 0.0080 0.0088 0.0096 0.0104 0.0112 0.0120 0.0127 0.0135 0.0143 0.0151 0.0159 0.0167 0.0175 0.0183 0.0191 0.0198 0.0206 0.0214 0.0222 0.0230 0.0237 0.0245 0.0253 0.0261

0.2718 0.2715 0.2711 0.2708 0.2704 0.2700 0.2697 0.2693 0.2690 0.2686 0.2683 0.2679 0.2676 0.2673 0.2669 0.2666 0.2663 0.2659 0.2656 0.2653 0.2649 0.2646 0.2643 0.2640 0.2637 0.2633 0.2630 0.2627 0.2624 0.2621 0.2618 0.2615

–38 –37 –36 –35 –34 –33 –32 –31 –30 –29 –28 –27 –26 –25 –24 –23 –22 –21 –20 –19 –18 –17 –16 –15 –14 –13 –12 –11 –10 –9 –8 –7 (continued)

Appendix 2 729

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Temp. °F

55.74 56.92 58.12 59.34 60.58 61.83 63.11 64.41 65.73 67.07 68.43 69.81 71.22 72.64 74.09 75.56 77.05 78.56 80.09 81.65 83.23 84.84 86.46 88.11 89.79 91.49 93.21

Liquid pf

55.58 56.75 57.95 59.16 60.40 61.65 62.93 64.22 65.54 66.87 68.23 69.61 71.00 72.42 73.86 75.33 76.81 78.32 79.85 81.40 82.98 84.58 86.20 87.84 89.51 91.21 92.93

Vapor pg

Pressure, psia

0.0127 0.0127 0.0128 0.0128 0.0128 0.0128 0.0128 0.0129 0.0129 0.0129 0.0129 0.0130 0.0130 0.0130 0.0130 0.0130 0.0131 0.0131 0.0131 0.0131 0.0132 0.0132 0.0132 0.0132 0.0133 0.0133 0.0133

Liquid vf 1.0772 1.0555 1.0344 1.0137 0.9935 0.9738 0.9546 0.9358 0.9175 0.8996 0.8821 0.8650 0.8483 0.8320 0.8160 0.8004 0.7852 0.7703 0.7557 0.7415 0.7276 0.7140 0.7007 0.6876 0.6749 0.6625 0.6503

Vapor vg

Volume, ft.3/lb.

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (Continued)

78.60 78.47 78.35 78.22 78.09 77.96 77.83 77.70 77.57 77.44 77.31 77.17 77.04 76.91 76.78 76.64 76.51 76.37 76.24 76.11 75.97 75.83 75.70 75.56 75.42 75.29 75.15

Liquid 1/vf 0.9283 0.9474 0.9668 0.9865 1.0065 1.0269 1.0475 1.0686 1.0899 1.1116 1.1337 1.1561 1.1788 1.2020 1.2255 1.2493 1.2736 1.2982 1.3232 1.3486 1.3744 1.4006 1.4272 1.4542 1.4817 1.5095 1.5378

Vapor 1/vg

Density, lb./ft.3

11.6 12.0 12.3 12.7 13.0 13.4 13.7 14.1 14.5 14.8 15.2 15.5 15.9 16.2 16.6 16.9 17.3 17.7 18.0 18.4 18.7 19.1 19.5 19.8 20.2 20.5 20.9

Liquid hf 106.3 106.0 105.8 105.5 105.3 105.0 104.7 104.5 104.2 104.0 103.7 103.4 103.2 102.9 102.6 102.3 102.1 101.8 101.5 101.2 101.0 100.7 100.4 100.1 99.8 99.6 99.3

Latent hfg 117.9 118.0 118.1 118.2 118.3 118.4 118.5 118.6 118.7 118.8 118.9 118.9 119.0 119.1 119.2 119.3 119.4 119.5 119.5 119.6 119.7 119.8 119.9 119.9 120.0 120.1 120.2

Vapor hg

Enthalpy, Btu/lb.

0.0269 0.0276 0.0284 0.0292 0.0299 0.0307 0.0315 0.0323 0.0330 0.0338 0.0346 0.0353 0.0361 0.0369 0.0376 0.0384 0.0392 0.0399 0.0407 0.0414 0.0422 0.0430 0.0437 0.0445 0.0452 0.0460 0.0467

Liquid sf 0.2612 0.2609 0.2606 0.2603 0.2600 0.2597 0.2594 0.2591 0.2588 0.2585 0.2582 0.2579 0.2576 0.2573 0.2570 0.2568 0.2565 0.2562 0.2559 0.2556 0.2554 0.2551 0.2548 0.2545 0.2543 0.2540 0.2537

Vapor sg

Entropy, Btu/(lb.)(°R)

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Temp. °F

730 Appendix 2

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

94.96 96.73 98.53 100.36 102.20 104.08 105.98 107.91 109.86 111.84 113.85 115.88 117.94 120.03 122.15 124.30 126.47 128.67 130.91 133.17 135.46 137.78 140.13 142.51 144.92 147.36 149.83 152.34 154.87 157.44 160.04 162.67

94.67 96.43 98.23 100.04 101.89 103.76 105.65 107.57 109.52 111.49 113.49 115.52 117.57 119.66 121.77 123.90 126.07 128.27 130.49 132.74 135.03 137.34 139.68 142.05 144.46 146.89 149.35 151.85 154.37 156.93 159.52 162.14

0.0133 0.0134 0.0134 0.0134 0.0134 0.0135 0.0135 0.0135 0.0135 0.0136 0.0136 0.0136 0.0136 0.0137 0.0137 0.0137 0.0137 0.0138 0.0138 0.0138 0.0139 0.0139 0.0139 0.0139 0.0140 0.0140 0.0140 0.0141 0.0141 0.0141 0.0142 0.0142

0.6383 0.6267 0.6152 0.6041 0.5931 0.5824 0.5719 0.5616 0.5516 0.5417 0.5321 0.5227 0.5134 0.5043 0.4955 0.4868 0.4782 0.4699 0.4617 0.4537 0.4458 0.4381 0.4305 0.4231 0.4159 0.4087 0.4018 0.3949 0.3882 0.3816 0.3751 0.3688

75.01 74.87 74.73 74.59 74.45 74.31 74.17 74.03 73.89 73.74 73.60 73.46 73.31 73.17 73.02 72.88 72.73 72.58 72.43 72.29 72.14 71.99 71.84 71.69 71.54 71.39 71.23 71.08 70.93 70.77 70.62 70.46

1.5666 1.5958 1.6254 1.6555 1.6860 1.7170 1.7485 1.7805 1.8130 1.8459 1.8794 1.9133 1.9478 1.9828 2.0183 2.0544 2.0910 2.1282 2.1659 2.2042 2.2431 2.2826 2.3226 2.3633 2.4046 2.4465 2.4890 2.5322 2.5761 2.6206 2.6657 2.7116

21.3 21.6 22.0 22.4 22.7 23.1 23.5 23.8 24.2 24.6 24.9 25.3 25.7 26.1 26.4 26.8 27.2 27.5 27.9 28.3 28.7 29.1 29.4 29.8 30.2 30.6 30.9 31.3 31.7 32.1 32.5 32.9

99.0 98.7 98.4 98.1 97.8 97.5 97.2 96.9 96.6 96.3 96.0 95.7 95.4 95.1 94.8 94.5 94.2 93.9 93.6 93.3 93.0 92.7 92.3 92.0 91.7 91.4 91.0 90.7 90.4 90.1 89.7 89.4

120.3 120.3 120.4 120.5 120.6 120.6 120.7 120.8 120.9 120.9 121.0 121.1 121.1 121.2 121.3 121.3 121.4 121.5 121.5 121.6 121.6 121.7 121.8 121.8 121.9 121.9 122.0 122.0 122.1 122.2 122.2 122.3

0.0475 0.0483 0.0490 0.0498 0.0505 0.0513 0.0520 0.0528 0.0535 0.0543 0.0550 0.0558 0.0565 0.0573 0.0580 0.0588 0.0595 0.0602 0.0610 0.0617 0.0625 0.0632 0.0640 0.0647 0.0655 0.0662 0.0669 0.0677 0.0684 0.0692 0.0699 0.0706

0.2534 0.2532 0.2529 0.2526 0.2524 0.2521 0.2518 0.2516 0.2513 0.2510 0.2508 0.2505 0.2502 0.2500 0.2497 0.2495 0.2492 0.2489 0.2487 0.2484 0.2482 0.2479 0.2477 0.2474 0.2471 0.2469 0.2466 0.2464 0.2461 0.2459 0.2456 0.2454

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 (continued)

Appendix 2 731

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

Temp. °F

165.33 168.03 170.76 173.52 176.32 179.15 182.01 184.91 187.84 190.81 193.82 196.86 199.93 203.04 206.19 209.38 212.60 215.86 219.15 222.49 225.86 229.27 232.72 236.20 239.73 243.30 246.91

Liquid pf

164.80 167.48 170.20 172.96 175.74 178.57 181.42 184.31 187.23 190.19 193.18 196.21 199.28 202.38 205.51 208.69 211.90 215.14 218.43 221.75 225.11 228.51 231.94 235.42 238.93 242.49 246.08

Vapor pg

Pressure, psia

0.0142 0.0143 0.0143 0.0143 0.0144 0.0144 0.0144 0.0145 0.0145 0.0145 0.0146 0.0146 0.0146 0.0147 0.0147 0.0147 0.0148 0.0148 0.0148 0.0149 0.0149 0.0150 0.0150 0.0150 0.0151 0.0151 0.0152

Liquid vf 0.3626 0.3565 0.3505 0.3446 0.3388 0.3332 0.3276 0.3221 0.3168 0.3115 0.3064 0.3013 0.2963 0.2914 0.2866 0.2819 0.2773 0.2727 0.2682 0.2638 0.2595 0.2553 0.2511 0.2470 0.2430 0.2390 0.2351

Vapor vg

Volume, ft.3/lb.

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (Continued)

70.31 70.15 69.99 69.83 69.67 69.51 69.35 69.19 69.03 68.87 68.70 68.54 68.37 68.21 68.04 67.87 67.71 67.54 67.37 67.19 67.02 66.85 66.68 66.50 66.32 66.15 65.97

Liquid 1/vf 2.7581 2.8054 2.8533 2.9020 2.9514 3.0016 3.0526 3.1043 3.1568 3.2101 3.2642 3.3191 3.3749 3.4316 3.4891 3.5475 3.6068 3.6670 3.7281 3.7902 3.8533 3.9173 3.9823 4.0484 4.1155 4.1836 4.2529

Vapor 1/vg

Density, lb./ft.3

33.2 33.6 34.0 34.4 34.8 35.2 35.6 36.0 36.3 36.7 37.1 37.5 37.9 38.3 38.7 39.1 39.5 39.9 40.3 40.7 41.1 41.5 41.9 42.3 42.7 43.1 43.5

Liquid hf 89.1 88.7 88.4 88.0 87.7 87.4 87.0 86.7 86.3 86.0 85.6 85.3 84.9 84.5 84.2 83.8 83.4 83.1 82.7 82.3 81.9 81.6 81.2 80.8 80.4 80.0 79.6

Latent hfg 122.3 122.3 122.4 122.4 122.5 122.5 122.6 122.6 122.7 122.7 122.7 122.8 122.8 122.8 122.9 122.9 122.9 123.0 123.0 123.0 123.0 123.1 123.1 123.1 123.1 123.1 123.2

Vapor hg

Enthalpy, Btu/lb.

0.0714 0.0721 0.0729 0.0736 0.0743 0.0751 0.0758 0.0766 0.0773 0.0780 0.0788 0.0795 0.0802 0.0810 0.0817 0.0825 0.0832 0.0839 0.0847 0.0854 0.0861 0.0869 0.0876 0.0884 0.0891 0.0898 0.0906

Liquid sf 0.2451 0.2448 0.2446 0.2443 0.2441 0.2438 0.2436 0.2433 0.2431 0.2428 0.2426 0.2423 0.2420 0.2418 0.2415 0.2413 0.2410 0.2408 0.2405 0.2402 0.2400 0.2397 0.2395 0.2392 0.2389 0.2387 0.2384

Vapor sg

Entropy, Btu/(lb.)(°R)

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

Temp. °F

732 Appendix 2

80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

250.55 254.24 257.97 261.74 265.55 269.40 273.29 277.23 281.21 285.23 289.29 293.40 297.55 301.75 305.99 310.27 314.60 318.98 323.40 327.87 332.38 336.94 341.54 346.20 350.90 355.65 360.45 365.29 370.19 375.13 380.12

249.71 253.39 257.10 260.85 264.65 268.49 272.37 276.29 280.25 284.26 288.31 292.40 296.54 300.72 304.95 309.22 313.53 317.89 322.29 326.75 331.24 335.79 340.38 345.02 349.70 354.44 359.22 364.05 368.93 373.86 378.84

0.0152 0.0152 0.0153 0.0153 0.0154 0.0154 0.0155 0.0155 0.0155 0.0156 0.0156 0.0157 0.0157 0.0158 0.0158 0.0159 0.0159 0.0160 0.0160 0.0161 0.0161 0.0162 0.0163 0.0163 0.0164 0.0164 0.0165 0.0165 0.0166 0.0167 0.0167

0.2313 0.2276 0.2239 0.2202 0.2166 0.2131 0.2097 0.2063 0.2029 0.1996 0.1964 0.1932 0.1901 0.1870 0.1840 0.1810 0.1781 0.1752 0.1723 0.1695 0.1668 0.1640 0.1614 0.1587 0.1561 0.1536 0.1511 0.1486 0.1462 0.1438 0.1414

65.79 65.61 65.43 65.25 65.06 64.88 64.69 64.51 64.32 64.13 63.94 63.74 63.55 63.36 63.16 62.96 62.76 62.56 62.36 62.16 61.95 61.74 61.53 61.32 61.11 60.90 60.68 60.46 60.24 60.02 59.79

4.3232 4.3946 4.4672 4.5409 4.6159 4.6920 4.7693 4.8480 4.9278 5.0090 5.0916 5.1755 5.2608 5.3474 5.4356 5.5252 5.6164 5.7090 5.8033 5.8992 5.9967 6.0959 6.1969 6.2996 6.4041 6.5105 6.6188 6.7290 6.8413 6.9555 7.0719

43.9 44.3 44.8 45.2 45.6 46.0 46.4 46.8 47.3 47.7 48.1 48.5 48.9 49.4 49.8 50.2 50.7 51.1 51.5 52.0 52.4 52.8 53.3 53.7 54.2 54.6 55.1 55.5 56.0 56.5 56.9

79.2 78.8 78.4 78.0 77.6 77.2 76.8 76.4 76.0 75.5 75.1 74.7 74.3 73.8 73.4 72.9 72.5 72.1 71.6 71.1 70.7 70.2 69.7 69.3 68.8 68.3 67.8 67.3 66.8 66.3 65.8

123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.2 123.1 123.1 123.1 123.1 123.1 123.0 123.0 123.0 122.9 122.9 122.9 122.8 122.8 122.7

0.0913 0.0921 0.0928 0.0936 0.0943 0.0950 0.0958 0.0965 0.0973 0.0980 0.0988 0.0995 0.1003 0.1010 0.1018 0.1025 0.1033 0.1040 0.1048 0.1056 0.1063 0.1071 0.1079 0.1086 0.1094 0.1102 0.1109 0.1117 0.1125 0.1133 0.1141

0.2381 0.2379 0.2376 0.2373 0.2371 0.2368 0.2365 0.2363 0.2360 0.2357 0.2354 0.2352 0.2349 0.2346 0.2343 0.2340 0.2338 0.2335 0.2332 0.2329 0.2326 0.2323 0.2320 0.2317 0.2314 0.2311 0.2308 0.2305 0.2302 0.2299 0.2296

80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 (continued)

Appendix 2 733

111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

Temp. °F

385.17 390.26 395.40 400.60 405.84 411.14 416.49 421.89 427.34 432.85 438.41 444.02 449.68 455.40 461.18 467.01 472.89 478.83 484.83 490.88 496.98 503.15 509.37

Liquid pf

383.86 388.94 394.07 399.25 404.49 409.77 415.11 420.49 425.94 431.43 436.98 442.58 448.24 453.95 459.72 465.54 471.42 477.35 483.35 489.39 495.50 501.66 507.89

Vapor pg

Pressure, psia

0.0168 0.0169 0.0169 0.0170 0.0171 0.0171 0.0172 0.0173 0.0173 0.0174 0.0175 0.0176 0.0177 0.0177 0.0178 0.0179 0.0180 0.0181 0.0182 0.0183 0.0184 0.0185 0.0186

Liquid vf 0.1391 0.1368 0.1345 0.1323 0.1301 0.1279 0.1258 0.1237 0.1216 0.1195 0.1175 0.1155 0.1136 0.1116 0.1097 0.1078 0.1060 0.1041 0.1023 0.1005 0.0987 0.0970 0.0952

Vapor vg

Volume, ft.3/lb.

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (Continued)

59.57 59.34 59.10 58.87 58.63 58.39 58.15 57.91 57.66 57.41 57.16 56.90 56.64 56.37 56.11 55.83 55.56 55.28 54.99 54.70 54.41 54.11 53.80

Liquid 1/vf 7.1904 7.3112 7.4342 7.5596 7.6873 7.8176 7.9504 8.0858 8.2239 8.3648 8.5085 8.6553 8.8051 8.9581 9.1144 9.2741 9.4374 9.6043 9.7752 9.9500 10.1290 10.3125 10.5005

Vapor 1/vg

Density, lb./ft.3

57.4 57.8 58.3 58.8 59.3 59.7 60.2 60.7 61.2 61.7 62.2 62.7 63.2 63.7 64.2 64.8 65.3 65.8 66.3 66.9 67.4 68.0 68.6

Liquid hf 65.3 64.8 64.3 63.7 63.2 62.6 62.1 61.5 61.0 60.4 59.8 59.2 58.7 58.1 57.4 56.8 56.2 55.6 54.9 54.3 53.6 52.9 52.2

Latent hfg 122.7 122.6 122.6 122.5 122.5 122.4 122.3 122.3 122.2 122.1 122.0 121.9 121.9 121.8 121.7 121.6 121.5 121.4 121.3 121.2 121.0 120.9 120.8

Vapor hg

Enthalpy, Btu/lb.

0.1148 0.1156 0.1164 0.1172 0.1180 0.1188 0.1196 0.1204 0.1213 0.1221 0.1229 0.1237 0.1246 0.1254 0.1263 0.1271 0.1280 0.1289 0.1298 0.1306 0.1315 0.1324 0.1334

Liquid sf

0.2293 0.2289 0.2286 0.2283 0.2280 0.2276 0.2273 0.2270 0.2266 0.2263 0.2259 0.2256 0.2252 0.2249 0.2245 0.2242 0.2238 0.2234 0.2230 0.2227 0.2223 0.2219 0.2215

Vapor sg

Entropy, Btu/(lb.)(°R)

111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

Temp. °F

734 Appendix 2

515.65 521.98 528.37 534.83 541.34 547.90 554.53 561.22 567.97 574.77 581.64 588.57 595.55 602.60 609.71 616.88 624.12 631.41 638.77 646.19 653.67 661.22 668.82 676.49 684.23 692.02 699.88

514.17 520.51 526.91 533.37 539.89 546.47 553.12 559.82 566.59 573.42 580.31 587.27 594.29 601.37 608.52 615.74 623.02 630.37 637.78 645.26 652.81 660.43 668.12 675.87 683.70 691.60 699.56

0.0187 0.0188 0.0189 0.0190 0.0192 0.0193 0.0194 0.0196 0.0197 0.0199 0.0200 0.0202 0.0204 0.0205 0.0207 0.0209 0.0212 0.0214 0.0217 0.0219 0.0222 0.0226 0.0230 0.0234 0.0239 0.0246 0.0255

0.0935 0.0918 0.0901 0.0885 0.0868 0.0852 0.0835 0.0819 0.0803 0.0787 0.0771 0.0755 0.0739 0.0723 0.0706 0.0690 0.0673 0.0656 0.0639 0.0621 0.0602 0.0583 0.0562 0.0541 0.0518 0.0496 0.0476

53.49 53.18 52.85 52.52 52.18 51.84 51.48 51.12 50.74 50.36 49.96 49.55 49.13 48.69 48.23 47.76 47.26 46.73 46.18 45.59 44.96 44.28 43.54 42.71 41.77 40.65 39.25

10.6935 10.8915 11.0950 11.3043 11.5197 11.7418 11.9709 12.2077 12.4528 12.7071 12.9714 13.2468 13.5347 13.8367 14.1547 14.4913 14.8496 15.2337 15.6486 16.1014 16.6006 17.1576 17.7852 18.4945 19.2867 20.1422 21.0231

69.1 69.7 70.3 70.9 71.5 72.1 72.8 73.4 74.1 74.8 75.4 76.2 76.9 77.6 78.4 79.2 80.0 80.9 81.8 82.8 83.8 84.9 86.0 87.3 88.7 90.3 92.3

51.5 50.8 50.1 49.3 48.6 47.8 47.0 46.2 45.4 44.5 43.6 42.7 41.8 40.8 39.8 38.7 37.6 36.5 35.3 34.0 32.7 31.3 29.8 28.2 26.5 24.8 23.0

120.7 120.5 120.4 120.3 120.1 119.9 119.8 119.6 119.4 119.3 119.1 118.9 118.7 118.4 118.2 117.9 117.7 117.4 117.1 116.8 116.5 116.1 115.8 115.5 115.2 115.1 115.2

Source: Thermodynamic Properties of DuPont Suva 410A Refrigerant. With permission of E. I. Du Pont de Nemours and Co.

134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

0.1343 0.1352 0.1362 0.1372 0.1381 0.1391 0.1401 0.1412 0.1422 0.1433 0.1444 0.1455 0.1467 0.1479 0.1491 0.1504 0.1517 0.1531 0.1545 0.1560 0.1576 0.1593 0.1612 0.1632 0.1654 0.1680 0.1711

0.2211 0.2207 0.2203 0.2198 0.2194 0.2190 0.2185 0.2181 0.2176 0.2171 0.2167 0.2162 0.2157 0.2151 0.2146 0.2140 0.2135 0.2129 0.2122 0.2116 0.2109 0.2102 0.2095 0.2089 0.2083 0.2080 0.2081

134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Appendix 2 735

(47.6197)

48.4112 49.9202 51.4258 52.9283 54.4281 55.9256 57.4211 58.9148 60.4069 61.8976 63.3871 64.8755 66.3630 67.8496 69.3354 70.8206 72.3051 73.7891 75.2727 76.7558 78.2385 79.7209 81.2030 82.6848 84.1663

Temp. °F

–130 –120 –110 –100 –90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110

V

103.0 104.5 106.1 107.6 109.2 110.8 112.5 114.1 115.8 117.5 119.2 120.9 122.7 124.5 126.2 128.1 129.9 131.8 133.6 135.5 137.5 139.4 141.4 143.3 145.3

(102.2)

0.3281 0.3327 0.3372 0.3416 0.3459 0.3502 0.3544 0.3586 0.3627 0.3668 0.3709 0.3748 0.3788 0.3827 0.3866 0.3904 0.3942 0.3979 0.4017 0.4054 0.4090 0.4126 0.4162 0.4198 0.4234

(0.3257)

S – – 25.5747 26.3382 27.0990 27.8575 28.6138 29.3684 30.1213 30.8728 31.6231 32.3723 33.1205 33.8679 34.6145 35.3604 36.1057 36.8505 37.5948 38.3387 39.0821 39.8253 40.5681 41.3106 42.0529

(24.8559)

V – – 105.9 107.4 109.1 110.7 112.3 114.0 115.7 117.4 119.1 120.8 122.6 124.4 126.2 128.0 129.8 131.7 133.6 135.5 137.4 139.4 141.3 143.3 145.3

(104.4)

H

(–119.38°F)

(–135.23°F)

H

2.00

1.00

– – 0.3177 0.3222 0.3266 0.3309 0.3352 0.3394 0.3435 0.3476 0.3517 0.3557 0.3597 0.3636 0.3675 0.3713 0.3751 0.3789 0.3826 0.3863 0.3900 0.3936 0.3972 0.4008 0.4043

(0.3135)

S – – – 17.4741 17.9887 18.5009 19.0110 19.5192 20.0258 20.5310 21.0349 21.5378 22.0396 22.5406 23.0408 23.5403 24.0392 24.5376 25.0355 25.5329 26.0300 26.5267 27.0231 27.5192 28.0151

(17.0005)

V

Absolute Pressure, psia

– – – 107.2 108.9 110.5 112.2 113.8 115.5 117.2 119.0 120.7 122.5 124.3 126.1 127.9 129.8 131.6 133.5 135.4 137.4 139.3 141.3 143.3 145.3

(105.8)

H

(–109.16°F)

3.00

– – – 0.3107 0.3151 0.3195 0.3238 0.3280 0.3322 0.3363 0.3404 0.3444 0.3484 0.3523 0.3562 0.3601 0.3639 0.3677 0.3714 0.3751 0.3788 0.3824 0.3861 0.3896 0.3932

(0.3065)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19

– – – 13.0415 13.4331 13.8223 14.2093 14.5944 14.9779 15.3599 15.7407 16.1204 16.4990 16.8768 17.2538 17.6302 18.0059 18.3811 18.7558 19.1300 19.5039 19.8774 20.2506 20.6235 20.9962

(12.9842)

V – – – 107.0 108.7 110.3 112.0 113.7 115.4 117.1 118.9 120.6 122.4 124.2 126.0 127.8 129.7 131.6 133.5 135.4 137.3 139.3 141.2 143.2 145.2

(106.8)

H

(–101.46°F)

4.00

– – – 0.3024 0.3069 0.3113 0.3156 0.3199 0.3241 0.3282 0.3323 0.3364 0.3404 0.3443 0.3482 0.3521 0.3559 0.3597 0.3635 0.3672 0.3709 0.3745 0.3781 0.3817 0.3853

(0.3017)

S –130 –120 –110 –100 –90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110

Temp. °F

736 Appendix 2

–

190

(10.5348)

10.6994 11.0148 11.3280 11.6393 11.9490 12.2572 12.5641 12.8698 13.1746 13.4785 13.7816 14.0841 14.3859 14.6871 14.9879 15.2882

Temp. °F

–90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60

V

85.6477 87.1288 88.6097 90.0905 91.5711 93.0516 – –

120 130 140 150 160 170 170 180

108.5 110.2 111.9 113.6 115.3 117.0 118.7 120.5 122.3 124.1 125.9 127.8 129.6 131.5 133.4 135.3

(107.6)

H

0.3004 0.3048 0.3092 0.3135 0.3177 0.3219 0.3260 0.3301 0.3341 0.3381 0.3420 0.3459 0.3497 0.3535 0.3573 0.3610

(0.2980)

S – 9.1429 9.4070 9.6691 9.9295 10.1885 10.4462 10.7027 10.9583 11.2129 11.4668 11.7199 11.9725 12.2245 12.4760 12.7270

(8.8803)

V – 110.0 111.7 113.4 115.1 116.9 118.6 120.4 122.2 124.0 125.8 127.7 129.6 131.4 133.3 135.3

(108.3)

H

(–89.86°F)

–

147.3 149.4 151.4 153.5 155.6 157.7 159.9 162.0

(–95.19°F)

–

42.7950 43.5369 44.2785 45.0201 45.7614 46.5026 47.2437 47.9847

6.00

–

0.4269 0.4304 0.4338 0.4373 0.4407 0.4441 – –

5.00

–

147.4 149.4 151.5 153.5 155.6 157.8 – –

– 0.2995 0.3039 0.3082 0.3125 0.3167 0.3209 0.3249 0.3290 0.3329 0.3369 0.3408 0.3446 0.3484 0.3522 0.3559

(0.2951)

S

–

0.4079 0.4114 0.4148 0.4183 0.4217 0.4251 0.4284 0.4318

– 7.8056 8.0346 8.2616 8.4870 8.7108 8.9334 9.1547 9.3751 9.5946 9.8133 10.0313 10.2486 10.4654 10.6817 10.8976

(7.6853)

V

32.4700

28.5108 29.0062 29.5015 29.9966 30.4915 30.9863 31.4810 31.9756

– 109.8 111.5 113.3 115.0 116.8 118.5 120.3 122.1 123.9 125.8 127.6 129.5 131.4 133.3 135.2

(108.9)

H

(–85.21°F)

7.00

164.2

147.3 149.3 151.4 153.5 155.6 157.7 159.8 162.0

– 0.2949 0.2994 0.3037 0.3080 0.3123 0.3164 0.3205 0.3246 0.3286 0.3325 0.3364 0.3403 0.3441 0.3479 0.3516

(0.2926)

S

0.4240

0.3967 0.4002 0.4037 0.4071 0.4106 0.4139 0.4173 0.4207

– 6.8024 7.0052 7.2059 7.4050 7.6025 7.7987 7.9937 8.1877 8.3808 8.5731 8.7647 8.9557 9.1461 9.3360 9.5255

(6.7804)

V

24.3423

21.3686 21.7409 22.1129 22.4848 22.8566 23.2282 23.5996 23.9710

– 109.7 111.4 113.1 114.9 116.6 118.4 120.2 122.0 123.8 125.7 127.5 129.4 131.3 133.2 135.1

(109.5)

H

(–81.08°F)

8.00

164.2

147.2 149.3 151.4 153.4 155.5 157.7 159.8 162.0

– 0.2909 0.2954 0.2998 0.3041 0.3084 0.3126 0.3167 0.3208 0.3248 0.3287 0.3327 0.3365 0.3404 0.3441 0.3479

(0.2904)

S

0.4161

0.3888 0.3923 0.3958 0.3992 0.4026 0.4060 0.4094 0.4128

–90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 (continued)

Temp. °F

190

120 130 140 150 160 170 170 180

Appendix 2 737

15.5882 15.8878 16.1871 16.4861 16.7848 17.0834 17.3817 17.6798 17.9778 18.2756 18.5733 18.8708 19.1682 19.4656 19.7628 –

70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

(6.0708)

6.2043 6.3847

Temp. °F

–70 –60

V

(10.5348)

Temp. °F

V

111.2 113.0

(109.9)

H

0.2919 0.2963

(0.2886)

S

5.5635 5.7276

(5.4988)

V

111.1 112.8

(110.4)

H

(–73.91°F)

137.2 139.2 141.1 143.1 145.1 147.2 149.2 151.3 153.4 155.5 157.6 159.8 161.9 164.1 166.3 168.5

(108.3)

(–77.33°F)

12.9777 13.2280 13.4780 13.7278 13.9772 14.2265 14.4755 14.7244 14.9731 15.2216 15.4700 15.7183 15.9664 16.2145 16.4624 16.7103

(8.8803)

H

10.00

0.3647 0.3683 0.3720 0.3755 0.3791 0.3826 0.3861 0.3896 0.3931 0.3965 0.3999 0.4033 0.4066 0.4100 0.4133 –

(0.2980)

V

9.00

137.2 139.2 141.2 143.2 145.2 147.2 149.3 151.3 153.4 155.5 157.6 159.8 161.9 164.1 166.3 –

(107.6)

S

(–89.86°F)

(–95.19°F)

H

6.00

5.00

0.2887 0.2931

(0.2869)

S

0.3596 0.3633 0.3669 0.3705 0.3741 0.3776 0.3811 0.3846 0.3880 0.3915 0.3949 0.3983 0.4016 0.4049 0.4083 0.4115

(0.2951)

S

5.0391 5.1899

(5.0277)

V

11.1131 11.3282 11.5430 11.7575 11.9718 12.1859 12.3997 12.6134 12.8268 13.0402 13.2534 13.4664 13.6794 13.8922 14.1050 14.3176

(7.6853)

V

Absolute Pressure, psia

110.9 112.7

(110.8)

H

(–70.75°F)

11.00

137.1 139.1 141.1 143.1 145.1 147.1 149.2 151.3 153.3 155.5 157.6 159.7 161.9 164.1 166.3 168.5

(108.9)

H

(–85.21°F)

7.00

0.2857 0.2903

(0.2854)

S

0.3553 0.3590 0.3626 0.3662 0.3698 0.3733 0.3768 0.3803 0.3838 0.3872 0.3906 0.3940 0.3974 0.4007 0.4040 0.4073

(0.2926)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– 4.7417

(4.6327)

V

9.7146 9.9033 10.0917 10.2799 10.4677 10.6554 10.8428 11.0301 11.2172 11.4041 11.5909 11.7776 11.9641 12.1505 12.3369 12.5232

(6.7804)

V

– 112.5

(111.1)

H

(–67.81°F)

12.00

137.1 139.1 141.0 143.0 145.1 147.1 149.1 151.2 153.3 155.4 157.5 159.7 161.9 164.0 166.2 168.5

(109.5)

H

(–81.08°F)

8.00

– 0.2876

(0.2840)

S

0.3516 0.3553 0.3589 0.3625 0.3661 0.3696 0.3731 0.3766 0.3801 0.3835 0.3869 0.3903 0.3937 0.3970 0.4003 0.4036

(0.2904)

S

–70 –60

Temp. °F

70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

Temp. °F

738 Appendix 2

–50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240

6.5633 6.7403 6.9161 7.0906 7.2641 7.4367 7.6085 7.7796 7.9501 8.1199 8.2893 8.4583 8.6269 8.7951 8.9630 9.1306 9.2979 9.4650 9.6319 9.7986 9.9652 10.1316 10.2978 10.4640 10.6300 10.7959 10.9617 11.1275 11.2931 –

114.7 116.5 118.3 120.1 121.9 123.8 125.6 127.5 129.3 131.2 133.2 135.1 137.0 139.0 141.0 143.0 145.0 147.0 149.1 151.2 153.3 155.4 157.5 159.7 161.8 164.0 166.2 168.4 170.7 –

0.3007 0.3050 0.3092 0.3133 0.3174 0.3214 0.3254 0.3293 0.3332 0.3370 0.3408 0.3446 0.3483 0.3520 0.3556 0.3592 0.3628 0.3664 0.3699 0.3734 0.3768 0.3803 0.3837 0.3871 0.3904 0.3938 0.3971 0.4004 0.4036 –

5.8899 6.0506 6.2099 6.3681 6.5252 6.6814 6.8368 6.9915 7.1455 7.2990 7.4520 7.6045 7.7567 7.9085 8.0599 8.2111 8.3620 8.5127 8.6632 8.8135 8.9636 9.1136 9.2634 9.4131 9.5627 9.7122 9.8616 10.0109 10.1601 –

114.6 116.4 118.2 120.0 121.8 123.7 125.5 127.4 129.3 131.2 133.1 135.0 137.0 138.9 140.9 142.9 145.0 147.0 149.1 151.1 153.2 155.4 157.5 159.6 161.8 164.0 166.2 168.4 170.7 –

0.2975 0.3018 0.3061 0.3102 0.3143 0.3184 0.3224 0.3263 0.3302 0.3341 0.3379 0.3416 0.3453 0.3490 0.3527 0.3563 0.3599 0.3634 0.3669 0.3704 0.3739 0.3773 0.3808 0.3841 0.3875 0.3908 0.3942 0.3975 0.4007 –

5.3388 5.4861 5.6321 5.7769 5.9206 6.0634 6.2054 6.3466 6.4873 6.6273 6.7669 6.9060 7.0447 7.1830 7.3211 7.4588 7.5963 7.7335 7.8706 8.0074 8.1441 8.2807 8.4171 8.5533 8.6895 8.8255 8.9615 9.0973 9.2331 –

114.5 116.3 118.1 119.9 121.7 123.6 125.4 127.3 129.2 131.1 133.0 135.0 136.9 138.9 140.9 142.9 144.9 147.0 149.0 151.1 153.2 155.3 157.5 159.6 161.8 164.0 166.2 168.4 170.6 –

0.2947 0.2990 0.3033 0.3075 0.3116 0.3156 0.3196 0.3236 0.3275 0.3313 0.3352 0.3389 0.3427 0.3463 0.3500 0.3536 0.3572 0.3608 0.3643 0.3678 0.3713 0.3747 0.3781 0.3815 0.3849 0.3882 0.3915 0.3948 0.3981 –

4.8795 5.0157 5.1505 5.2842 5.4167 5.5484 5.6792 5.8092 5.9387 6.0676 6.1959 6.3238 6.4514 6.5785 6.7053 6.8319 6.9582 7.0842 7.2101 7.3357 7.4612 7.5866 7.7118 7.8368 7.9618 8.0866 8.2114 8.3360 8.4606 8.5851

114.3 116.1 118.0 119.8 121.6 123.5 125.4 127.2 129.1 131.0 133.0 134.9 136.9 138.8 140.8 142.9 144.9 146.9 149.0 151.1 153.2 155.3 157.4 159.6 161.7 163.9 166.1 168.4 170.6 172.9

0.2920 0.2964 0.3007 0.3049 0.3090 0.3131 0.3171 0.3211 0.3250 0.3289 0.3327 0.3365 0.3402 0.3439 0.3476 0.3512 0.3548 0.3583 0.3619 0.3654 0.3688 0.3723 0.3757 0.3791 0.3825 0.3858 0.3891 0.3924 0.3957 0.3989 (continued)

–50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240

Appendix 2 739

(4.2967)

4.3623 4.4908 4.6176 4.7430 4.8672 4.9903 5.1125 5.2339 5.3545 5.4745 5.5939 5.7128 5.8313 5.9493 6.0670 6.1843 6.3014 6.4182 6.5348 6.6512 6.7674 6.8834 6.9993 7.1150

Temp. °F

–60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

V

112.4 114.2 116.0 117.8 119.7 121.5 123.4 125.3 127.2 129.1 131.0 132.9 134.9 136.8 138.8 140.8 142.8 144.8 146.9 149.0 151.0 153.1 155.3 157.4

(111.5)

0.2851 0.2896 0.2940 0.2983 0.3025 0.3067 0.3108 0.3148 0.3188 0.3227 0.3266 0.3304 0.3342 0.3379 0.3416 0.3453 0.3489 0.3525 0.3561 0.3596 0.3631 0.3666 0.3701 0.3735

(0.2828)

S

4.0371 4.1575 4.2763 4.3937 4.5098 4.6248 4.7389 4.8522 4.9647 5.0766 5.1879 5.2987 5.4090 5.5190 5.6285 5.7378 5.8467 5.9554 6.0639 6.1721 6.2802 6.3881 6.4958 6.6034

(4.0070)

V

112.2 114.1 115.9 117.7 119.6 121.4 123.3 125.2 127.1 129.0 130.9 132.8 134.8 136.8 138.7 140.7 142.8 144.8 146.8 148.9 151.0 153.1 155.2 157.4

(111.8)

H

(–62.48°F)

(–65.06°F)

H

14.00

13.00

0.2828 0.2873 0.2917 0.2961 0.3003 0.3045 0.3086 0.3126 0.3166 0.3206 0.3244 0.3283 0.3321 0.3358 0.3395 0.3432 0.3468 0.3504 0.3540 0.3576 0.3611 0.3645 0.3680 0.3714

(0.2817)

S

3.8368 3.9523 4.0662 4.1786 4.2897 4.3998 4.5089 4.6172 4.7247 4.8316 4.9379 5.0437 5.1491 5.2540 5.3586 5.4628 5.5668 5.6705 5.7739 5.8772 5.9803 6.0832 6.1859 6.2885

(3.8280)

V

Absolute Pressure, psia

112.1 114.0 115.8 117.7 119.5 121.4 123.2 125.1 127.0 128.9 130.9 132.8 134.8 136.7 138.7 140.7 142.7 144.8 146.8 148.9 151.0 153.1 155.2 157.3

(112.0)

H

(–60.76°F)

14.696

0.2813 0.2858 0.2902 0.2946 0.2989 0.3030 0.3072 0.3112 0.3152 0.3192 0.3230 0.3269 0.3307 0.3344 0.3382 0.3418 0.3455 0.3491 0.3527 0.3562 0.3597 0.3632 0.3666 0.3701

(0.2809)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

3.7552 3.8687 3.9805 4.0909 4.2000 4.3080 4.4151 4.5214 4.6269 4.7317 4.8360 4.9398 5.0431 5.1460 5.2485 5.3507 5.4527 5.5543 5.6557 5.7570 5.8580 5.9588 6.0595 6.1601

(3.7548)

V

112.1 113.9 115.8 117.6 119.5 121.3 123.2 125.1 127.0 128.9 130.8 132.8 134.7 136.7 138.7 140.7 142.7 144.8 146.8 148.9 151.0 153.1 155.2 157.3

(112.1)

H

(–60.03°F)

15.00

0.2806 0.2852 0.2896 0.2940 0.2982 0.3024 0.3066 0.3106 0.3146 0.3186 0.3225 0.3263 0.3301 0.3339 0.3376 0.3413 0.3449 0.3485 0.3521 0.3556 0.3591 0.3626 0.3661 0.3695

(0.2806)

S

–60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

Temp. °F

740 Appendix 2

(3.5331)

3.6158 3.7216 3.8259 3.9289 4.0308 4.1318 4.2319 4.3313 4.4300 4.5281 4.6257 4.7229 4.8196 4.9160 5.0121 5.1078 5.2033 5.2986 5.3937

–50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130

V

7.2306 7.3460 7.4614 7.5767 7.6919 7.8070 7.9220

Temp. °F

180 190 200 210 220 230 240

113.8 115.6 117.5 119.4 121.2 123.1 125.0 126.9 128.8 130.8 132.7 134.7 136.7 138.6 140.6 142.7 144.7 146.8 148.8

(112.4)

H

0.2831 0.2876 0.2920 0.2963 0.3005 0.3046 0.3087 0.3127 0.3167 0.3206 0.3244 0.3283 0.3320 0.3357 0.3394 0.3431 0.3467 0.3503 0.3538

(0.2796)

S

3.3927 3.4931 3.5920 3.6897 3.7862 3.8818 3.9765 4.0704 4.1637 4.2564 4.3486 4.4403 4.5317 4.6226 4.7132 4.8036 4.8937 4.9835 5.0731

(3.3367)

V

113.6 115.5 117.4 119.3 121.1 123.0 124.9 126.8 128.8 130.7 132.7 134.6 136.6 138.6 140.6 142.6 144.7 146.7 148.8

(112.6)

H

(–55.50°F)

159.5 161.7 163.9 166.1 168.3 170.6 172.8

(–57.71°F)

6.7109 6.8183 6.9255 7.0327 7.1397 7.2467 7.3536 17.00

0.3769 0.3802 0.3836 0.3869 0.3902 0.3935 0.3967

16.00

159.5 161.7 163.9 166.1 168.3 170.6 172.8

0.2812 0.2857 0.2901 0.2944 0.2987 0.3028 0.3069 0.3109 0.3149 0.3188 0.3227 0.3265 0.3303 0.3340 0.3377 0.3414 0.3450 0.3485 0.3521

(0.2787)

S

0.3748 0.3782 0.3815 0.3848 0.3881 0.3914 0.3947

3.1943 3.2899 3.3841 3.4770 3.5687 3.6595 3.7494 3.8385 3.9270 4.0149 4.1023 4.1892 4.2757 4.3618 4.4476 4.5331 4.6184 4.7034 4.7882

(3.1614)

V

6.3910 6.4933 6.5956 6.6977 6.7998 6.9018 7.0037

113.5 115.4 117.3 119.2 121.0 122.9 124.9 126.8 128.7 130.6 132.6 134.6 136.5 138.5 140.6 142.6 144.6 146.7 148.8

(112.9)

H

(–53.40°F)

18.00

159.5 161.7 163.9 166.1 168.3 170.5 172.8

0.2794 0.2839 0.2884 0.2927 0.2969 0.3011 0.3052 0.3093 0.3132 0.3172 0.3210 0.3249 0.3286 0.3324 0.3361 0.3397 0.3433 0.3469 0.3505

(0.2778)

S

0.3735 0.3768 0.3802 0.3835 0.3868 0.3901 0.3933

3.0167 3.1081 3.1980 3.2866 3.3741 3.4606 3.5462 3.6310 3.7152 3.7988 3.8819 3.9645 4.0467 4.1285 4.2100 4.2911 4.3721 4.4528 4.5332

(3.0039)

V

6.2605 6.3608 6.4611 6.5612 6.6612 6.7611 6.8610

113.4 115.3 117.2 119.0 120.9 122.9 124.8 126.7 128.6 130.6 132.5 134.5 136.5 138.5 140.5 142.5 144.6 146.6 148.7

(113.1)

H

(–51.38°F)

19.00

159.5 161.7 163.9 166.1 168.3 170.5 172.8

0.2776 0.2822 0.2867 0.2910 0.2953 0.2995 0.3036 0.3077 0.3116 0.3156 0.3195 0.3233 0.3271 0.3308 0.3345 0.3382 0.3418 0.3454 0.3490

(0.2770)

S

0.3729 0.3763 0.3796 0.3829 0.3862 0.3895 0.3928

–50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 (continued)

Temp. °F

180 190 200 210 220 230 240

Appendix 2 741

5.4885 5.5832 5.6778 5.7722 5.8664 5.9606 6.0547 6.1486 6.2425 6.3363 6.4300 6.5236

140 150 160 170 180 190 200 210 220 230 240 250

(2.8617)

2.9445 3.0305 3.1153 3.1989

Temp. °F

–40 –30 –20 –10

V

(3.5331)

Temp. °F

V

115.1 117.0 118.9 120.8

(113.3)

H

0.2806 0.2850 0.2894 0.2937

(0.2762)

S

2.7963 2.8790 2.9603 3.0404

(2.7326)

V

115.0 116.9 118.8 120.7

(113.5)

H

(–47.59°F)

150.9 153.0 155.1 157.3 159.4 161.6 163.8 166.0 168.2 170.5 172.8 175.0

(112.6)

(–49.45°F)

5.1626 5.2518 5.3409 5.4299 5.5187 5.6075 5.6961 5.7846 5.8730 5.9614 6.0497 6.1379

(3.3367)

H

21.00

0.3573 0.3608 0.3643 0.3677 0.3711 0.3745 0.3778 0.3811 0.3844 0.3877 0.3910 0.3942

(0.2796)

V

20.00

150.9 153.0 155.2 157.3 159.5 161.6 163.8 166.0 168.3 170.5 172.8 175.1

(112.4)

S

(–55.50°F)

(–57.71°F)

H

17.00

16.00

0.2790 0.2835 0.2879 0.2922

(0.2755)

S

0.3556 0.3591 0.3626 0.3660 0.3694 0.3728 0.3761 0.3795 0.3828 0.3860 0.3893 0.3925

(0.2787)

S

2.6616 2.7412 2.8193 2.8963

(2.6148)

V

4.8728 4.9572 5.0415 5.1256 5.2096 5.2935 5.3773 5.4610 5.5446 5.6281 5.7116 5.7950

(3.1614)

V

Absolute Pressure, psia

114.9 116.8 118.7 120.6

(113.8)

H

(–45.80°F)

22.00

150.9 153.0 155.1 157.2 159.4 161.6 163.8 166.0 168.2 170.5 172.7 175.0

(112.9)

H

(–53.40°F)

18.00

0.2775 0.2820 0.2864 0.2908

(0.2748)

S

0.3540 0.3575 0.3610 0.3644 0.3678 0.3712 0.3745 0.3779 0.3812 0.3845 0.3877 0.3910

(0.2778)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

2.5386 2.6153 2.6906 2.7647

(2.5070)

V

4.6135 4.6936 4.7736 4.8534 4.9331 5.0127 5.0921 5.1715 5.2508 5.3300 5.4091 5.4882

(3.0039)

V

114.7 116.7 118.6 120.5

(114.0)

H

(–44.07°F)

23.00

150.8 152.9 155.1 157.2 159.4 161.6 163.7 166.0 168.2 170.4 172.7 175.0

(113.1)

H

(–51.38°F)

19.00

0.2760 0.2806 0.2850 0.2894

(0.2741)

S

0.3525 0.3560 0.3594 0.3629 0.3663 0.3697 0.3730 0.3764 0.3797 0.3829 0.3862 0.3894

(0.2770)

S

–40 –30 –20 –10

Temp. °F

140 150 160 170 180 190 200 210 220 230 240 250

Temp. °F

742 Appendix 2

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

3.2816 3.3633 3.4443 3.5246 3.6043 3.6835 3.7622 3.8405 3.9184 3.9960 4.0734 4.1504 4.2272 4.3038 4.3802 4.4564 4.5325 4.6084 4.6842 4.7599 4.8355 4.9109 4.9863 5.0616 5.1369 5.2120 5.2871

122.8 124.7 126.6 128.6 130.5 132.5 134.4 136.4 138.4 140.5 142.5 144.5 146.6 148.7 150.8 152.9 155.0 157.2 159.3 161.5 163.7 165.9 168.2 170.4 172.7 175.0 177.3

0.2979 0.3021 0.3061 0.3101 0.3141 0.3180 0.3218 0.3256 0.3294 0.3331 0.3367 0.3404 0.3439 0.3475 0.3510 0.3545 0.3580 0.3614 0.3648 0.3682 0.3716 0.3749 0.3782 0.3815 0.3848 0.3880 0.3912

3.1196 3.1978 3.2753 3.3521 3.4283 3.5040 3.5792 3.6540 3.7284 3.8025 3.8763 3.9498 4.0231 4.0962 4.1691 4.2418 4.3143 4.3867 4.4590 4.5312 4.6032 4.6752 4.7471 4.8188 4.8906 4.9622 5.0338

122.7 124.6 126.5 128.5 130.4 132.4 134.4 136.4 138.4 140.4 142.4 144.5 146.6 148.6 150.7 152.9 155.0 157.1 159.3 161.5 163.7 165.9 168.1 170.4 172.7 174.9 177.3

0.2964 0.3006 0.3047 0.3087 0.3126 0.3165 0.3204 0.3242 0.3279 0.3317 0.3353 0.3390 0.3426 0.3461 0.3497 0.3532 0.3566 0.3601 0.3635 0.3669 0.3702 0.3736 0.3769 0.3802 0.3834 0.3867 0.3899

2.9723 3.0474 3.1217 3.1953 3.2683 3.3408 3.4128 3.4844 3.5557 3.6266 3.6972 3.7675 3.8376 3.9075 3.9771 4.0467 4.1160 4.1852 4.2543 4.3233 4.3921 4.4609 4.5295 4.5981 4.6666 4.7351 4.8035

122.6 124.5 126.5 128.4 130.4 132.3 134.3 136.3 138.3 140.4 142.4 144.5 146.5 148.6 150.7 152.8 155.0 157.1 159.3 161.5 163.7 165.9 168.1 170.4 172.6 174.9 177.2

0.2950 0.2992 0.3033 0.3073 0.3113 0.3152 0.3190 0.3228 0.3266 0.3303 0.3340 0.3376 0.3412 0.3448 0.3483 0.3518 0.3553 0.3588 0.3622 0.3656 0.3689 0.3723 0.3756 0.3789 0.3821 0.3854 0.3886

2.8378 2.410A 2.9814 3.0521 3.1222 3.1918 3.2609 3.3296 3.3979 3.4659 3.5336 3.6010 3.6682 3.7351 3.8019 3.8685 3.9349 4.0012 4.0674 4.1334 4.1994 4.2652 4.3309 4.3966 4.4622 4.5277 4.5932

122.5 124.4 126.4 128.3 130.3 132.3 134.3 136.3 138.3 140.3 142.4 144.4 146.5 148.6 150.7 152.8 154.9 157.1 159.3 161.4 163.6 165.9 168.1 170.3 172.6 174.9 177.2

0.2936 0.2978 0.3019 0.3060 0.3099 0.3139 0.3177 0.3215 0.3253 0.3290 0.3327 0.3364 0.3400 0.3435 0.3471 0.3506 0.3541 0.3575 0.3609 0.3643 0.3677 0.3710 0.3743 0.3776 0.3809 0.3841 0.3874 (continued)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

Appendix 2 743

(2.4078)

2.4258 2.4999 2.5726 2.6440 2.7145 2.7840 2.8528 2.9209 2.9883 3.0552 3.1217 3.1877 3.2533 3.3186 3.3837 3.4484 3.5129 3.5772 3.6413 3.7052 3.7689 3.8325 3.8960 3.9594

Temp. °F

–40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

V

114.6 116.6 118.5 120.4 122.4 124.3 126.3 128.3 130.2 132.2 134.2 136.2 138.2 140.3 142.3 144.4 146.4 148.5 150.6 152.8 154.9 157.1 159.2 161.4

(114.1)

0.2746 0.2792 0.2837 0.2880 0.2923 0.2965 0.3006 0.3047 0.3087 0.3126 0.3165 0.3203 0.3241 0.3278 0.3315 0.3351 0.3388 0.3423 0.3459 0.3494 0.3529 0.3563 0.3597 0.3631

(0.2735)

S

2.3220 2.3937 2.4639 2.5330 2.6010 2.6681 2.7345 2.8001 2.8651 2.9296 2.9936 3.0571 3.1203 3.1832 3.2457 3.3080 3.3700 3.4318 3.4935 3.5549 3.6162 3.6774 3.7384 3.7993

(2.3163)

V

114.5 116.4 118.4 120.3 122.3 124.3 126.2 128.2 130.2 132.2 134.1 136.2 138.2 140.2 142.3 144.3 146.4 148.5 150.6 152.7 154.9 157.0 159.2 161.4

(114.3)

H

(–40.78°F)

(–42.40°F)

H

25.00

24.00

0.2732 0.2779 0.2824 0.2868 0.2911 0.2953 0.2994 0.3035 0.3075 0.3114 0.3153 0.3191 0.3229 0.3266 0.3303 0.3340 0.3376 0.3412 0.3447 0.3482 0.3517 0.3552 0.3586 0.3620

(0.2729)

S

– 2.2956 2.3637 2.4305 2.4963 2.5612 2.6252 2.6886 2.7513 2.8136 2.8753 2.9366 2.9975 3.0581 3.1184 3.1784 3.2381 3.2977 3.3571 3.4162 3.4753 3.5341 3.5929 3.6515

(2.2316)

V

Absolute Pressure, psia

– 116.3 118.3 120.2 122.2 124.2 126.1 128.1 130.1 132.1 134.1 136.1 138.1 140.2 142.2 144.3 146.4 148.5 150.6 152.7 154.8 157.0 159.2 161.4

(114.5)

H

(–39.21°F)

26.00

– 0.2766 0.2811 0.2855 0.2898 0.2941 0.2982 0.3023 0.3063 0.3102 0.3141 0.3180 0.3217 0.3255 0.3292 0.3328 0.3365 0.3400 0.3436 0.3471 0.3506 0.3540 0.3575 0.3609

(0.2723)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– 2.2048 2.2708 2.3356 2.3993 2.4621 2.5241 2.5854 2.6460 2.7061 2.7658 2.8250 2.8838 2.9423 3.0005 3.0584 3.1160 3.1735 3.2307 3.2878 3.3447 3.4015 3.4581 3.5147

(2.1530)

V

– 116.2 118.2 120.1 122.1 124.1 126.1 128.0 130.0 132.0 134.0 136.0 138.1 140.1 142.2 144.2 146.3 148.4 150.5 152.7 154.8 157.0 159.1 161.3

(114.7)

H

(–37.69°F)

27.00

– 0.2753 0.2799 0.2843 0.2886 0.2929 0.2970 0.3011 0.3051 0.3091 0.3130 0.3168 0.3206 0.3244 0.3281 0.3318 0.3354 0.3390 0.3425 0.3460 0.3495 0.3530 0.3564 0.3598

(0.2717)

S

–40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

Temp. °F

744 Appendix 2

(2.0798)

2.1204 2.1845 2.2474 2.3092 2.3701 2.4301 2.4895 2.5482 2.6064 2.6641 2.7213 2.7782 2.8347 2.8910 2.9469 3.0026 3.0581 3.1134

–30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

V

4.0227 4.0858 4.1489 4.2119 4.2748 4.3376 4.4004 –

Temp. °F

200 210 220 230 240 250 260 270

116.1 118.1 120.0 122.0 124.0 126.0 128.0 130.0 132.0 134.0 136.0 138.0 140.1 142.1 144.2 146.3 148.4 150.5

(114.8)

H

0.2741 0.2787 0.2831 0.2875 0.2917 0.2959 0.3000 0.3040 0.3080 0.3119 0.3158 0.3196 0.3233 0.3270 0.3307 0.3343 0.3379 0.3415

(0.2712)

S

2.0418 2.1042 2.1653 2.2253 2.2844 2.3427 2.4002 2.4571 2.5135 2.5694 2.6248 2.6799 2.7346 2.7890 2.8432 2.8971 2.9507 3.0042

(2.0115)

V

115.9 117.9 119.9 121.9 123.9 125.9 127.9 129.9 131.9 133.9 135.9 138.0 140.0 142.1 144.2 146.2 148.3 150.5

(115.0)

H

(–34.78°F)

163.6 165.8 168.0 170.3 172.6 174.9 177.2 –

(–36.21°F)

3.8601 3.9208 3.9814 4.0419 4.1024 4.1628 4.2231 – 29.00

0.3665 0.3698 0.3731 0.3764 0.3797 0.3829 0.3862 –

28.00

163.6 165.8 168.1 170.3 172.6 174.9 177.2 –

0.2729 0.2775 0.2820 0.2864 0.2906 0.2948 0.2989 0.3030 0.3070 0.3109 0.3147 0.3185 0.3223 0.3260 0.3297 0.3333 0.3369 0.3405

(0.2707)

S

0.3653 0.3687 0.3720 0.3753 0.3786 0.3818 0.3850 –

1.9685 2.0292 2.0887 2.1470 2.2044 2.2610 2.3169 2.3721 2.4268 2.4810 2.5348 2.5881 2.6412 2.6939 2.7463 2.7985 2.8505 2.9023

(1.9476)

V

3.7100 3.7685 3.8268 3.8850 3.9432 4.0013 4.0594 4.1174

115.8 117.8 119.8 121.8 123.8 125.8 127.8 129.8 131.8 133.9 135.9 137.9 140.0 142.0 144.1 146.2 148.3 150.4

(115.1)

H

(–33.38°F)

30.00

163.6 165.8 168.0 170.3 172.5 174.8 177.1 179.5

0.2718 0.2764 0.2809 0.2853 0.2896 0.2938 0.2979 0.3020 0.3059 0.3099 0.3137 0.3175 0.3213 0.3250 0.3287 0.3323 0.3359 0.3395

(0.2702)

S

0.3642 0.3676 0.3709 0.3742 0.3775 0.3807 0.3839 0.3871

1.8998 1.9590 2.0169 2.0738 2.1296 2.1846 2.2389 2.2926 2.3457 2.3983 2.4505 2.5023 2.5537 2.6049 2.6557 2.7063 2.7567 2.8069

(1.8877)

V

3.5711 3.6274 3.6836 3.7398 3.7959 3.8519 3.9078 3.9637

115.7 117.7 119.7 121.7 123.7 125.7 127.7 129.8 131.8 133.8 135.8 137.9 139.9 142.0 144.1 146.2 148.3 150.4

(115.3)

H

(–32.02°F)

31.00

163.5 165.8 168.0 170.3 172.5 174.8 177.1 179.4

0.2706 0.2753 0.2798 0.2842 0.2885 0.2928 0.2969 0.3009 0.3049 0.3089 0.3128 0.3166 0.3203 0.3241 0.3277 0.3314 0.3350 0.3386

(0.2697)

S

0.3632 0.3665 0.3698 0.3731 0.3764 0.3797 0.3829 0.3861

–30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 (continued)

Temp. °F

200 210 220 230 240 250 260 270

Appendix 2 745

3.1686 3.2235 3.2783 3.3330 3.3876 3.4421 3.4964 3.5507 3.6049 3.6590 3.7131 3.7671 3.8210

150 160 170 180 190 200 210 220 230 240 250 260 270

(1.8314)

1.8354 1.8932 1.9497

Temp. °F

–30 –20 –10

V

(2.0798)

Temp. °F

V

115.6 117.6 119.6

(115.4)

H

0.2695 0.2742 0.2788

(0.2692)

S

– 1.8314 1.8865

(1.7784)

V

– 117.5 119.5

(115.6)

H

(–29.39°F)

152.6 154.7 156.9 159.1 161.3 163.5 165.7 167.9 170.2 172.5 174.8 177.1 179.4

(115.0)

(–30.69°F)

3.0575 3.1107 3.1637 3.2166 3.2693 3.3219 3.3745 3.4269 3.4793 3.5316 3.5839 3.6360 3.6881

(2.0115)

H

33.00

0.3450 0.3485 0.3519 0.3554 0.3588 0.3621 0.3655 0.3688 0.3721 0.3754 0.3786 0.3819 0.3851

(0.2712)

V

32.00

152.6 154.8 156.9 159.1 161.3 163.5 165.7 168.0 170.2 172.5 174.8 177.1 179.4

(114.8)

S

(–34.78°F)

(–36.21°F)

H

29.00

28.00

– 0.2732 0.2777

(0.2688)

S

0.3440 0.3475 0.3509 0.3544 0.3578 0.3612 0.3645 0.3678 0.3711 0.3744 0.3777 0.3809 0.3841

(0.2707)

S

– 1.7731 1.8270

(1.7284)

V

2.9539 3.0054 3.0567 3.1078 3.1589 3.2098 3.2607 3.3114 3.3621 3.4127 3.4632 3.5137 3.5641

(1.9476)

V

Absolute Pressure, psia

– 117.4 119.4

(115.7)

H

(–28.13°F)

34.00

152.6 154.7 156.9 159.0 161.2 163.4 165.7 167.9 170.2 172.5 174.7 177.1 179.4

(115.1)

H

(–33.38°F)

30.00

– 0.2722 0.2767

(0.2683)

S

0.3430 0.3465 0.3500 0.3534 0.3568 0.3602 0.3635 0.3669 0.3702 0.3735 0.3767 0.3799 0.3831

(0.2702)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– 1.7182 1.7709

(1.6812)

V

2.8570 2.9068 2.9565 3.0061 3.0556 3.1050 3.1542 3.2034 3.2525 3.3015 3.3504 3.3993 3.4481

(1.8877)

V

– 117.3 119.3

(115.8)

H

(–26.89°F)

35.00

152.5 154.7 156.8 159.0 161.2 163.4 165.7 167.9 170.2 172.4 174.7 177.0 179.4

(115.3)

H

(–32.02°F)

31.00

– 0.2712 0.2758

(0.2679)

S

0.3421 0.3456 0.3491 0.3525 0.3559 0.3593 0.3626 0.3660 0.3693 0.3725 0.3758 0.3790 0.3822

(0.2697)

S

–30 –20 –10

Temp. °F

150 160 170 180 190 200 210 220 230 240 250 260 270

Temp. °F

746 Appendix 2

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280

2.0051 2.0595 2.1130 2.1658 2.2180 2.2697 2.3208 2.3715 2.4218 2.4718 2.5214 2.5708 2.6199 2.6688 2.7175 2.7661 2.8145 2.8627 2.9108 2.9588 3.0066 3.0544 3.1021 3.1497 3.1972 3.2446 3.2920 3.3394 –

121.6 123.6 125.7 127.7 129.7 131.7 133.7 135.8 137.8 139.9 141.9 144.0 146.1 148.2 150.3 152.5 154.6 156.8 159.0 161.2 163.4 165.6 167.9 170.1 172.4 174.7 177.0 179.3 –

0.2832 0.2875 0.2918 0.2959 0.3000 0.3040 0.3079 0.3118 0.3156 0.3194 0.3231 0.3268 0.3305 0.3341 0.3376 0.3412 0.3447 0.3481 0.3516 0.3550 0.3584 0.3617 0.3651 0.3684 0.3716 0.3749 0.3781 0.3813 –

1.9405 1.9935 2.0457 2.0972 2.1480 2.1982 2.2480 2.2973 2.3462 2.3948 2.4430 2.4910 2.5387 2.5863 2.6336 2.6807 2.7277 2.7745 2.8212 2.8678 2.9143 2.9606 3.0069 3.0531 3.0992 3.1453 3.1913 3.2372 3.2831

121.5 123.6 125.6 127.6 129.6 131.6 133.7 135.7 137.8 139.8 141.9 144.0 146.1 148.2 150.3 152.4 154.6 156.8 159.0 161.2 163.4 165.6 167.8 170.1 172.4 174.7 177.0 179.3 181.7

0.2822 0.2865 0.2908 0.2949 0.2990 0.3030 0.3070 0.3109 0.3147 0.3185 0.3222 0.3259 0.3296 0.3332 0.3368 0.3403 0.3438 0.3473 0.3507 0.3541 0.3575 0.3609 0.3642 0.3675 0.3708 0.3740 0.3773 0.3805 0.3837

1.8797 1.9315 1.9824 2.0325 2.0821 2.1310 2.1794 2.2274 2.2750 2.3223 2.3692 2.4159 2.4623 2.5085 2.5545 2.6004 2.6460 2.6915 2.7369 2.7822 2.8273 2.8724 2.9173 2.9622 3.0070 3.0518 3.0964 3.1411 3.1856

121.4 123.5 125.5 127.5 129.5 131.6 133.6 135.7 137.7 139.8 141.8 143.9 146.0 148.1 150.3 152.4 154.6 156.7 158.9 161.1 163.3 165.6 167.8 170.1 172.4 174.7 177.0 179.3 181.6

0.2812 0.2856 0.2898 0.2940 0.2981 0.3021 0.3061 0.3100 0.3138 0.3176 0.3214 0.3251 0.3287 0.3323 0.3359 0.3394 0.3429 0.3464 0.3499 0.3533 0.3567 0.3600 0.3633 0.3667 0.3699 0.3732 0.3764 0.3796 0.3828

1.8224 1.8730 1.9227 1.9716 2.0199 2.0676 2.1148 2.1616 2.2079 2.2540 2.2997 2.3451 2.3903 2.4352 2.4800 2.5246 2.5690 2.6133 2.6574 2.7014 2.7454 2.7892 2.8329 2.8765 2.9201 2.9636 3.0070 3.0504 3.0937

121.3 123.4 125.4 127.4 129.5 131.5 133.6 135.6 137.7 139.7 141.8 143.9 146.0 148.1 150.2 152.4 154.5 156.7 158.9 161.1 163.3 165.5 167.8 170.1 172.3 174.6 176.9 179.3 181.6

0.2803 0.2846 0.2889 0.2931 0.2972 0.3012 0.3052 0.3091 0.3130 0.3168 0.3205 0.3242 0.3279 0.3315 0.3351 0.3386 0.3421 0.3456 0.3490 0.3524 0.3558 0.3592 0.3625 0.3658 0.3691 0.3724 0.3756 0.3788 0.3820 (continued)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280

Appendix 2 747

(1.6365)

1.6663 1.7179 1.7683 1.8177 1.8662 1.9140 1.9612 2.0077 2.0538 2.0994 2.1446 2.1894 2.2340 2.2782 2.3222 2.3660 2.4096 2.4530 2.4963 2.5394 2.5823 2.6252 2.6679 2.7106

Temp. °F

–20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

V

117.1 119.2 121.3 123.3 125.3 127.4 129.4 131.4 133.5 135.5 137.6 139.7 141.8 143.8 146.0 148.1 150.2 152.3 154.5 156.7 158.9 161.1 163.3 165.5

(116.0)

0.2702 0.2748 0.2793 0.2837 0.2880 0.2922 0.2963 0.3004 0.3043 0.3083 0.3121 0.3159 0.3197 0.3234 0.3270 0.3307 0.3342 0.3378 0.3413 0.3448 0.3482 0.3516 0.3550 0.3584

(0.2675)

S

1.6172 1.6678 1.7171 1.7654 1.8129 1.8596 1.9056 1.9511 1.9960 2.0405 2.0846 2.1284 2.1718 2.2150 2.2579 2.3006 2.3430 2.3853 2.4275 2.4695 2.5113 2.5531 2.5947 2.6362

(1.5941)

V

117.0 119.1 121.2 123.2 125.2 127.3 129.3 131.4 133.4 135.5 137.6 139.6 141.7 143.8 145.9 148.0 150.2 152.3 154.5 156.6 158.8 161.0 163.3 165.5

(116.1)

H

(–24.49°F)

(–25.67°F)

H

37.00

36.00

0.2692 0.2739 0.2784 0.2828 0.2871 0.2913 0.2955 0.2995 0.3035 0.3074 0.3113 0.3151 0.3189 0.3226 0.3262 0.3299 0.3334 0.3370 0.3405 0.3440 0.3474 0.3509 0.3543 0.3576

(0.2671)

S

1.5707 1.6202 1.6686 1.7159 1.7623 1.8080 1.8530 1.8974 1.9413 1.9847 2.0278 2.0705 2.1129 2.1550 2.1969 2.2385 2.2800 2.3212 2.3623 2.4032 2.4441 2.4848 2.5253 2.5658

(1.5539)

V

38.00

116.9 119.0 121.1 123.1 125.2 127.2 129.3 131.3 133.4 135.4 137.5 139.6 141.7 143.8 145.9 148.0 150.1 152.3 154.4 156.6 158.8 161.0 163.2 165.5

(116.2)

H

(–23.33°F)

Absolute Pressure, psia

0.2683 0.2730 0.2775 0.2819 0.2863 0.2905 0.2946 0.2987 0.3027 0.3066 0.3105 0.3143 0.3181 0.3218 0.3255 0.3291 0.3327 0.3362 0.3397 0.3432 0.3467 0.3501 0.3535 0.3569

(0.2667)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

1.5265 1.5751 1.6225 1.6688 1.7143 1.7590 1.8030 1.8465 1.8894 1.9318 1.9739 2.0156 2.0570 2.0982 2.1390 2.1797 2.2201 2.2604 2.3005 2.3404 2.3802 2.4199 2.4595 2.4990

(1.5157)

V

116.8 118.9 121.0 123.0 125.1 127.1 129.2 131.2 133.3 135.4 137.4 139.5 141.6 143.7 145.8 148.0 150.1 152.2 154.4 156.6 158.8 161.0 163.2 165.4

(116.3)

H

(–22.19°F)

39.00

0.2674 0.2721 0.2766 0.2811 0.2854 0.2897 0.2938 0.2979 0.3019 0.3058 0.3097 0.3135 0.3173 0.3210 0.3247 0.3283 0.3319 0.3355 0.3390 0.3425 0.3459 0.3494 0.3528 0.3561

(0.2663)

S

–20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

Temp. °F

748 Appendix 2

–20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temp. °F

220 230 240 250 260 270 280

1.4846 1.5323 1.5787 1.6242 1.6687 1.7125 1.7556 1.7981 1.8401 1.8816 1.9227 1.9635 2.0040 2.0441 2.0841 2.1238 2.1633 2.2026 2.2417

(1.4793)

V

2.7531 2.7956 2.8380 2.8803 2.9226 2.9648 3.0069

116.7 118.8 120.9 122.9 125.0 127.1 129.1 131.2 133.2 135.3 137.4 139.5 141.6 143.7 145.8 147.9 150.1 152.2 154.4

(116.4)

H

0.2665 0.2712 0.2758 0.2802 0.2846 0.2889 0.2930 0.2971 0.3011 0.3051 0.3089 0.3128 0.3165 0.3203 0.3239 0.3276 0.3312 0.3347 0.3383

(0.2659)

S

– 1.4915 1.5371 1.5817 1.6253 1.6682 1.7104 1.7520 1.7931 1.8338 1.8740 1.9139 1.9535 1.9927 2.0318 2.0706 2.1092 2.1476 2.1858

(1.4447)

V

– 118.7 120.8 122.8 124.9 127.0 129.1 131.1 133.2 135.3 137.3 139.4 141.5 143.6 145.7 147.9 150.0 152.2 154.3

(116.6)

H

(–19.98°F)

167.7 170.0 172.3 174.6 176.9 179.2 181.6

(–21.08°F)

2.6777 2.7190 2.7603 2.8015 2.8427 2.8838 2.9248 41.00

0.3617 0.3650 0.3683 0.3716 0.3748 0.3780 0.3812

40.00

167.8 170.0 172.3 174.6 176.9 179.3 181.6

– 0.2703 0.2749 0.2794 0.2838 0.2881 0.2922 0.2963 0.3003 0.3043 0.3082 0.3120 0.3158 0.3195 0.3232 0.3269 0.3305 0.3340 0.3375

(0.2656)

S

0.3610 0.3643 0.3675 0.3708 0.3740 0.3773 0.3805

– 1.4526 1.4974 1.5412 1.5840 1.6261 1.6674 1.7082 1.7485 1.7882 1.8276 1.8667 1.9054 1.9438 1.9820 2.0199 2.0577 2.0952 2.1326

(1.4116)

V

2.6062 2.6465 2.6867 2.7269 2.7670 2.8070 2.8470

– 118.6 120.7 122.8 124.8 126.9 129.0 131.1 133.1 135.2 137.3 139.4 141.5 143.6 145.7 147.8 150.0 152.1 154.3

(116.7)

H

(–18.91°F)

42.00

167.7 170.0 172.3 174.6 176.9 179.2 181.6

– 0.2695 0.2741 0.2786 0.2830 0.2873 0.2915 0.2956 0.2996 0.3036 0.3075 0.3113 0.3151 0.3188 0.3225 0.3261 0.3298 0.3333 0.3368

(0.2652)

S

0.3602 0.3635 0.3668 0.3701 0.3733 0.3765 0.3797

– 1.4155 1.4596 1.5025 1.5446 1.5858 1.6264 1.6664 1.7058 1.7448 1.7834 1.8216 1.8595 1.8971 1.9345 1.9716 2.0086 2.0453 2.0819

(1.3801)

V

2.5384 2.5777 2.6169 2.6561 2.6952 2.7342 2.7732

– 118.4 120.6 122.7 124.8 126.8 128.9 131.0 133.1 135.1 137.2 139.3 141.4 143.5 145.7 147.8 149.9 152.1 154.3

(116.8)

H

(–17.86°F)

43.00

167.7 170.0 172.2 174.5 176.9 179.2 181.5

– 0.2687 0.2733 0.2778 0.2822 0.2865 0.2907 0.2948 0.2989 0.3028 0.3067 0.3106 0.3144 0.3181 0.3218 0.3255 0.3291 0.3326 0.3362

(0.2649)

S

0.3595 0.3628 0.3661 0.3693 0.3726 0.3758 0.3790

–20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 (continued)

Temp. °F

220 230 240 250 260 270 280

Appendix 2 749

2.2807 2.3196 2.3583 2.3970 2.4355 2.4740 2.5123 2.5506 2.5888 2.6270 2.6651 2.7031 2.6735

170 180 190 200 210 220 230 240 250 260 270 280 290

(1.3499)

1.3801 1.4234 1.4657 1.5070

Temp. °F

–10 0 10 20

V

(1.4793)

Temp. °F

V

118.3 120.5 122.6 124.7

(116.9)

H

0.2678 0.2725 0.2770 0.2815

(0.2646)

S

1.3463 1.3889 1.4304 1.4710

(1.3210)

V

118.2 120.4 122.5 124.6

(117.0)

H

(–15.81°F)

156.5 158.7 160.9 163.1 165.4 167.6 169.9 172.2 174.5 176.8 179.2 181.5 183.8

(116.6)

(–16.82°F)

2.2239 2.2619 2.2998 2.3375 2.3751 2.4127 2.4502 2.4875 2.5249 2.5621 2.5993 2.6364 2.6092

(1.4447)

H

45.00

0.3417 0.3452 0.3486 0.3520 0.3554 0.3587 0.3621 0.3653 0.3686 0.3719 0.3751 0.3783 0.3807

(0.2659)

V

44.00

156.6 158.7 161.0 163.2 165.4 167.7 169.9 172.2 174.5 176.8 179.2 181.5 183.9

(116.4)

S

(–19.98°F)

(–21.08°F)

H

41.00

40.00

0.2670 0.2717 0.2763 0.2807

(0.2642)

S

0.3410 0.3445 0.3479 0.3513 0.3547 0.3580 0.3614 0.3646 0.3679 0.3712 0.3744 0.3776 0.3801

(0.2656)

S

1.3139 1.3559 1.3967 1.4366

(1.2933)

V

2.1699 2.2070 2.2440 2.2809 2.3176 2.3543 2.3909 2.4275 2.4639 2.5003 2.5367 2.5729 2.5478

(1.4116)

V

Absolute Pressure, psia

118.1 120.3 122.4 124.5

(117.1)

H

(–14.81°F)

46.00

156.5 158.7 160.9 163.1 165.4 167.6 169.9 172.2 174.5 176.8 179.1 181.5 183.8

(116.7)

H

(–18.91°F)

42.00

0.2662 0.2710 0.2755 0.2800

(0.2639)

S

0.3403 0.3438 0.3472 0.3506 0.3540 0.3573 0.3607 0.3640 0.3672 0.3705 0.3737 0.3769 0.3794

(0.2652)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

1.2829 1.3242 1.3644 1.4037

(1.2668)

V

2.1183 2.1546 2.1908 2.2268 2.2628 2.2987 2.3345 2.3702 2.4058 2.4414 2.4769 2.5124 –

(1.3801)

V

118.0 120.2 122.3 124.4

(117.2)

H

(–13.82°F)

47.00

156.5 158.7 160.9 163.1 165.3 167.6 169.9 172.2 174.5 176.8 179.1 181.5 –

(116.8)

H

(–17.86°F)

43.00

0.2655 0.2702 0.2748 0.2792

(0.2636)

S

0.3397 0.3431 0.3466 0.3500 0.3533 0.3567 0.3600 0.3633 0.3666 0.3698 0.3730 0.3762 –

(0.2649)

S

–10 0 10 20

Temp. °F

170 180 190 200 210 220 230 240 250 260 270 280 290

Temp. °F

750 Appendix 2

30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290

1.5475 1.5873 1.6265 1.6652 1.7034 1.7412 1.7786 1.8158 1.8526 1.8892 1.9255 1.9617 1.9976 2.0334 2.0691 2.1046 2.1400 2.1753 2.2105 2.2456 2.2806 2.3155 2.3504 2.3852 2.4199 2.4546 2.4892

126.8 128.8 130.9 133.0 135.1 137.2 139.3 141.4 143.5 145.6 147.8 149.9 152.1 154.2 156.4 158.6 160.8 163.1 165.3 167.6 169.8 172.1 174.4 176.8 179.1 181.4 183.8

0.2858 0.2900 0.2941 0.2981 0.3021 0.3060 0.3099 0.3137 0.3174 0.3211 0.3248 0.3284 0.3320 0.3355 0.3390 0.3425 0.3459 0.3493 0.3527 0.3560 0.3593 0.3626 0.3659 0.3692 0.3724 0.3756 0.3788

1.5108 1.5499 1.5883 1.6263 1.6638 1.7008 1.7375 1.7739 1.8100 1.8459 1.8815 1.9169 1.9521 1.9872 2.0221 2.0568 2.0915 2.1260 2.1605 2.1948 2.2291 2.2633 2.2974 2.3314 2.3654 2.3993 2.4332

126.7 128.8 130.9 132.9 135.0 137.1 139.2 141.3 143.5 145.6 147.7 149.9 152.0 154.2 156.4 158.6 160.8 163.0 165.3 167.5 169.8 172.1 174.4 176.7 179.1 181.4 183.8

0.2850 0.2893 0.2934 0.2974 0.3014 0.3053 0.3092 0.3130 0.3168 0.3205 0.3241 0.3277 0.3313 0.3348 0.3383 0.3418 0.3452 0.3487 0.3520 0.3554 0.3587 0.3620 0.3653 0.3685 0.3717 0.3749 0.3781

1.4757 1.5141 1.5519 1.5891 1.6259 1.6622 1.6982 1.7339 1.7693 1.8044 1.8393 1.8740 1.9085 1.9429 1.9771 2.0111 2.0451 2.0789 2.1126 2.1463 2.1798 2.2133 2.2467 2.2800 2.3133 2.3465 2.3797

126.6 128.7 130.8 132.9 135.0 137.1 139.2 141.3 143.4 145.5 147.7 149.8 152.0 154.2 156.4 158.6 160.8 163.0 165.3 167.5 169.8 172.1 174.4 176.7 179.0 181.4 183.8

0.2843 0.2885 0.2927 0.2968 0.3007 0.3047 0.3085 0.3123 0.3161 0.3198 0.3235 0.3271 0.3307 0.3342 0.3377 0.3412 0.3446 0.3480 0.3514 0.3548 0.3581 0.3614 0.3646 0.3679 0.3711 0.3743 0.3775

1.4421 1.4798 1.5169 1.5535 1.5896 1.6253 1.6606 1.6956 1.7303 1.7648 1.7990 1.8330 1.8668 1.9005 1.9340 1.9674 2.0006 2.0338 2.0668 2.0998 2.1326 2.1654 2.1981 2.2308 2.2634 2.2959 2.3284

126.5 128.6 130.7 132.8 134.9 137.0 139.1 141.2 143.4 145.5 147.6 149.8 152.0 154.1 156.3 158.5 160.8 163.0 165.2 167.5 169.8 172.1 174.4 176.7 179.0 181.4 183.8

0.2836 0.2878 0.2920 0.2961 0.3001 0.3040 0.3079 0.3117 0.3155 0.3192 0.3228 0.3264 0.3300 0.3336 0.3371 0.3406 0.3440 0.3474 0.3508 0.3541 0.3575 0.3608 0.3640 0.3673 0.3705 0.3737 0.3769 (continued)

30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290

Appendix 2 751

(1.2413)

1.2532 1.2939 1.3335 1.3721 1.4099 1.4470 1.4834 1.5194 1.5548 1.5899 1.6245 1.6589 1.6929 1.7267 1.7603 1.7937 1.8269 1.8599 1.8927 1.9254 1.9580 1.9905 2.0229 2.0552

Temp. °F

–10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

V

117.9 120.1 122.2 124.3 126.4 128.6 130.7 132.8 134.9 137.0 139.1 141.2 143.3 145.5 147.6 149.8 151.9 154.1 156.3 158.5 160.7 163.0 165.2 167.5

(117.3)

0.2647 0.2694 0.2741 0.2785 0.2829 0.2872 0.2913 0.2954 0.2994 0.3034 0.3072 0.3111 0.3148 0.3185 0.3222 0.3258 0.3294 0.3330 0.3365 0.3399 0.3434 0.3468 0.3502 0.3535

(0.2633)

S

1.2247 1.2648 1.3038 1.3418 1.3790 1.4155 1.4513 1.4866 1.5215 1.5559 1.5899 1.6237 1.6571 1.6903 1.7232 1.7560 1.7885 1.8209 1.8531 1.8852 1.9172 1.9491 1.9808 2.0125

(1.2169)

V

117.8 120.0 122.1 124.2 126.4 128.5 130.6 132.7 134.8 136.9 139.0 141.1 143.3 145.4 147.6 149.7 151.9 154.1 156.3 158.5 160.7 162.9 165.2 167.4

(117.4)

H

(–11.91°F)

(–12.86°F)

H

49.00

48.00

0.2639 0.2687 0.2733 0.2778 0.2822 0.2865 0.2907 0.2948 0.2988 0.3027 0.3066 0.3104 0.3142 0.3179 0.3216 0.3252 0.3288 0.3324 0.3359 0.3393 0.3428 0.3462 0.3496 0.3529

(0.2630)

S

1.1972 1.2368 1.2752 1.3127 1.3493 1.3852 1.4205 1.4552 1.4894 1.5233 1.5567 1.5899 1.6227 1.6553 1.6876 1.7198 1.7517 1.7835 1.8151 1.8466 1.8780 1.9092 1.9404 1.9715

(1.1933)

V

Absolute Pressure, psia

117.7 119.9 122.0 124.2 126.3 128.4 130.5 132.6 134.7 136.9 139.0 141.1 143.2 145.4 147.5 149.7 151.9 154.0 156.2 158.4 160.7 162.9 165.2 167.4

(117.5)

H

(–10.97°F)

50.00

0.2632 0.2680 0.2726 0.2771 0.2815 0.2858 0.2900 0.2941 0.2981 0.3021 0.3060 0.3098 0.3136 0.3173 0.3210 0.3246 0.3282 0.3318 0.3353 0.3388 0.3422 0.3456 0.3490 0.3524

(0.2627)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– 1.1121 1.1481 1.1830 1.2171 1.2504 1.2830 1.3151 1.3468 1.3779 1.4088 1.4392 1.4694 1.4993 1.5290 1.5585 1.5877 1.6168 1.6458 1.6746 1.7033 1.7319 1.7603 1.7887

(1.0882)

V

– 119.3 121.5 123.7 125.9 128.0 130.2 132.3 134.5 136.6 138.7 140.9 143.0 145.2 147.3 149.5 151.7 153.9 156.1 158.3 160.5 162.8 165.0 167.3

(117.9)

H

(–6.50°F)

55.00

– 0.2645 0.2692 0.2738 0.2783 0.2827 0.2869 0.2910 0.2951 0.2991 0.3030 0.3069 0.3107 0.3144 0.3181 0.3218 0.3254 0.3290 0.3325 0.3360 0.3394 0.3429 0.3463 0.3496

(0.2613)

S

–10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

Temp. °F

752 Appendix 2

(1.0000)

1.0080 1.0419 1.0748 1.1067 1.1379 1.1684 1.1984 1.2278 1.2568 1.2854 1.3137 1.3416 1.3693 1.3968 1.4240 1.4511 1.4779 1.5047

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

V

2.0874 2.1196 2.1516 2.1836 2.2156 2.2475 2.2793 –

Temp. °F

230 240 250 260 270 280 290 300

118.8 121.1 123.3 125.5 127.7 129.8 132.0 134.2 136.3 138.5 140.6 142.8 145.0 147.1 149.3 151.5 153.7 155.9

(118.3)

H

0.2612 0.2661 0.2708 0.2753 0.2797 0.2840 0.2882 0.2923 0.2963 0.3003 0.3042 0.3080 0.3118 0.3155 0.3192 0.3228 0.3264 0.3299

(0.2601)

S – 0.9519 0.9831 1.0133 1.0427 1.0714 1.0995 1.1271 1.1542 1.1810 1.2074 1.2335 1.2593 1.2849 1.3102 1.3354 1.3604 1.3853

(0.9249)

V – 120.6 122.8 125.1 127.3 129.5 131.7 133.9 136.0 138.2 140.4 142.6 144.7 146.9 149.1 151.3 153.5 155.8

(118.6)

H

(1.59°F)

169.7 172.0 174.3 176.6 179.0 181.3 183.7 –

(–2.32°F)

2.0441 2.0756 2.1070 2.1384 2.1697 2.2010 2.2322 – 65.00

0.3569 0.3602 0.3634 0.3667 0.3699 0.3731 0.3763 –

60.00

169.7 172.0 174.3 176.7 179.0 181.4 183.7 –

– 0.2631 0.2678 0.2725 0.2769 0.2813 0.2855 0.2897 0.2938 0.2978 0.3017 0.3055 0.3093 0.3131 0.3167 0.3204 0.3240 0.3275

(0.2589)

S

0.3563 0.3596 0.3629 0.3661 0.3693 0.3725 0.3757 –

– 0.8746 0.9043 0.9331 0.9610 0.9881 1.0147 1.0407 1.0663 1.0915 1.1163 1.1408 1.1650 1.1890 1.2127 1.2363 1.2597 1.2829

(0.8602)

V

2.0024 2.0334 2.0642 2.0950 2.1257 2.1563 2.1869 –

– 120.1 122.4 124.7 126.9 129.1 131.4 133.6 135.8 137.9 140.1 142.3 144.5 146.7 148.9 151.1 153.4 155.6

(119.0)

H

(5.28°F)

70.00

169.7 172.0 174.3 176.6 179.0 181.3 183.7 –

– 0.2602 0.2651 0.2698 0.2743 0.2787 0.2830 0.2872 0.2913 0.2954 0.2993 0.3032 0.3070 0.3108 0.3145 0.3181 0.3218 0.3253

(0.2578)

S

0.3557 0.3590 0.3623 0.3655 0.3688 0.3720 0.3752 –

– 0.8074 0.8360 0.8634 0.8900 0.9159 0.9411 0.9658 0.9900 1.0138 1.0373 1.0604 1.0832 1.1058 1.1282 1.1503 1.1723 1.1942

(0.8039)

V

1.8170 1.8452 1.8734 1.9015 1.9295 1.9575 1.9854 2.0133

– 119.6 121.9 124.2 126.5 128.8 131.0 133.3 135.5 137.7 139.9 142.1 144.3 146.5 148.7 151.0 153.2 155.4

(119.3)

H

(8.78°F)

75.00

169.6 171.9 174.2 176.5 178.9 181.2 183.6 186.0

– 0.2574 0.2624 0.2672 0.2718 0.2763 0.2807 0.2849 0.2891 0.2931 0.2971 0.3010 0.3049 0.3086 0.3124 0.3160 0.3197 0.3233

(0.2568)

S

0.3530 0.3563 0.3596 0.3628 0.3660 0.3693 0.3724 0.3756

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 (continued)

Temp. °F

230 240 250 260 270 280 290 300

Appendix 2 753

1.5313 1.5577 1.5841 1.6103 1.6364 1.6625 1.6885 1.7144 1.7403 1.7660 1.7918 1.8175 1.8431 –

180 190 200 210 220 230 240 250 260 270 280 290 300 310

(0.7543)

0.7760 0.8024 0.8279 0.8526

Temp. °F

20 30 40 50

V

(1.0000)

Temp. °F

V

121.5 123.8 126.1 128.4

(119.5)

H

0.2599 0.2648 0.2695 0.2740

(0.2559)

S

0.7229 0.7484 0.7730 0.7967

(0.7105)

V

121.0 123.4 125.7 128.1

(119.8)

H

(15.26°F)

158.0 160.2 162.5 164.8 167.0 169.3 171.6 174.0 176.3 178.7 181.0 183.4 185.8 188.2

(118.6)

(12.10°F)

1.4100 1.4345 1.4590 1.4833 1.5076 1.5318 1.5559 1.5799 1.6038 1.6277 1.6516 1.6754 1.6991 1.7228

(0.9249)

H

85.00

0.3334 0.3369 0.3403 0.3437 0.3471 0.3505 0.3538 0.3571 0.3603 0.3636 0.3668 0.3700 0.3731 –

(0.2601)

V

80.00

158.1 160.4 162.6 164.9 167.2 169.5 171.8 174.1 176.4 178.8 181.1 183.5 185.9 –

(118.3)

S

(1.59°F)

(–2.32°F)

H

65.00

60.00

0.2574 0.2624 0.2672 0.2718

(0.2550)

S

0.3311 0.3345 0.3380 0.3414 0.3448 0.3481 0.3515 0.3548 0.3580 0.3613 0.3645 0.3677 0.3709 0.3740

(0.2589)

S

0.6756 0.7004 0.7241 0.7470

(0.6713)

V

1.3060 1.3289 1.3518 1.3745 1.3971 1.4197 1.4422 1.4646 1.4869 1.5092 1.5314 1.5535 1.5757 1.5977

(0.8602)

V

Absolute Pressure, psia

120.5 122.9 125.3 127.7

(120.1)

H

(18.29°F)

90.00

157.8 160.1 162.3 164.6 166.9 169.2 171.5 173.8 176.2 178.5 180.9 183.3 185.7 188.1

(119.0)

H

(5.28°F)

70.00

0.2551 0.2601 0.2650 0.2697

(0.2542)

S

0.3289 0.3323 0.3358 0.3392 0.3426 0.3460 0.3493 0.3526 0.3559 0.3591 0.3624 0.3656 0.3687 0.3719

(0.2578)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– 0.6572 0.6803 0.7024

(0.6361)

V

1.2158 1.2374 1.2588 1.2802 1.3014 1.3226 1.3436 1.3646 1.3855 1.4064 1.4272 1.4480 1.4687 1.4894

(0.8039)

V

– 122.5 124.9 127.3

(120.3)

H

(21.19°F)

95.00

157.7 159.9 162.2 164.5 166.8 169.1 171.4 173.7 176.1 178.4 180.8 183.2 185.6 188.0

(119.3)

H

(8.78°F)

75.00

– 0.2579 0.2629 0.2676

(0.2534)

S

0.3268 0.3303 0.3338 0.3372 0.3406 0.3440 0.3473 0.3506 0.3539 0.3571 0.3604 0.3636 0.3668 0.3699

(0.2568)

S

20 30 40 50

Temp. °F

180 190 200 210 220 230 240 250 260 270 280 290 300 310

Temp. °F

754 Appendix 2

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330

0.8767 0.9002 0.9233 0.9459 0.9681 0.9900 1.0117 1.0330 1.0542 1.0751 1.0959 1.1165 1.1370 1.1573 1.1775 1.1976 1.2176 1.2376 1.2574 1.2772 1.2969 1.3165 1.3361 1.3556 1.3751 1.3945 1.4139 1.2029

130.7 133.0 135.2 137.4 139.6 141.9 144.1 146.3 148.5 150.8 153.0 155.3 157.5 159.8 162.1 164.4 166.6 169.0 171.3 173.6 176.0 178.3 180.7 183.1 185.5 187.9 190.4 192.6

0.2784 0.2827 0.2869 0.2910 0.2950 0.2989 0.3028 0.3066 0.3104 0.3141 0.3177 0.3213 0.3249 0.3284 0.3318 0.3353 0.3387 0.3421 0.3454 0.3487 0.3520 0.3553 0.3585 0.3617 0.3649 0.3681 0.3712 0.3694

0.8198 0.8423 0.8643 0.8859 0.9071 0.9279 0.9485 0.9688 0.9889 1.0088 1.0285 1.0480 1.0674 1.0866 1.1058 1.1248 1.1437 1.1626 1.1813 1.2000 1.2186 1.2372 1.2557 1.2741 1.2925 1.3109 1.3292 –

130.4 132.6 134.9 137.2 139.4 141.6 143.9 146.1 148.4 150.6 152.8 155.1 157.4 159.6 161.9 164.2 166.5 168.8 171.2 173.5 175.9 178.2 180.6 183.0 185.4 187.8 190.3 –

0.2763 0.2806 0.2848 0.2890 0.2930 0.2970 0.3009 0.3047 0.3085 0.3122 0.3158 0.3194 0.3230 0.3265 0.3300 0.3335 0.3369 0.3403 0.3436 0.3470 0.3502 0.3535 0.3568 0.3600 0.3632 0.3663 0.3695 –

0.7692 0.7908 0.8119 0.8325 0.8528 0.8727 0.8923 0.9117 0.9308 0.9498 0.9685 0.9871 1.0055 1.0238 1.0420 1.0601 1.0780 1.0959 1.1137 1.1314 1.1491 1.1667 1.1842 1.2017 1.2191 1.2365 1.2538 –

130.0 132.3 134.6 136.9 139.2 141.4 143.7 145.9 148.2 150.4 152.7 154.9 157.2 159.5 161.8 164.1 166.4 168.7 171.0 173.4 175.8 178.1 180.5 182.9 185.3 187.7 190.2 –

0.2742 0.2786 0.2829 0.2870 0.2911 0.2951 0.2990 0.3029 0.3067 0.3104 0.3141 0.3177 0.3213 0.3248 0.3283 0.3318 0.3352 0.3386 0.3419 0.3453 0.3486 0.3518 0.3551 0.3583 0.3615 0.3647 0.3678 –

0.7238 0.7446 0.7649 0.7848 0.8042 0.8233 0.8421 0.8606 0.8789 0.8970 0.9149 0.9326 0.9502 0.9676 0.9849 1.0021 1.0192 1.0362 1.0532 1.0700 1.0868 1.1036 1.1202 1.1369 1.1534 1.1699 1.1864 –

129.7 132.0 134.3 136.6 138.9 141.2 143.4 145.7 148.0 150.2 152.5 154.8 157.1 159.3 161.6 163.9 166.3 168.6 170.9 173.3 175.6 178.0 180.4 182.8 185.2 187.7 190.1 –

0.2722 0.2767 0.2810 0.2852 0.2893 0.2933 0.2973 0.3011 0.3049 0.3087 0.3124 0.3160 0.3196 0.3232 0.3267 0.3301 0.3336 0.3370 0.3403 0.3437 0.3470 0.3503 0.3535 0.3567 0.3599 0.3631 0.3663 – (continued)

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330

Appendix 2 755

(0.6043)

0.6183 0.6407 0.6622 0.6830 0.7031 0.7226 0.7417 0.7604 0.7788 0.7968 0.8146 0.8321 0.8494 0.8666 0.8835 0.9003 0.9170 0.9335 0.9500 0.9663 0.9826 0.9987 1.0148 1.0308

Temp. °F

30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

V

122.0 124.5 126.9 129.3 131.7 134.0 136.3 138.6 140.9 143.2 145.5 147.8 150.0 152.3 154.6 156.9 159.2 161.5 163.8 166.1 168.5 170.8 173.2 175.5

(120.5)

0.2558 0.2608 0.2656 0.2703 0.2748 0.2792 0.2834 0.2875 0.2916 0.2956 0.2995 0.3033 0.3071 0.3108 0.3144 0.3180 0.3216 0.3251 0.3286 0.3320 0.3354 0.3388 0.3422 0.3455

(0.2526) 0.5508 0.5722 0.5926 0.6122 0.6311 0.6495 0.6673 0.6848 0.7019 0.7186 0.7351 0.7513 0.7673 0.7831 0.7988 0.8142 0.8296 0.8448 0.8599 0.8749 0.8898 0.9046 0.9194 0.9341

(0.5491) 121.1 123.7 126.2 128.6 131.0 133.4 135.8 138.1 140.5 142.8 145.1 147.4 149.7 152.0 154.3 156.6 158.9 161.2 163.5 165.9 168.2 170.6 172.9 175.3

(120.9)

H

H

V

(29.25°F)

(23.98°F)

S

110.00

100.00

0.2516 0.2569 0.2618 0.2666 0.2712 0.2757 0.2800 0.2842 0.2884 0.2924 0.2963 0.3002 0.3040 0.3077 0.3114 0.3151 0.3186 0.3222 0.3257 0.3291 0.3326 0.3360 0.3393 0.3426

(0.2512)

S

– 0.5148 0.5344 0.5531 0.5710 0.5884 0.6053 0.6217 0.6377 0.6534 0.6688 0.6839 0.6988 0.7135 0.7281 0.7425 0.7567 0.7708 0.7848 0.7987 0.8125 0.8262 0.8399 0.8534

(0.5029)

V

Absolute Pressure, psia

– 122.8 125.4 127.9 130.4 132.8 135.2 137.6 140.0 142.3 144.6 147.0 149.3 151.6 153.9 156.3 158.6 160.9 163.3 165.6 168.0 170.3 172.7 175.1

(121.2)

H

(34.16°F)

120.00

– 0.2531 0.2582 0.2632 0.2679 0.2724 0.2769 0.2812 0.2853 0.2894 0.2934 0.2973 0.3012 0.3049 0.3087 0.3123 0.3159 0.3195 0.3230 0.3265 0.3299 0.3333 0.3367 0.3400

(0.2499)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– 0.4659 0.4848 0.5028 0.5200 0.5366 0.5526 0.5682 0.5833 0.5981 0.6126 0.6269 0.6409 0.6547 0.6683 0.6817 0.6950 0.7082 0.7213 0.7343 0.7471 0.7599 0.7726 0.7852

(0.4635)

V

– 121.8 124.5 127.2 129.7 132.2 134.7 137.1 139.5 141.9 144.2 146.6 148.9 151.3 153.6 155.9 158.3 160.6 163.0 165.3 167.7 170.1 172.5 174.9

(121.5)

H

(38.78°F)

130.00

– 0.2494 0.2548 0.2598 0.2647 0.2694 0.2739 0.2782 0.2825 0.2866 0.2907 0.2946 0.2985 0.3023 0.3061 0.3098 0.3134 0.3170 0.3205 0.3240 0.3275 0.3309 0.3343 0.3376

(0.2487)

S

30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

Temp. °F

756 Appendix 2

(0.4295)

0.4421 0.4596 0.4762 0.4921 0.5074 0.5222 0.5366 0.5507 0.5644 0.5779 0.5911 0.6042 0.6170 0.6297 0.6422 0.6546 0.6668 0.6790

50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

V

1.0468 1.0627 1.0785 1.0943 1.1101 1.1258 1.1414 –

Temp. °F

270 280 290 300 310 320 330 340

123.7 126.4 129.0 131.6 134.1 136.5 139.0 141.4 143.8 146.2 148.5 150.9 153.3 155.6 158.0 160.3 162.7 165.1

(121.8)

H

0.2514 0.2566 0.2616 0.2664 0.2710 0.2755 0.2798 0.2840 0.2881 0.2921 0.2960 0.2999 0.3036 0.3074 0.3110 0.3146 0.3182 0.3217

(0.2476)

S 0.4048 0.4219 0.4380 0.4534 0.4681 0.4823 0.4961 0.5096 0.5226 0.5355 0.5480 0.5604 0.5725 0.5845 0.5963 0.6080 0.6196 0.6311

(0.4000)

V 122.8 125.6 128.3 130.9 133.5 136.0 138.5 140.9 143.3 145.7 148.1 150.5 152.9 155.3 157.7 160.0 162.4 164.8

(122.0)

H

(47.26°F)

177.7 180.1 182.5 184.9 (187.40) 189.8 192.3 –

(43.14°F)

0.9487 0.9632 0.9777 0.9922 1.0066 1.0210 1.0353 – 150.00

0.3488 0.3520 0.3552 0.3584 0.3616 0.3648 0.3679 –

140.00

177.9 180.3 182.7 185.1 187.6 190.0 192.5 –

0.2481 0.2535 0.2587 0.2636 0.2683 0.2728 0.2772 0.2815 0.2856 0.2897 0.2936 0.2975 0.3013 0.3051 0.3088 0.3124 0.3160 0.3195

(0.2466)

S

0.3459 0.3492 0.3524 0.3557 0.3588 0.3620 0.3652 –

– 0.3887 0.4044 0.4194 0.4336 0.4474 0.4606 0.4735 0.4860 0.4983 0.5103 0.5220 0.5336 0.5450 0.5562 0.5673 0.5783 0.5892

(0.3740)

V

0.8669 0.8804 0.8938 0.9071 0.9204 0.9337 0.9469 0.9600

– 124.8 127.5 130.2 132.9 135.4 137.9 140.4 142.9 145.3 147.8 150.2 152.6 155.0 157.4 159.7 162.1 164.5

(122.2)

H

(51.18°F)

160.00

177.5 179.9 182.3 184.7 187.2 189.6 192.1 194.6

– 0.2505 0.2558 0.2608 0.2657 0.2703 0.2747 0.2791 0.2833 0.2874 0.2914 0.2953 0.2992 0.3029 0.3067 0.3103 0.3139 0.3175

(0.2456)

S

0.3433 0.3466 0.3499 0.3531 0.3563 0.3595 0.3626 0.3657

– 0.3592 0.3747 0.3893 0.4031 0.4164 0.4292 0.4416 0.4537 0.4654 0.4769 0.4882 0.4992 0.5101 0.5208 0.5314 0.5418 0.5522

(0.3509)

V

0.7978 0.8103 0.8227 0.8351 0.8475 0.8598 0.8720 0.8843

– 123.9 126.8 129.5 132.2 134.8 137.4 139.9 142.4 144.9 147.4 149.8 152.2 154.6 157.0 159.5 161.9 164.3

(122.4)

H

(54.93°F)

170.00

177.3 179.7 182.1 184.5 187.0 189.5 191.9 194.4

– 0.2475 0.2530 0.2582 0.2631 0.2678 0.2724 0.2768 0.2810 0.2852 0.2892 0.2932 0.2971 0.3009 0.3046 0.3083 0.3119 0.3155

(0.2446)

S

0.3409 0.3442 0.3475 0.3507 0.3539 0.3571 0.3603 0.3634

50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 (continued)

Temp. °F

270 280 290 300 310 320 330 340

Appendix 2 757

0.6910 0.7030 0.7149 0.7267 0.7385 0.7502 0.7618 0.7734 0.7850 0.7964 0.8079 0.8193 0.8307 –

230 240 250 260 270 280 290 300 310 320 330 340 350 360

(0.3303)

0.3327 0.3480 0.3624 0.3759

Temp. °F

60 70 80 90

V

(0.4295)

Temp. °F

V

123.0 126.0 128.8 131.6

(122.6)

H

0.2446 0.2503 0.2556 0.2606

(0.2437)

S

– 0.3240 0.3382 0.3515

(0.3119)

V

– 125.2 128.1 130.9

(122.7)

H

(61.94°F)

167.2 169.6 172.0 174.4 176.8 179.3 181.7 184.2 186.6 189.1 191.6 194.1 196.6 –

(122.0)

(58.50°F)

0.6424 0.6537 0.6649 0.6761 0.6871 0.6981 0.7090 0.7199 0.7308 0.7416 0.7523 0.7630 0.7737 –

(0.4000)

H

190.00

0.3252 0.3286 0.3320 0.3354 0.3387 0.3420 0.3453 0.3485 0.3517 0.3549 0.3581 0.3612 0.3643 –

(0.2476)

V

180.00

167.5 169.8 172.2 174.6 177.1 179.5 181.9 184.4 186.8 189.3 191.8 194.3 196.8 –

(121.8)

S

(47.26°F)

(43.14°F)

H

150.00

140.00

– 0.2475 0.2530 0.2582

(0.2428)

S

0.3230 0.3265 0.3299 0.3333 0.3366 0.3399 0.3432 0.3464 0.3497 0.3528 0.3560 0.3592 0.3623 –

(0.2466)

S

– 0.3022 0.3162 0.3293

(0.2951)

V

0.5999 0.6106 0.6212 0.6317 0.6421 0.6525 0.6629 0.6731 0.6834 0.6935 0.7037 0.7138 0.7239 0.7339

(0.3740)

V

Absolute Pressure, psia

– 124.3 127.3 130.2

(122.8)

H

(65.23°F)

200.00

166.9 169.4 171.8 174.2 176.6 179.1 181.5 184.0 186.4 188.9 191.4 193.9 196.4 199.0

(122.2)

H

(51.18°F)

160.00

– 0.2448 0.2505 0.2558

(0.2420)

S

0.3210 0.3244 0.3279 0.3313 0.3346 0.3379 0.3412 0.3445 0.3477 0.3509 0.3541 0.3572 0.3604 0.3635

(0.2456)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– – 0.2780 0.2908

(0.2661)

V

0.5624 0.5725 0.5826 0.5926 0.6025 0.6123 0.6221 0.6318 0.6415 0.6512 0.6608 0.6703 0.6799 0.6894

(0.3509)

V

– – 125.8 128.8

(123.0)

H

(71.48°F)

220.00

166.7 169.1 171.5 174.0 176.4 178.8 181.3 183.8 186.2 188.7 191.2 193.7 196.3 198.8

(122.4)

H

(54.93°F)

170.00

– – 0.2455 0.2512

(0.2404)

S

0.3190 0.3225 0.3260 0.3294 0.3327 0.3361 0.3394 0.3426 0.3459 0.3491 0.3523 0.3554 0.3586 0.3617

(0.2446)

S

60 70 80 90

Temp. °F

230 240 250 260 270 280 290 300 310 320 330 340 350 360

Temp. °F

758 Appendix 2

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380

0.3888 0.4013 0.4133 0.4249 0.4362 0.4472 0.4581 0.4686 0.4791 0.4893 0.4994 0.5094 0.5193 0.5290 0.5387 0.5483 0.5578 0.5672 0.5766 0.5859 0.5951 0.6044 0.6135 0.6226 0.6317 0.6408 0.6498 0.6229 –

134.3 136.9 139.4 142.0 144.5 147.0 149.4 151.9 154.3 156.7 159.1 161.6 164.0 166.4 168.9 171.3 173.7 176.2 178.6 181.1 183.6 186.1 188.6 191.1 193.6 196.1 198.6 201.0 –

0.2655 0.2701 0.2746 0.2789 0.2831 0.2872 0.2912 0.2951 0.2989 0.3027 0.3064 0.3101 0.3137 0.3172 0.3207 0.3242 0.3276 0.3309 0.3343 0.3376 0.3409 0.3441 0.3473 0.3505 0.3537 0.3569 0.3600 0.3614 –

0.3641 0.3762 0.3878 0.3991 0.4100 0.4207 0.4311 0.4413 0.4513 0.4611 0.4708 0.4804 0.4898 0.4992 0.5084 0.5176 0.5266 0.5356 0.5446 0.5535 0.5623 0.5711 0.5798 0.5885 0.5972 0.6058 0.6144 0.5907 –

133.7 136.3 138.9 141.5 144.0 146.5 149.0 151.5 154.0 156.4 158.8 161.3 163.7 166.2 168.6 171.1 173.5 176.0 178.4 180.9 183.4 185.9 188.4 190.9 193.4 195.9 198.5 200.9 –

0.2631 0.2679 0.2724 0.2768 0.2811 0.2852 0.2892 0.2932 0.2971 0.3009 0.3046 0.3083 0.3119 0.3154 0.3190 0.3224 0.3259 0.3293 0.3326 0.3359 0.3392 0.3425 0.3457 0.3489 0.3521 0.3552 0.3583 0.3599 –

0.3417 0.3536 0.3649 0.3758 0.3864 0.3967 0.4068 0.4166 0.4263 0.4357 0.4451 0.4543 0.4633 0.4723 0.4811 0.4899 0.4986 0.5072 0.5158 0.5243 0.5328 0.5412 0.5495 0.5578 0.5661 0.5743 0.5825 0.5350 –

133.0 135.8 138.4 141.0 143.6 146.1 148.6 151.1 153.6 156.1 158.5 161.0 163.4 165.9 168.4 170.8 173.3 175.7 178.2 180.7 183.2 185.7 188.2 190.7 193.2 195.8 198.3 200.6 –

0.2609 0.2657 0.2703 0.2748 0.2791 0.2833 0.2874 0.2914 0.2953 0.2991 0.3029 0.3065 0.3102 0.3138 0.3173 0.3208 0.3242 0.3276 0.3310 0.3343 0.3376 0.3409 0.3441 0.3473 0.3505 0.3537 0.3568 0.3570 –

0.3029 0.3143 0.3251 0.3355 0.3456 0.3553 0.3648 0.3740 0.3830 0.3919 0.4006 0.4091 0.4175 0.4258 0.4341 0.4422 0.4502 0.4582 0.4661 0.4739 0.4817 0.4894 0.4971 0.5048 0.5124 0.5199 0.5275 – 0.5424

131.8 134.6 137.4 140.1 142.7 145.3 147.9 150.4 152.9 155.4 157.9 160.4 162.9 165.4 167.8 170.3 172.8 175.3 177.8 180.3 182.8 185.3 187.8 190.3 192.9 195.4 198.0 – 203.1

0.2565 0.2615 0.2663 0.2709 0.2753 0.2796 0.2838 0.2879 0.2919 0.2957 0.2996 0.3033 0.3070 0.3106 0.3142 0.3177 0.3211 0.3246 0.3280 0.3313 0.3346 0.3379 0.3412 0.3444 0.3476 0.3508 0.3539 – 0.3601

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 (continued)

Appendix 2 759

(0.2418)

0.2455 0.2583 0.2702 0.2813 0.2918 0.3018 0.3114 0.3207 0.3297 0.3384 0.3469 0.3553 0.3634 0.3715 0.3794 0.3871 0.3948 0.4024 0.4099 0.4173 0.4247 0.4319 0.4392 0.4464

Temp. °F

80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310

V

124.1 127.3 130.4 133.4 136.3 139.1 141.8 144.4 147.1 149.7 152.2 154.8 157.3 159.8 162.3 164.8 167.3 169.8 172.3 174.8 177.4 179.9 182.4 184.9

(123.1)

0.2406 0.2466 0.2522 0.2575 0.2624 0.2672 0.2718 0.2762 0.2804 0.2846 0.2886 0.2926 0.2965 0.3003 0.3040 0.3076 0.3112 0.3148 0.3183 0.3217 0.3252 0.3285 0.3319 0.3352

(0.2389)

S

– 0.2303 0.2422 0.2531 0.2634 0.2731 0.2824 0.2913 0.2999 0.3083 0.3164 0.3243 0.3320 0.3396 0.3470 0.3544 0.3616 0.3687 0.3757 0.3827 0.3896 0.3964 0.4032 0.4099

(0.2210)

V

– 125.7 129.0 132.1 135.1 138.0 140.8 143.6 146.2 148.9 151.5 154.1 156.7 159.2 161.8 164.3 166.8 169.3 171.9 174.4 176.9 179.4 182.0 184.5

(123.2)

H

(82.77°F)

(77.30°F)

H

260.00

240.00

– 0.2420 0.2480 0.2535 0.2587 0.2636 0.2683 0.2729 0.2772 0.2815 0.2856 0.2896 0.2936 0.2974 0.3012 0.3049 0.3085 0.3121 0.3156 0.3191 0.3225 0.3259 0.3293 0.3326

(0.2374)

S

– 0.2058 0.2178 0.2287 0.2389 0.2484 0.2574 0.2660 0.2743 0.2823 0.2901 0.2976 0.3050 0.3122 0.3193 0.3262 0.3331 0.3398 0.3465 0.3530 0.3595 0.3660 0.3723 0.3787

(0.2031)

V

Absolute Pressure, psia

– 124.0 127.5 130.8 133.9 136.9 139.8 142.6 145.4 148.1 150.8 153.4 156.0 158.6 161.2 163.7 166.3 168.8 171.4 173.9 176.5 179.0 181.6 184.1

(123.2)

H

(87.94°F)

280.00

– 0.2374 0.2438 0.2496 0.2550 0.2602 0.2650 0.2697 0.2742 0.2785 0.2827 0.2868 0.2908 0.2947 0.2985 0.3022 0.3059 0.3095 0.3131 0.3166 0.3201 0.3235 0.3269 0.3302

(0.2360)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– – 0.1962 0.2073 0.2174 0.2268 0.2356 0.2440 0.2521 0.2598 0.2673 0.2745 0.2816 0.2885 0.2953 0.3019 0.3084 0.3148 0.3211 0.3273 0.3335 0.3396 0.3456 0.3516

(0.1875)

V

– – 125.9 129.4 132.7 135.8 138.8 141.7 144.5 147.3 150.0 152.7 155.4 158.0 160.6 163.2 165.8 168.3 170.9 173.5 176.0 178.6 181.2 183.7

(123.2)

H

(92.83°F)

300.00

– – 0.2395 0.2457 0.2514 0.2568 0.2618 0.2666 0.2712 0.2756 0.2799 0.2841 0.2881 0.2921 0.2960 0.2998 0.3035 0.3071 0.3107 0.3143 0.3177 0.3212 0.3246 0.3279

(0.2347)

S

80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310

Temp. °F

760 Appendix 2

–

400

(0.1738)

0.1769 0.1882 0.1984 0.2077 0.2164 0.2247 0.2325 0.2400 0.2473 0.2543 0.2611 0.2677 0.2742 0.2805 0.2868 0.2929

Temp. °F

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

V

0.4535 0.4606 0.4676 0.4746 0.4816 0.4885 0.4955 0.4621

320 330 340 350 360 370 380 390

124.1 127.9 131.4 134.6 137.7 140.7 143.7 146.5 149.3 152.0 154.7 157.4 160.0 162.6 165.2 167.8

(123.1)

H

0.2351 0.2418 0.2478 0.2534 0.2587 0.2636 0.2683 0.2729 0.2773 0.2815 0.2856 0.2896 0.2935 0.2974 0.3011 0.3048

(0.2333)

S

– 0.1710 0.1813 0.1907 0.1994 0.2075 0.2152 0.2225 0.2296 0.2364 0.2430 0.2494 0.2556 0.2617 0.2677 0.2735

(0.1616)

V

– 126.3 130.0 133.4 136.6 139.7 142.7 145.6 148.5 151.3 154.0 156.7 159.4 162.1 164.7 167.3

(123.0)

H

(101.92°F)

–

187.1 189.6 192.2 194.8 197.3 199.9 202.5 204.8

(97.48°F)

–

0.4166 0.4232 0.4298 0.4363 0.4428 0.4493 0.4557 0.4277

340.00

–

0.3384 0.3417 0.3449 0.3481 0.3512 0.3543 0.3575 0.3581

320.00

–

187.4 190.0 192.5 195.1 197.7 200.2 202.8 205.1

– 0.2378 0.2442 0.2501 0.2555 0.2607 0.2655 0.2702 0.2747 0.2790 0.2832 0.2872 0.2912 0.2951 0.2989 0.3026

(0.2320)

S

–

0.3359 0.3391 0.3424 0.3456 0.3487 0.3519 0.3550 0.3558

– 0.1552 0.1659 0.1754 0.1841 0.1921 0.1997 0.2069 0.2138 0.2204 0.2268 0.2330 0.2390 0.2449 0.2507 0.2563

(0.1507)

V

–

0.3849 0.3911 0.3973 0.4035 0.4096 0.4156 0.4217 0.3978

– 124.5 128.5 132.1 135.5 138.7 141.8 144.8 147.7 150.5 153.3 156.1 158.8 161.5 164.2 166.8

(122.9)

H

(106.16°F)

360.00

–

186.7 189.3 191.8 194.4 197.0 199.6 202.2 204.5

– 0.2337 0.2406 0.2468 0.2524 0.2578 0.2628 0.2676 0.2721 0.2765 0.2808 0.2849 0.2890 0.2929 0.2967 0.3005

(0.2308)

S

–

0.3335 0.3368 0.3400 0.3432 0.3464 0.3496 0.3527 0.3536

– – 0.1517 0.1614 0.1702 0.1783 0.1858 0.1929 0.1996 0.2061 0.2123 0.2184 0.2242 0.2299 0.2355 0.2409

(0.1409)

V

0.4035

0.3575 0.3634 0.3692 0.3750 0.3808 0.3865 0.3922 390

– – 126.9 130.8 134.3 137.6 140.8 143.9 146.9 149.8 152.6 155.4 158.2 160.9 163.6 166.3

(122.7)

H

(110.23°F)

380.00

207.2

186.3 188.9 191.5 194.1 196.7 199.3 201.9

– – 0.2368 0.2434 0.2494 0.2549 0.2601 0.2650 0.2697 0.2742 0.2785 0.2827 0.2868 0.2908 0.2947 0.2985

(0.2295)

S

0.3567

0.3313 0.3346 0.3378 0.3410 0.3442 0.3474 0.3505

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 (continued)

Temp. °F

400

320 330 340 350 360 370 380

Appendix 2 761

0.2989 0.3048 0.3107 0.3165 0.3222 0.3279 0.3335 0.3391 0.3446 0.3501 0.3556 0.3610 0.3664 0.3717 0.3770 – –

260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

(0.1320)

0.1386 0.1487

Temp. °F

120 130

V

(0.1738)

Temp. °F

V

125.2 129.3

(122.5)

0.2329 0.2399

(0.2283) – 0.1205

(0.1130)

V – 125.2

(121.8)

H

(123.31°F)

H

S

169.9 172.5 175.2 177.8 180.3 182.9 185.6 188.2 190.8 193.4 196.0 198.6 201.3 203.9 206.6 209.2 –

(123.0)

(114.14°F)

0.2793 0.2850 0.2906 0.2961 0.3016 0.3070 0.3124 0.3177 0.3229 0.3281 0.3333 0.3385 0.3436 0.3487 0.3537 0.3588 –

(0.1616)

450.00

0.3084 0.3120 0.3155 0.3190 0.3224 0.3258 0.3291 0.3324 0.3357 0.3389 0.3422 0.3453 0.3485 0.3516 0.3547 – –

(0.2333)

H

400.00

170.4 173.0 175.6 178.2 180.8 183.3 185.9 188.5 191.1 193.7 196.3 199.0 201.6 204.2 206.9 – –

(123.1)

V

(101.92°F)

S

(97.48°F)

H

340.00

320.00

– 0.2308

(0.2251)

S

0.3063 0.3099 0.3134 0.3169 0.3204 0.3238 0.3271 0.3304 0.3337 0.3370 0.3402 0.3434 0.3465 0.3497 0.3528 0.3559 –

(0.2320)

S

– –

(0.0974)

V

0.2619 0.2673 0.2727 0.2780 0.2832 0.2884 0.2935 0.2986 0.3036 0.3086 0.3136 0.3185 0.3234 0.3282 0.3330 0.3378 –

(0.1507)

V

Absolute Pressure, psia

– –

(121.0)

H

(131.73°F)

500.00

169.4 172.1 174.7 177.3 179.9 182.6 185.2 187.8 190.4 193.0 195.7 198.3 201.0 203.6 206.3 209.0 –

(122.9)

H

(106.16°F)

360.00

– –

(0.2220)

S

0.3042 0.3078 0.3114 0.3149 0.3184 0.3218 0.3252 0.3285 0.3318 0.3351 0.3383 0.3415 0.3447 0.3478 0.3510 0.3541 –

(0.2308)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (Continued)

– –

(0.0843)

V

0.2463 0.2515 0.2567 0.2618 0.2668 0.2718 0.2767 0.2816 0.2864 0.2912 0.2959 0.3006 0.3053 0.3099 0.3145 0.3191 0.3237

(0.1409)

V

– –

(119.9)

H

(139.53°F)

550.00

168.9 171.6 174.2 176.9 179.5 182.2 184.8 187.4 190.1 192.7 195.3 198.0 200.6 203.3 206.0 208.7 211.4

(122.7)

H

(110.23°F)

380.00

– –

(0.2187)

S

0.3022 0.3059 0.3095 0.3130 0.3165 0.3199 0.3233 0.3267 0.3300 0.3333 0.3365 0.3398 0.3429 0.3461 0.3492 0.3523 0.3554

(0.2295)

S

120 130

Temp. °F

260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

Temp. °F

762 Appendix 2

0.1576 0.1656 0.1731 0.1802 0.1868 0.1932 0.1993 0.2051 0.2108 0.2164 0.2218 0.2271 0.2322 0.2373 0.2423 0.2472 0.2521 0.2569 0.2616 0.2663 0.2709 0.2755 0.2800 0.2845 0.2890 0.2934 0.2979 0.3022 0.3066 – –

133.0 136.5 139.8 143.0 146.0 149.0 151.9 154.8 157.5 160.3 163.0 165.8 168.4 171.1 173.8 176.4 179.1 181.7 184.4 187.0 189.7 192.3 195.0 197.7 200.3 203.0 205.7 208.4 211.1 – –

0.2462 0.2520 0.2574 0.2624 0.2672 0.2718 0.2763 0.2806 0.2847 0.2887 0.2927 0.2965 0.3003 0.3040 0.3076 0.3112 0.3147 0.3182 0.3216 0.3249 0.3283 0.3316 0.3348 0.3381 0.3413 0.3444 0.3476 0.3507 0.3538 – –

0.1301 0.1385 0.1461 0.1530 0.1596 0.1657 0.1716 0.1772 0.1826 0.1878 0.1928 0.1978 0.2026 0.2073 0.2119 0.2164 0.2209 0.2253 0.2296 0.2339 0.2381 0.2423 0.2465 0.2506 0.2547 0.2587 0.2627 0.2667 0.2706 0.2746 –

129.6 133.5 137.2 140.6 143.9 147.0 150.1 153.0 155.9 158.8 161.6 164.4 167.2 169.9 172.6 175.3 178.0 180.7 183.4 186.1 188.8 191.5 194.2 196.8 199.5 202.2 204.9 207.7 210.4 213.1 –

0.2382 0.2448 0.2507 0.2562 0.2613 0.2662 0.2709 0.2753 0.2797 0.2838 0.2879 0.2919 0.2957 0.2995 0.3032 0.3068 0.3104 0.3139 0.3174 0.3208 0.3242 0.3275 0.3308 0.3341 0.3373 0.3405 0.3437 0.3468 0.3499 0.3530 –

0.1066 0.1158 0.1237 0.1309 0.1374 0.1435 0.1492 0.1546 0.1598 0.1648 0.1696 0.1743 0.1788 0.1832 0.1876 0.1918 0.1960 0.2001 0.2041 0.2081 0.2120 0.2158 0.2197 0.2235 0.2272 0.2309 0.2346 0.2383 0.2419 0.2455 0.2491

125.4 130.1 134.2 138.0 141.5 144.9 148.1 151.2 154.3 157.2 160.1 163.0 165.9 168.7 171.4 174.2 177.0 179.7 182.4 185.2 187.9 190.6 193.3 196.0 198.7 201.5 204.2 206.9 209.7 212.4 215.2

0.2295 0.2372 0.2439 0.2499 0.2555 0.2607 0.2657 0.2704 0.2749 0.2792 0.2834 0.2875 0.2914 0.2953 0.2991 0.3028 0.3065 0.3100 0.3136 0.3170 0.3205 0.3238 0.3272 0.3305 0.3337 0.3370 0.3401 0.3433 0.3464 0.3495 0.3526

Source: Thermodynamic Properties of DuPont Suva 410A Refrigerant. With permission of E. I. Du Pont de Nemours and Co. Note: V = volume in ft.3/lb.; H = enthalpy in Btu/lb; S = entropy in Btu/(lb.) (°R).

140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440

0.0849 0.0958 0.1046 0.1121 0.1188 0.1250 0.1307 0.1360 0.1411 0.1459 0.1505 0.1550 0.1593 0.1635 0.1676 0.1716 0.1756 0.1794 0.1832 0.1869 0.1906 0.1942 0.1978 0.2013 0.2048 0.2083 0.2117 0.2151 0.2184 0.2218 0.2251

120.2 126.0 130.8 135.1 138.9 142.6 146.0 149.3 152.5 155.6 158.6 161.6 164.5 167.4 170.2 173.1 175.9 178.7 181.4 184.2 186.9 189.7 192.4 195.2 197.9 200.7 203.4 206.2 209.0 211.7 214.5

0.2193 0.2289 0.2367 0.2435 0.2497 0.2553 0.2605 0.2655 0.2702 0.2748 0.2791 0.2833 0.2874 0.2914 0.2953 0.2991 0.3028 0.3064 0.3100 0.3135 0.3170 0.3204 0.3238 0.3271 0.3304 0.3337 0.3369 0.3401 0.3432 0.3463 0.3494

140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440

Appendix 2 763

−20

0.04

Pressure (psia)

0

20

80

100

40

120

40

20

Temperature = 0oF

20

40

60

60

80

100

100

Enthalpy (BTU/lb)

80

120

140

120 6

0.0

0.08 10 0.

140

160

120

140

160

Source: Thermodynamic Properties of DuPont Suva 410A Refrigerant. With permission of E. I. Du Pont de Nemours and Co.

1

2

4

6

10 8

te d

liqu

id

0.00

20

0.1

0.02

40

0.06

60

0.2

0.04

100 80

0.08

200

0.3

0.10

Pressure–Enthalpy Diagram (English Units)

0.16

ura

Sat

0.02

lity =

0.5

0.18

400

0.7

DuPont TM Suva 410A

0.6

0.20

DuPont Fluorochemicals

0.8

0.22 0.24

Vapor Saturate d

100

4

80

6

60

0.3

600

0.4

0.12

0.9

0.26 0.28

40

8

20

.4 =0

Q ua

0.14

lb- o F

0.40

0.30

0.20

0.15

180 200

0 f /lb

0.80 1.0

e = 0.5 Volum 0.60

2 0.4

0

80.0 100

50.0 60.0

40.0

30.0

20.0

15.0

8.0

10.0

4.0 5.0 6.0

3.0

1.5

180

4

−20

0.4

1000 800

0.3 100 80 60 40

0.3 E

6

200

48

U/ 0B T py ntr o

0.30 0.32

20 0 20 40 60 80 100 120 140 160 180 o Temperature = 200 F 220 240 260 280 300 320 340 360 0.4 0.

Enthalpy (BTU/lb)

1

2

4

6

10 8

20

40

60

100 80

200

400

600

1000 800

764 Appendix 2

Pressure (psia)

–100 –99 –98 –97 –96 –95 –94 –93 –92 –91 –90 –89 –88 –87 –86 –85 –84 –83 –82 –81 –80 –79 –78 –77 –76 –75 –74

Temp. °C

3.8 4.1 4.5 4.9 5.4 5.9 6.4 6.9 7.5 8.2 8.8 9.6 10.3 11.2 12.0 13.0 14.0 15.0 16.2 17.4 18.6 20.0 21.4 22.9 24.5 26.2 27.9

Liquid pf

3.7 4.1 4.4 4.9 5.3 5.8 6.3 6.8 7.4 8.1 8.8 9.5 10.2 11.1 12.0 12.9 13.9 14.9 16.1 17.3 18.5 19.9 21.3 22.8 24.4 26.1 27.8

Vapor pg

Pressure, kPa

0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007

Liquid vf 5.3267 4.8882 4.4913 4.1317 3.8053 3.5088 3.2391 2.9935 2.7694 2.5649 2.3780 2.2069 2.0502 1.9065 1.7746 1.6534 1.5419 1.4391 1.3445 1.2571 1.1764 1.1019 1.0328 0.9689 0.9097 0.8547 0.8037

Vapor vg

Volume, m3/kg

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (SI)

1509.0 1506.2 1503.4 1500.6 1497.8 1494.9 1492.1 1489.3 1486.4 1483.6 1480.7 1477.9 1475.0 1472.1 1469.2 1466.3 1463.4 1460.5 1457.6 1454.7 1451.7 1448.8 1445.8 1442.8 1439.9 1436.9 1433.9

Liquid 1/vf 0.188 0.205 0.223 0.242 0.263 0.285 0.309 0.334 0.361 0.390 0.421 0.453 0.488 0.525 0.564 0.605 0.649 0.695 0.744 0.795 0.850 0.908 0.968 1.032 1.099 1.170 1.244

Vapor 1/vg

Density, kg/m3

63.3 64.5 65.7 66.9 68.1 69.3 70.5 71.7 73.0 74.2 75.4 76.6 77.9 79.1 80.4 81.6 82.9 84.1 85.4 86.6 87.9 89.2 90.4 91.7 93.0 94.2 95.5

Liquid hf 311.4 310.8 310.2 309.5 308.9 308.3 307.6 307.0 306.3 305.7 305.0 304.4 303.7 303.0 302.4 301.7 301.0 300.3 299.7 299.0 298.3 297.6 296.9 296.1 295.4 294.7 294.0

Latent hfg

Enthalpy, kJ/kg

374.7 375.3 375.8 376.4 377.0 377.6 378.2 378.7 379.3 379.9 380.5 381.0 381.6 382.2 382.7 383.3 383.9 384.4 385.0 385.6 386.1 386.7 387.3 387.8 388.4 389.0 389.5

Vapor hg 0.3789 0.3857 0.3925 0.3993 0.4061 0.4128 0.4196 0.4263 0.4330 0.4398 0.4465 0.4532 0.4599 0.4666 0.4732 0.4799 0.4866 0.4932 0.4998 0.5064 0.5130 0.5196 0.5262 0.5328 0.5393 0.5459 0.5524

Liquid sf 2.1774 2.1703 2.1633 2.1565 2.1498 2.1432 2.1367 2.1304 2.1241 2.1180 2.1120 2.1061 2.1003 2.0945 2.0889 2.0834 2.0780 2.0727 2.0674 2.0623 2.0572 2.0523 2.0474 2.0426 2.0378 2.0332 2.0286

Vapor sg

Entropy, kJ/(kg)(K)

–100 –99 –98 –97 –96 –95 –94 –93 –92 –91 –90 –89 –88 –87 –86 –85 –84 –83 –82 –81 –80 –79 –78 –77 –76 –75 –74 (continued)

Temp. °C

Appendix 2 765

–73 –72 –71 –70 –69 –68 –67 –66 –65 –64 –63 –62 –61 –60 –59 –58 –57 –56 –55 –54 –53 –52 –51 –50 –49 –48 –47 –46

Temp. °C

29.8 31.8 33.9 36.0 38.3 40.7 43.3 45.9 48.7 51.7 54.7 57.9 61.3 64.8 68.5 72.3 76.4 80.6 84.9 89.5 94.2 99.2 104.3 109.7 115.3 121.1 127.1 133.4

Liquid pf

29.7 31.7 33.7 35.9 38.2 40.6 43.2 45.8 48.6 51.5 54.6 57.8 61.2 64.7 68.3 72.2 76.2 80.4 84.7 89.3 94.0 99.0 104.1 109.4 115.0 120.8 126.8 133.0

Vapor pg

Pressure, kPa

0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007

Liquid vf 0.7563 0.7121 0.6711 0.6328 0.5972 0.5639 0.5328 0.5038 0.4766 0.4512 0.4274 0.4051 0.3842 0.3646 0.3461 0.3288 0.3126 0.2972 0.2828 0.2692 0.2565 0.2444 0.2330 0.2222 0.2121 0.2025 0.1934 0.1848

Vapor vg

Volume, m3/kg

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (SI) (Continued)

1430.9 1427.9 1424.8 1421.8 1418.8 1415.7 1412.7 1409.6 1406.5 1403.4 1400.3 1397.2 1394.1 1390.9 1387.8 1384.6 1381.4 1378.3 1375.1 1371.9 1368.7 1365.4 1362.2 1358.9 1355.7 1352.4 1349.1 1345.8

Liquid 1/vf 1.322 1.404 1.490 1.580 1.675 1.773 1.877 1.985 2.098 2.216 2.340 2.469 2.603 2.743 2.889 3.041 3.199 3.364 3.536 3.714 3.899 4.092 4.292 4.500 4.715 4.939 5.171 5.411

Vapor 1/vg

Density, kg/m3

96.8 98.1 99.4 100.7 102.0 103.3 104.6 105.9 107.2 108.5 109.9 111.2 112.5 113.8 115.2 116.5 117.9 119.2 120.5 121.9 123.2 124.6 126.0 127.3 128.7 130.1 131.4 132.8

Liquid hf 293.2 292.5 291.8 291.0 290.3 289.5 288.8 288.0 287.2 286.4 285.7 284.9 284.1 283.3 282.5 281.6 280.8 280.0 279.2 278.3 277.5 276.6 275.8 274.9 274.1 273.2 272.3 271.4

Latent hfg

Enthalpy, kJ/kg

390.1 390.6 391.2 391.7 392.3 392.8 393.4 393.9 394.4 395.0 395.5 396.0 396.6 397.1 397.6 398.2 398.7 399.2 399.7 400.2 400.7 401.2 401.7 402.2 402.7 403.2 403.7 404.2

Vapor hg 0.5589 0.5654 0.5719 0.5784 0.5849 0.5913 0.5978 0.6042 0.6106 0.6170 0.6234 0.6298 0.6361 0.6425 0.6488 0.6551 0.6614 0.6677 0.6740 0.6803 0.6865 0.6928 0.6990 0.7052 0.7114 0.7176 0.7238 0.7299

Liquid sf 2.0241 2.0196 2.0153 2.0110 2.0067 2.0026 1.9985 1.9944 1.9904 1.9865 1.9827 1.9788 1.9751 1.9714 1.9678 1.9642 1.9606 1.9571 1.9537 1.9503 1.9470 1.9437 1.9404 1.9372 1.9340 1.9309 1.9278 1.9248

Vapor sg

Entropy, kJ/(kg)(K)

–73 –72 –71 –70 –69 –68 –67 –66 –65 –64 –63 –62 –61 –60 –59 –58 –57 –56 –55 –54 –53 –52 –51 –50 –49 –48 –47 –46

Temp. °C

766 Appendix 2

–45 –44 –43 –42 –41 –40 –39 –38 –37 –36 –35 –34 –33 –32 –31 –30 –29 –28 –27 –26 –25 –24 –23 –22 –21 –20 –19 –18 –17 –16 –15 –14

139.9 146.6 153.6 160.9 168.4 176.2 184.3 192.7 201.3 210.3 219.6 229.2 239.1 249.3 259.9 270.8 282.1 293.7 305.7 318.1 330.9 344.0 357.6 371.5 385.9 400.7 415.9 431.6 447.7 464.3 481.3 498.9

139.5 146.3 153.2 160.5 168.0 175.8 183.8 192.2 200.8 209.8 219.0 228.6 238.4 248.6 259.2 270.1 281.3 292.9 304.9 317.2 329.9 343.0 356.6 370.5 384.8 399.5 414.7 430.3 446.4 462.9 479.9 497.4

0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008

0.1767 0.1690 0.1617 0.1547 0.1482 0.1419 0.1360 0.1304 0.1251 0.1200 0.1151 0.1105 0.1062 0.1020 0.0980 0.0942 0.0906 0.0872 0.0839 0.0807 0.0777 0.0749 0.0721 0.0695 0.0670 0.0646 0.0623 0.0601 0.0580 0.0559 0.0540 0.0521

1342.5 1339.2 1335.8 1332.5 1329.1 1325.7 1322.3 1318.9 1315.5 1312.1 1308.6 1305.2 1301.7 1298.2 1294.7 1291.2 1287.6 1284.1 1280.5 1276.9 1273.3 1269.7 1266.0 1262.3 1258.7 1255.0 1251.3 1247.5 1243.8 1240.0 1236.2 1232.4

5.660 5.918 6.186 6.462 6.749 7.045 7.352 7.669 7.996 8.335 8.685 9.046 9.419 9.805 10.202 10.613 11.036 11.473 11.923 12.388 12.866 13.360 13.868 14.391 14.931 15.486 16.058 16.647 17.253 17.877 18.519 19.179

134.2 135.6 137.0 138.4 139.7 141.1 142.5 144.0 145.4 146.8 148.2 149.6 151.0 152.4 153.9 155.3 156.7 158.2 159.6 161.1 162.5 164.0 165.4 166.9 168.4 169.8 171.3 172.8 174.3 175.7 177.2 178.7

270.5 269.6 268.7 267.8 266.9 265.9 265.0 264.1 263.1 262.2 261.2 260.2 259.3 258.3 257.3 256.3 255.3 254.3 253.3 252.2 251.2 250.1 249.1 248.0 247.0 245.9 244.8 243.7 242.6 241.5 240.4 239.3

404.7 405.2 405.7 406.1 406.6 407.1 407.6 408.0 408.5 408.9 409.4 409.8 410.3 410.7 411.2 411.6 412.0 412.5 412.9 413.3 413.7 414.1 414.5 414.9 415.3 415.7 416.1 416.5 416.9 417.2 417.6 418.0

0.7361 0.7422 0.7483 0.7544 0.7605 0.7666 0.7727 0.7787 0.7847 0.7908 0.7968 0.8028 0.8088 0.8148 0.8207 0.8267 0.8326 0.8385 0.8445 0.8504 0.8562 0.8621 0.8680 0.8738 0.8797 0.8855 0.8913 0.8971 0.9029 0.9087 0.9145 0.9203

1.9217 1.9188 1.9158 1.9129 1.9101 1.9072 1.9045 1.9017 1.8990 1.8963 1.8936 1.8910 1.8884 1.8858 1.8832 1.8807 1.8782 1.8757 1.8733 1.8709 1.8685 1.8661 1.8638 1.8614 1.8591 1.8569 1.8546 1.8523 1.8501 1.8479 1.8457 1.8436

–45 –44 –43 –42 –41 –40 –39 –38 –37 –36 –35 –34 –33 –32 –31 –30 –29 –28 –27 –26 –25 –24 –23 –22 –21 –20 –19 –18 –17 –16 –15 –14 (continued)

Appendix 2 767

–13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Temp. °C

516.9 535.4 554.4 573.9 593.9 614.4 635.5 657.2 679.3 702.1 725.4 749.3 773.9 799.0 824.7 851.0 878.0 905.6 933.9 962.9 992.5 1022.8 1053.8 1085.5 1117.9 1151.0 1184.9 1219.5

Liquid pf

515.3 533.7 552.7 572.1 592.1 612.6 633.6 655.1 677.3 699.9 723.2 747.0 771.4 796.5 822.1 848.4 875.3 902.8 931.0 959.8 989.3 1019.5 1050.4 1082.0 1114.3 1147.3 1181.1 1215.6

Vapor pg

Pressure, kPa

0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009

Liquid vf 0.0504 0.0486 0.0470 0.0454 0.0439 0.0425 0.0411 0.0397 0.0384 0.0372 0.0360 0.0348 0.0337 0.0326 0.0316 0.0306 0.0297 0.0287 0.0278 0.0270 0.0261 0.0253 0.0246 0.0238 0.0231 0.0224 0.0217 0.0211

Vapor vg

Volume, m3/kg

Suva® 410A Saturation Properties—Temperature Table

TABLE A.18 (SI) (Continued)

1228.6 1224.7 1220.8 1216.9 1213.0 1209.1 1205.1 1201.1 1197.1 1193.1 1189.0 1184.9 1180.8 1176.7 1172.5 1168.3 1164.1 1159.8 1155.5 1151.2 1146.9 1142.5 1138.1 1133.7 1129.2 1124.7 1120.1 1115.6

Liquid 1/vf 19.859 20.558 21.276 22.016 22.776 23.558 24.361 25.187 26.036 26.909 27.806 28.728 29.675 30.649 31.649 32.676 33.732 34.817 35.931 37.076 38.252 39.461 40.702 41.977 43.288 44.634 46.017 47.437

Vapor 1/vg

Density, kg/m3

180.2 181.7 183.2 184.7 186.2 187.7 189.3 190.8 192.3 193.8 195.4 196.9 198.5 200.0 201.6 203.1 204.7 206.2 207.8 209.4 211.0 212.6 214.1 215.7 217.3 219.0 220.6 222.2

Liquid hf 238.1 237.0 235.8 234.7 233.5 232.3 231.1 229.9 228.7 227.5 226.3 225.1 223.8 222.5 221.3 220.0 218.7 217.4 216.1 214.8 213.4 212.1 210.7 209.3 207.9 206.5 205.1 203.7

Latent hfg

Enthalpy, kJ/kg

418.3 418.7 419.1 419.4 419.7 420.1 420.4 420.7 421.0 421.4 421.7 422.0 422.3 422.5 422.8 423.1 423.4 423.6 423.9 424.1 424.4 424.6 424.9 425.1 425.3 425.5 425.7 425.9

Vapor hg 0.9260 0.9318 0.9375 0.9432 0.9489 0.9547 0.9604 0.9660 0.9717 0.9774 0.9830 0.9887 0.9943 1.0000 1.0056 1.0112 1.0168 1.0225 1.0281 1.0337 1.0392 1.0448 1.0504 1.0560 1.0616 1.0671 1.0727 1.0783

Liquid sf 1.8414 1.8393 1.8372 1.8351 1.8330 1.8309 1.8288 1.8268 1.8247 1.8227 1.8207 1.8187 1.8167 1.8147 1.8128 1.8108 1.8088 1.8069 1.8049 1.8030 1.8011 1.7991 1.7972 1.7953 1.7934 1.7914 1.7895 1.7876

Vapor sg

Entropy, kJ/(kg)(K)

–13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Temp. °C

768 Appendix 2

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

1254.9 1291.0 1328.0 1365.7 1404.2 1443.6 1483.7 1524.7 1566.6 1609.3 1652.9 1697.3 1742.7 1788.9 1836.1 1884.2 1933.3 1983.3 2034.3 2086.3 2139.2 2193.2 2248.1 2304.2 2361.2 2419.3 2478.5 2538.8 2600.1 2662.6 2726.1 2790.9

1250.8 1286.9 1323.7 1361.3 1399.6 1438.8 1478.9 1519.7 1561.4 1604.0 1647.4 1691.7 1736.9 1783.0 1830.0 1877.9 1926.8 1976.6 2027.4 2079.2 2132.0 2185.7 2240.5 2296.3 2353.2 2411.1 2470.1 2530.2 2591.3 2653.6 2717.0 2781.6

0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0010 0.0011 0.0011 0.0011

0.0205 0.0198 0.0193 0.0187 0.0181 0.0176 0.0171 0.0166 0.0161 0.0156 0.0152 0.0147 0.0143 0.0139 0.0135 0.0131 0.0127 0.0123 0.0120 0.0116 0.0113 0.0110 0.0107 0.0103 0.0100 0.0098 0.0095 0.0092 0.0089 0.0087 0.0084 0.0082

1110.9 1106.3 1101.6 1096.9 1092.1 1087.2 1082.4 1077.5 1072.5 1067.5 1062.4 1057.3 1052.1 1046.9 1041.6 1036.3 1030.9 1025.4 1019.9 1014.2 1008.6 1002.8 996.9 991.0 985.0 978.9 972.7 966.4 960.0 953.4 946.8 940.0

48.897 50.398 51.939 53.523 55.152 56.825 58.545 60.314 62.132 64.001 65.924 67.901 69.935 72.028 74.181 76.398 78.679 81.028 83.447 85.939 88.506 91.151 93.879 96.691 99.592 102.585 105.674 108.864 112.159 115.564 119.085 122.727

223.8 225.4 227.1 228.7 230.4 232.0 233.7 235.4 237.1 238.7 240.4 242.1 243.9 245.6 247.3 249.1 250.8 252.6 254.3 256.1 257.9 259.7 261.5 263.4 265.2 267.1 269.0 270.9 272.8 274.8 276.7 278.7

202.2 200.8 199.3 197.8 196.3 194.8 193.2 191.7 190.1 188.5 186.9 185.3 183.6 181.9 180.2 178.5 176.8 175.0 173.2 171.4 169.5 167.7 165.8 163.8 161.9 159.9 157.8 155.8 153.7 151.5 149.3 147.1

426.1 426.2 426.4 426.5 426.7 426.8 426.9 427.1 427.2 427.3 427.3 427.4 427.5 427.5 427.5 427.6 427.6 427.6 427.5 427.5 427.5 427.4 427.3 427.2 427.1 427.0 426.8 426.7 426.5 426.3 426.0 425.8

1.0838 1.0894 1.0949 1.1005 1.1060 1.1116 1.1172 1.1227 1.1283 1.1338 1.1394 1.1450 1.1506 1.1562 1.1618 1.1674 1.1730 1.1786 1.1843 1.1899 1.1956 1.2013 1.2070 1.2127 1.2185 1.2243 1.2301 1.2359 1.2418 1.2477 1.2537 1.2597

1.7857 1.7838 1.7818 1.7799 1.7780 1.7760 1.7741 1.7721 1.7702 1.7682 1.7662 1.7643 1.7623 1.7603 1.7582 1.7562 1.7541 1.7521 1.7500 1.7479 1.7458 1.7436 1.7414 1.7392 1.7370 1.7348 1.7325 1.7302 1.7278 1.7255 1.7230 1.7206

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 (continued)

Appendix 2 769

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

Temp. °C

2856.7 2923.8 2991.9 3061.3 3131.9 3203.7 3276.7 3351.0 3426.5 3503.3 3581.3 3660.7 3741.3 3823.3 3906.6 3991.2 4077.2 4164.5 4253.2 4343.3 4434.7 4527.6 4621.8 4717.5

Liquid pf

2847.3 2914.2 2982.2 3051.5 3122.0 3193.7 3266.6 3340.9 3416.3 3493.1 3571.2 3650.7 3731.5 3813.6 3897.1 3982.0 4068.4 4156.1 4245.4 4336.1 4428.2 4521.9 4617.2 4713.9

Vapor pg

Pressure, kPa

0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014 0.0014 0.0015

Liquid vf 0.0079 0.0077 0.0074 0.0072 0.0070 0.0068 0.0066 0.0064 0.0062 0.0060 0.0058 0.0056 0.0054 0.0052 0.0050 0.0049 0.0047 0.0045 0.0043 0.0041 0.0039 0.0037 0.0035 0.0032

Vapor vg

Volume, m3/kg

Suva® 410A Saturation Properties–Temperature Table

TABLE A.18 (SI) (Continued)

933.1 926.0 918.8 911.4 903.9 896.1 888.2 880.0 871.5 862.8 853.8 844.5 834.8 824.7 814.1 802.9 791.1 778.5 765.0 750.3 734.2 716.0 694.9 669.1

Liquid 1/vf 126.497 130.402 134.448 138.645 143.001 147.527 152.235 157.139 162.252 167.594 173.187 179.056 185.232 191.757 198.680 206.069 214.014 222.641 232.131 242.755 254.940 269.366 287.059 308.947

Vapor 1/vg

Density, kg/m3

280.7 282.7 284.8 286.9 289.0 291.2 293.4 295.6 297.9 300.3 302.7 305.1 307.7 310.3 313.0 315.9 318.8 322.0 325.3 328.8 332.7 336.9 341.7 347.3

Liquid hf 144.8 142.5 140.1 137.7 135.2 132.6 130.0 127.3 124.6 121.7 118.7 115.7 112.5 109.2 105.8 102.2 98.4 94.3 90.0 85.3 80.3 74.6 68.4 61.6

Latent hfg

Enthalpy, kJ/kg

425.5 425.2 424.9 424.6 424.2 423.8 423.4 423.0 422.5 422.0 421.4 420.8 420.2 419.5 418.8 418.1 417.2 416.3 415.3 414.2 412.9 411.5 410.1 408.9

Vapor hg 1.2658 1.2719 1.2781 1.2843 1.2906 1.2971 1.3036 1.3102 1.3169 1.3238 1.3308 1.3380 1.3453 1.3529 1.3608 1.3689 1.3774 1.3863 1.3958 1.4059 1.4168 1.4289 1.4425 1.4586

Liquid sf 1.7181 1.7156 1.7130 1.7104 1.7077 1.7050 1.7022 1.6994 1.6965 1.6935 1.6904 1.6873 1.6841 1.6808 1.6773 1.6738 1.6700 1.6661 1.6620 1.6575 1.6527 1.6476 1.6424 1.6380

Vapor sg

Entropy, kJ/(kg)(K)

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

Temp. °C

770 Appendix 2

(2.0972)

2.1363 2.1951 2.2538 2.3123 2.3707 2.4290 2.4872 2.5453 2.6033 2.6613 2.7192 2.7770 2.8348 2.8926 2.9503 3.0079 3.0656 3.1232 3.1808 3.2383 3.2958 3.3534 3.4109

Temp. °C

–85 –80 –75 –70 –65 –60 –55 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25

V

383.5 386.8 390.1 393.4 396.7 400.1 403.6 407.0 410.5 414.1 417.7 421.3 425.0 428.7 432.4 436.2 440.0 443.9 447.8 451.7 455.7 459.7 463.8

(381.4)

2.1134 2.1304 2.1472 2.1637 2.1800 2.1962 2.2121 2.2278 2.2434 2.2588 2.2740 2.2891 2.3040 2.3188 2.3334 2.3479 2.3623 2.3766 2.3908 2.4048 2.4187 2.4325 2.4462

(2.1020)

S

– – 1.1188 1.1487 1.1784 1.2081 1.2377 1.2672 1.2966 1.3259 1.3551 1.3844 1.4135 1.4426 1.4717 1.5007 1.5297 1.5587 1.5876 1.6166 1.6455 1.6743 1.7032

(1.0953)

V

– – 389.4 392.7 396.2 399.6 403.1 406.6 410.1 413.7 417.3 421.0 424.7 428.4 432.2 436.0 439.8 443.7 447.6 451.5 455.5 459.5 463.6

(386.8)

H

(–78.91°C)

(–88.31°C)

H

20.0

10.0

– – 2.0651 2.0819 2.0985 2.1148 2.1309 2.1468 2.1625 2.1780 2.1934 2.2086 2.2236 2.2385 2.2532 2.2678 2.2822 2.2966 2.3108 2.3248 2.3388 2.3527 2.3664

(2.0518)

S

– – – 0.7607 0.7810 0.8011 0.8211 0.8411 0.8609 0.8807 0.9005 0.9201 0.9397 0.9593 0.9788 0.9983 1.0178 1.0372 1.0566 1.0760 1.0953 1.1147 1.1340

(0.7491)

V

30.0

– – – 392.1 395.6 399.0 402.6 406.1 409.7 413.3 416.9 420.6 424.3 428.1 431.9 435.7 439.5 443.4 447.4 451.3 455.3 459.4 463.4

(390.2)

H

(–72.84°C)

Absolute Pressure, kPa

– – – 2.0331 2.0499 2.0664 2.0827 2.0988 2.1146 2.1303 2.1458 2.1610 2.1762 2.1911 2.2059 2.2206 2.2351 2.2495 2.2637 2.2779 2.2919 2.3057 2.3195

(2.0234)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI)

– – – – 0.5822 0.5976 0.6129 0.6280 0.6431 0.6581 0.6731 0.6880 0.7028 0.7176 0.7324 0.7471 0.7618 0.7764 0.7911 0.8057 0.8203 0.8348 0.8494

(0.5721)

V

– – – – 395.0 398.5 402.0 405.6 409.2 412.9 416.6 420.3 424.0 427.8 431.6 435.4 439.3 443.2 447.1 451.1 455.1 459.2 463.3

(392.7)

H

(–68.26°C)

40.0

– – – – 2.0147 2.0315 2.0479 2.0642 2.0802 2.0960 2.1116 2.1270 2.1422 2.1573 2.1721 2.1869 2.2014 2.2159 2.2302 2.2444 2.2584 2.2723 2.2861

(2.0036)

S

–85 –80 –75 –70 –65 –60 –55 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 (continued)

Temp. °C

Appendix 2 771

3.4683 3.5258 3.5833 3.6407 3.6981 3.7555 3.8130 3.8704 – – – –

30 35 40 45 50 55 60 65 70 75 80 85

(0.4641)

0.4754 0.4879 0.5002 0.5124

Temp. °C

–60 –55 –50 –45

V

(2.0972)

Temp. °C

V

397.9 401.5 405.2 408.8

(394.7)

H

2.0039 2.0206 2.0370 2.0532

(1.9885)

S

0.3940 0.4045 0.4149 0.4253

(0.3911)

V

397.4 401.0 404.7 408.4

(396.4)

H

(–61.34°C)

467.7 471.8 476.0 480.2 484.5 488.8 493.1 497.4 501.8 506.3 – –

(386.8)

(–64.52°C)

1.7320 1.7609 1.7897 1.8185 1.8473 1.8761 1.9048 1.9336 1.9624 1.9911 – –

(1.0953)

H

60.0

2.4598 2.4733 2.4868 2.5001 2.5133 2.5264 2.5395 2.5524 – – – –

(2.1020)

V

50.0

467.9 472.0 476.2 480.4 484.6 488.9 493.2 497.6 – – – –

(381.4)

S

(–78.91°C)

(–88.31°C)

H

20.0

10.0

1.9810 1.9979 2.0145 2.0308

(1.9764)

S

2.3800 2.3936 2.4070 2.4204 2.4336 2.4468 2.4598 2.4728 2.4857 2.4985 – –

(2.0518)

S

– 0.3449 0.3540 0.3630

(0.3384)

V

1.1533 1.1726 1.1918 1.2111 1.2303 1.2496 1.2688 1.2880 1.3072 1.3264 1.3456 –

(0.7491)

V

30.0

– 400.5 404.2 407.9

(397.9)

H

(–58.56°C)

70.0

467.5 471.7 475.9 480.1 484.3 488.6 493.0 497.3 501.7 506.2 510.6 –

(390.2)

H

(–72.84°C)

Absolute Pressure, kPa

– 1.9783 1.9951 2.0116

(1.9662)

S

2.3332 2.3468 2.3602 2.3736 2.3869 2.4000 2.4131 2.4261 2.4390 2.4518 2.4646 –

(2.0234)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.3003 0.3083 0.3163

(0.2985)

V

0.8639 0.8784 0.8929 0.9074 0.9219 0.9363 0.9508 0.9652 0.9797 0.9941 1.0085 1.0229

(0.5721)

V

– 400.0 403.7 407.5

(399.1)

H

(–56.09°C)

80.0

467.4 471.5 475.7 480.0 484.2 488.5 492.8 497.2 501.6 506.1 510.5 515.0

(392.7)

H

(–68.26°C)

40.0

– 1.9612 1.9782 1.9948

(1.9574)

S

2.2998 2.3134 2.3269 2.3403 2.3536 2.3668 2.3799 2.3929 2.4058 2.4187 2.4314 2.4441

(2.0036)

S

–60 –55 –50 –45

Temp. °C

30 35 40 45 50 55 60 65 70 75 80 85

Temp. °C

772 Appendix 2

–40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

0.5246 0.5367 0.5487 0.5607 0.5726 0.5845 0.5964 0.6082 0.6200 0.6318 0.6435 0.6552 0.6669 0.6786 0.6903 0.7019 0.7135 0.7252 0.7368 0.7484 0.7600 0.7715 0.7831 0.7947 0.8062 0.8178 0.8294 –

412.5 416.2 419.9 423.7 427.5 431.3 435.2 439.0 443.0 446.9 450.9 454.9 459.0 463.1 467.2 471.4 475.6 479.8 484.1 488.4 492.7 497.1 501.5 505.9 510.4 514.9 519.5 –

2.0691 2.0848 2.1003 2.1156 2.1308 2.1457 2.1605 2.1752 2.1897 2.2040 2.2182 2.2323 2.2463 2.2601 2.2739 2.2875 2.3010 2.3144 2.3277 2.3409 2.3541 2.3671 2.3800 2.3929 2.4057 2.4183 2.4309 –

0.4355 0.4457 0.4558 0.4659 0.4759 0.4859 0.4959 0.5058 0.5157 0.5255 0.5354 0.5452 0.5550 0.5647 0.5745 0.5842 0.5940 0.6037 0.6134 0.6231 0.6327 0.6424 0.6521 0.6617 0.6714 0.6810 0.6907 –

412.1 415.8 419.6 423.4 427.2 431.0 434.9 438.8 442.7 446.7 450.7 454.7 458.8 462.9 467.1 471.2 475.4 479.7 483.9 488.3 492.6 497.0 501.4 505.8 510.3 514.8 519.4 –

2.0469 2.0627 2.0783 2.0937 2.1090 2.1240 2.1389 2.1536 2.1681 2.1825 2.1968 2.2109 2.2250 2.2388 2.2526 2.2662 2.2798 2.2932 2.3065 2.3198 2.3329 2.3460 2.3589 2.3718 2.3846 2.3973 2.4099 –

0.3719 0.3807 0.3895 0.3982 0.4069 0.4155 0.4241 0.4327 0.4412 0.4497 0.4581 0.4666 0.4750 0.4834 0.4918 0.5002 0.5085 0.5169 0.5252 0.5336 0.5419 0.5502 0.5585 0.5668 0.5751 0.5834 0.5916 0.5999

411.7 415.4 419.2 423.0 426.9 430.7 434.6 438.5 442.5 446.5 450.5 454.5 458.6 462.7 466.9 471.1 475.3 479.5 483.8 488.1 492.5 496.9 501.3 505.7 510.2 514.7 519.3 523.9

2.0279 2.0438 2.0596 2.0751 2.0904 2.1055 2.1205 2.1352 2.1498 2.1643 2.1786 2.1928 2.2068 2.2207 2.2345 2.2482 2.2618 2.2752 2.2886 2.3018 2.3150 2.3281 2.3410 2.3539 2.3667 2.3794 2.3920 2.4046

0.3242 0.3320 0.3397 0.3474 0.3551 0.3627 0.3703 0.3778 0.3853 0.3928 0.4002 0.4076 0.4150 0.4224 0.4298 0.4371 0.4445 0.4518 0.4591 0.4664 0.4737 0.4810 0.4883 0.4956 0.5028 0.5101 0.5174 0.5246

411.2 415.0 418.9 422.7 426.5 430.4 434.3 438.3 442.3 446.3 450.3 454.4 458.4 462.6 466.7 470.9 475.1 479.4 483.7 488.0 492.4 496.7 501.2 505.6 510.1 514.6 519.2 523.8

2.0112 2.0273 2.0431 2.0588 2.0742 2.0894 2.1044 2.1192 2.1339 2.1484 2.1628 2.1770 2.1911 2.2050 2.2188 2.2325 2.2461 2.2596 2.2730 2.2863 2.2994 2.3125 2.3255 2.3384 2.3512 2.3639 2.3766 2.3891 (continued)

–40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Appendix 2 773

(0.2672)

0.2728 0.2800 0.2870 0.2941 0.3010 0.3079 0.3148 0.3216 0.3284 0.3351 0.3418 0.3485 0.3552 0.3618 0.3684 0.3750 0.3816 0.3881 0.3947 0.4012 0.4077 0.4142 0.4207 0.4272

Temp. °C

–50 –45 –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65

V

403.2 407.0 410.8 414.6 418.5 422.4 426.2 430.1 434.1 438.0 442.0 446.0 450.1 454.2 458.3 462.4 466.6 470.8 475.0 479.3 483.5 487.9 492.2 496.6

(400.3)

1.9630 1.9798 1.9963 2.0125 2.0285 2.0442 2.0597 2.0750 2.0901 2.1050 2.1197 2.1343 2.1487 2.1630 2.1771 2.1911 2.2049 2.2187 2.2323 2.2458 2.2592 2.2725 2.2857 2.2988

(1.9498)

S

0.2443 0.2509 0.2573 0.2637 0.2701 0.2763 0.2826 0.2887 0.2949 0.3010 0.3071 0.3131 0.3191 0.3251 0.3311 0.3370 0.3430 0.3489 0.3548 0.3607 0.3666 0.3725 0.3783 0.3842

(0.2420)

V

402.7 406.6 410.4 414.3 418.1 422.0 425.9 429.9 433.8 437.8 441.8 445.8 449.9 454.0 458.1 462.2 466.4 470.6 474.8 479.1 483.4 487.7 492.1 496.5

(401.3)

H

(–51.79°C)

(–53.84°C)

H

100.0

90.0

1.9492 1.9662 1.9828 1.9992 2.0153 2.0311 2.0467 2.0621 2.0773 2.0922 2.1070 2.1216 2.1361 2.1504 2.1646 2.1786 2.1925 2.2062 2.2199 2.2334 2.2468 2.2601 2.2733 2.2865

(1.9430)

S

0.2410 0.2475 0.2538 0.2602 0.2664 0.2726 0.2788 0.2849 0.2909 0.2970 0.3030 0.3089 0.3149 0.3208 0.3267 0.3326 0.3384 0.3443 0.3501 0.3559 0.3617 0.3675 0.3733 0.3791

(0.2390)

V

101.325

402.7 406.5 410.3 414.2 418.1 422.0 425.9 429.8 433.8 437.7 441.8 445.8 449.8 453.9 458.0 462.2 466.4 470.6 474.8 479.1 483.4 487.7 492.1 496.5

(401.5)

H

(–51.53°C)

Absolute Pressure, kPa

1.9474 1.9645 1.9811 1.9975 2.0136 2.0295 2.0451 2.0605 2.0756 2.0906 2.1054 2.1200 2.1345 2.1488 2.1630 2.1770 2.1909 2.2047 2.2183 2.2319 2.2453 2.2586 2.2718 2.2849

(1.9421)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.2271 0.2330 0.2389 0.2447 0.2505 0.2562 0.2618 0.2675 0.2730 0.2786 0.2841 0.2896 0.2951 0.3005 0.3060 0.3114 0.3168 0.3222 0.3276 0.3329 0.3383 0.3436 0.3490

(0.2212)

V

– 406.1 410.0 413.9 417.8 421.7 425.6 429.6 433.5 437.5 441.5 445.6 449.7 453.8 457.9 462.0 466.2 470.4 474.7 479.0 483.3 487.6 492.0 496.4

(402.3)

H

(–49.90°C)

110.0

– 1.9537 1.9705 1.9870 2.0032 2.0192 2.0349 2.0503 2.0655 2.0806 2.0954 2.1101 2.1246 2.1390 2.1532 2.1672 2.1811 2.1949 2.2086 2.2222 2.2356 2.2489 2.2622 2.2753

(1.9369)

S

–50 –45 –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65

Temp. °C

774 Appendix 2

(0.2037)

0.2072 0.2128 0.2182 0.2236 0.2289 0.2342 0.2394 0.2446 0.2498 0.2549 0.2600 0.2650 0.2701 0.2751 0.2801 0.2851 0.2901 0.2950

–45 –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40

V

0.4337 0.4402 0.4467 0.4531 0.4596 0.4660 0.4725 –

Temp. °C

70 75 80 85 90 95 100 105

405.6 409.5 413.5 417.4 421.3 425.3 429.3 433.3 437.3 441.3 445.4 449.5 453.6 457.7 461.9 466.1 470.3 474.5

(403.2)

H

1.9421 1.9591 1.9758 1.9921 2.0082 2.0239 2.0395 2.0548 2.0699 2.0848 2.0995 2.1141 2.1285 2.1427 2.1568 2.1708 2.1846 2.1983

(1.9313)

S

0.1904 0.1956 0.2007 0.2057 0.2107 0.2156 0.2205 0.2253 0.2301 0.2348 0.2395 0.2442 0.2489 0.2536 0.2582 0.2628 0.2674 0.2720

(0.1889)

V

405.2 409.1 413.1 417.0 421.0 425.0 429.0 433.0 437.0 441.1 445.1 449.2 453.4 457.5 461.7 465.9 470.1 474.4

(404.0)

H

(–46.48°C)

501.0 505.4 509.9 514.4 519.0 523.6 528.2 –

(–48.13°C)

0.3900 0.3959 0.4017 0.4075 0.4134 0.4192 0.4250 – 130.0

2.3118 2.3247 2.3375 2.3502 2.3629 2.3754 2.3879 –

120.0

501.1 505.5 510.0 514.5 519.1 523.7 528.3 –

1.9314 1.9485 1.9653 1.9818 1.9979 2.0138 2.0294 2.0448 2.0600 2.0750 2.0898 2.1044 2.1188 2.1331 2.1472 2.1612 2.1750 2.1888

(1.9262)

S

2.2995 2.3124 2.3252 2.3380 2.3506 2.3632 2.3757 –

– 0.1809 0.1857 0.1904 0.1950 0.1996 0.2042 0.2087 0.2132 0.2176 0.2220 0.2264 0.2308 0.2351 0.2394 0.2437 0.2480 0.2523

(0.1761)

V

0.3849 0.3907 0.3964 0.4022 0.4079 0.4137 0.4194 –

– 408.7 412.7 416.7 420.7 424.7 428.7 432.7 436.8 440.8 444.9 449.0 453.2 457.3 461.5 465.7 470.0 474.2

(404.7)

H

(–44.93°C)

140.0

500.9 505.4 509.9 514.4 519.0 523.6 528.2 –

– 1.9386 1.9555 1.9721 1.9884 2.0044 2.0201 2.0355 2.0508 2.0658 2.0807 2.0953 2.1098 2.1241 2.1383 2.1523 2.1662 2.1799

(1.9215)

S

2.2979 2.3109 2.3237 2.3364 2.3491 2.3617 2.3742 –

– 0.1681 0.1727 0.1771 0.1815 0.1858 0.1901 0.1943 0.1985 0.2027 0.2068 0.2110 0.2151 0.2191 0.2232 0.2272 0.2312 0.2352

(0.1650)

V

0.3543 0.3596 0.3649 0.3702 0.3755 0.3808 0.3861 0.3914

– 408.2 412.3 416.3 420.3 424.3 428.4 432.4 436.5 440.6 444.7 448.8 453.0 457.1 461.3 465.6 469.8 474.1

(405.5)

H

(–43.46°C)

150.0

500.8 505.3 509.8 514.4 518.9 523.5 528.2 532.8

– 1.9292 1.9463 1.9630 1.9794 1.9955 2.0113 2.0268 2.0421 2.0572 2.0721 2.0868 2.1014 2.1157 2.1299 2.1440 2.1579 2.1717

(1.9172)

S

2.2883 2.3013 2.3141 2.3268 2.3395 2.3521 2.3646 2.3770

–45 –40 –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 (continued)

Temp. °C

70 75 80 85 90 95 100 105

Appendix 2 775

0.3000 0.3049 0.3098 0.3147 0.3196 0.3245 0.3294 0.3343 0.3392 0.3440 0.3489 0.3537 0.3586 –

45 50 55 60 65 70 75 80 85 90 95 100 105 110

(0.1552)

0.1570 0.1613 0.1655 0.1696

Temp. °C

–40 –35 –30 –25

V

(0.2037)

Temp. °C

V

407.8 411.9 415.9 420.0

(406.1)

1.9204 1.9376 1.9544 1.9709

(1.9131) 0.1471 0.1512 0.1552 0.1591

(0.1465)

V

407.4 411.4 415.5 419.6

(406.7)

H

(–40.74°C)

H

S

478.7 483.0 487.4 491.8 496.2 500.6 505.1 509.6 514.2 518.7 523.3 528.0 532.7 –

(404.0)

(–42.07°C)

0.2766 0.2812 0.2857 0.2903 0.2948 0.2993 0.3038 0.3083 0.3129 0.3174 0.3219 0.3263 0.3308 –

(0.1889)

H

170.0

2.2119 2.2253 2.2387 2.2519 2.2651 2.2781 2.2911 2.3039 2.3167 2.3294 2.3420 2.3545 2.3669 –

(1.9313)

V

160.0

478.8 483.1 487.5 491.9 496.3 500.7 505.2 509.7 514.3 518.8 523.4 528.1 532.7 –

(403.2)

S

(–46.48°C)

(–48.13°C)

H

130.0

120.0

1.9119 1.9293 1.9463 1.9629

(1.9093)

S

2.2024 2.2159 2.2292 2.2425 2.2556 2.2687 2.2817 2.2945 2.3073 2.3200 2.3326 2.3451 2.3576 –

(1.9262)

S

– 0.1423 0.1461 0.1498

(0.1388)

V

0.2566 0.2608 0.2651 0.2693 0.2735 0.2777 0.2819 0.2861 0.2903 0.2945 0.2987 0.3029 0.3070 0.3112

(0.1761)

V

140.0

– 411.0 415.1 419.3

(407.3)

H

(–39.47°C)

180.0

478.5 482.9 487.2 491.6 496.1 500.5 505.0 509.5 514.1 518.6 523.3 527.9 532.6 537.3

(404.7)

H

(–44.93°C)

Absolute Pressure, kPa

– 1.9214 1.9385 1.9553

(1.9058)

S

2.1936 2.2071 2.2205 2.2337 2.2469 2.2600 2.2730 2.2858 2.2986 2.3113 2.3240 2.3365 2.3489 2.3613

(1.9215)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.1342 0.1379 0.1415

(0.1318)

V

0.2392 0.2432 0.2472 0.2511 0.2551 0.2590 0.2629 0.2669 0.2708 0.2747 0.2786 0.2825 0.2864 0.2903

(0.1650)

V

– 410.6 414.8 418.9

(407.9)

H

(–38.26°C)

190.0

478.4 482.7 487.1 491.5 495.9 500.4 504.9 509.4 514.0 518.5 523.2 527.8 532.5 537.2

(405.5)

H

(–43.46°C)

150.0

– 1.9139 1.9311 1.9480

(1.9024)

S

2.1853 2.1988 2.2123 2.2256 2.2388 2.2518 2.2648 2.2777 2.2905 2.3032 2.3159 2.3284 2.3409 2.3533

(1.9172)

S

–40 –35 –30 –25

Temp. °C

45 50 55 60 65 70 75 80 85 90 95 100 105 110

Temp. °C

776 Appendix 2

–20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

0.1737 0.1778 0.1818 0.1857 0.1897 0.1936 0.1974 0.2013 0.2051 0.2089 0.2127 0.2165 0.2203 0.2240 0.2278 0.2315 0.2352 0.2389 0.2426 0.2463 0.2500 0.2537 0.2574 0.2610 0.2647 0.2684 0.2720 –

424.0 428.1 432.2 436.2 440.3 444.5 448.6 452.8 456.9 461.2 465.4 469.7 473.9 478.3 482.6 487.0 491.4 495.8 500.3 504.8 509.3 513.9 518.5 523.1 527.7 532.4 537.1 –

1.9871 2.0030 2.0186 2.0340 2.0492 2.0641 2.0789 2.0934 2.1078 2.1221 2.1362 2.1501 2.1639 2.1776 2.1911 2.2046 2.2179 2.2311 2.2442 2.2572 2.2701 2.2829 2.2957 2.3083 2.3209 2.3333 2.3457 –

0.1630 0.1669 0.1707 0.1744 0.1781 0.1818 0.1855 0.1892 0.1928 0.1964 0.2000 0.2035 0.2071 0.2106 0.2141 0.2177 0.2212 0.2247 0.2282 0.2317 0.2351 0.2386 0.2421 0.2455 0.2490 0.2524 0.2559 –

423.7 427.8 431.9 436.0 440.1 444.2 448.4 452.6 456.8 461.0 465.2 469.5 473.8 478.1 482.5 486.9 491.3 495.7 500.2 504.7 509.2 513.8 518.4 523.0 527.6 532.3 537.0 –

1.9792 1.9952 2.0109 2.0263 2.0416 2.0566 2.0714 2.0860 2.1004 2.1147 2.1288 2.1428 2.1566 2.1703 2.1839 2.1973 2.2107 2.2239 2.2370 2.2501 2.2630 2.2758 2.2885 2.3012 2.3137 2.3262 2.3386 –

0.1535 0.1572 0.1608 0.1644 0.1679 0.1714 0.1749 0.1784 0.1818 0.1852 0.1886 0.1920 0.1954 0.1987 0.2020 0.2054 0.2087 0.2120 0.2153 0.2186 0.2219 0.2252 0.2285 0.2317 0.2350 0.2383 0.2415 0.2448

423.4 427.5 431.6 435.7 439.9 444.0 448.2 452.4 456.6 460.8 465.1 469.3 473.6 478.0 482.3 486.7 491.1 495.6 500.1 504.6 509.1 513.7 518.3 522.9 527.5 532.2 537.0 541.7

1.9716 1.9877 2.0035 2.0190 2.0343 2.0494 2.0642 2.0789 2.0934 2.1077 2.1219 2.1359 2.1497 2.1634 2.1770 2.1905 2.2039 2.2171 2.2303 2.2433 2.2562 2.2691 2.2818 2.2945 2.3070 2.3195 2.3319 2.3442

0.1450 0.1485 0.1520 0.1554 0.1588 0.1621 0.1654 0.1687 0.1720 0.1752 0.1784 0.1817 0.1849 0.1880 0.1912 0.1944 0.1975 0.2007 0.2038 0.2070 0.2101 0.2132 0.2163 0.2194 0.2225 0.2256 0.2287 0.2318

423.0 427.2 431.3 435.5 439.6 443.8 448.0 452.2 456.4 460.6 464.9 469.2 473.5 477.8 482.2 486.6 491.0 495.5 499.9 504.5 509.0 513.6 518.2 522.8 527.5 532.2 536.9 541.6

1.9645 1.9806 1.9965 2.0121 2.0274 2.0426 2.0575 2.0722 2.0867 2.1011 2.1152 2.1293 2.1432 2.1569 2.1705 2.1840 2.1974 2.2107 2.2238 2.2369 2.2498 2.2627 2.2754 2.2881 2.3007 2.3132 2.3256 2.3379 (continued)

–20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

Appendix 2 777

–35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Temp. °C

0.1270 0.1306 0.1340 0.1374 0.1407 0.1440 0.1473 0.1505 0.1537 0.1569 0.1600 0.1631 0.1662 0.1693 0.1724 0.1754 0.1785 0.1815 0.1845 0.1875 0.1905 0.1935 0.1965 0.1994 0.2024

(0.1255)

V

410.2 414.4 418.5 422.7 426.9 431.0 435.2 439.4 443.5 447.7 452.0 456.2 460.4 464.7 469.0 473.3 477.7 482.1 486.5 490.9 495.3 499.8 504.3 508.9 513.5

(408.4)

1.9066 1.9240 1.9410 1.9576 1.9738 1.9898 2.0055 2.0209 2.0361 2.0510 2.0658 2.0803 2.0947 2.1090 2.1230 2.1369 2.1507 2.1644 2.1779 2.1913 2.2045 2.2177 2.2308 2.2437 2.2566

(1.8992)

S 0.1205 0.1239 0.1272 0.1305 0.1337 0.1368 0.1400 0.1431 0.1461 0.1491 0.1521 0.1551 0.1581 0.1610 0.1640 0.1669 0.1698 0.1727 0.1755 0.1784 0.1813 0.1841 0.1870 0.1898 0.1926

(0.1198)

V 409.8 414.0 418.2 422.4 426.6 430.7 434.9 439.1 443.3 447.5 451.8 456.0 460.3 464.6 468.9 473.2 477.5 481.9 486.3 490.8 495.2 499.7 504.2 508.8 513.4

(409.0)

H

(–35.97°C)

(–37.09°C)

H

210.0

200.0

1.8997 1.9172 1.9343 1.9510 1.9673 1.9834 1.9991 2.0146 2.0298 2.0449 2.0597 2.0743 2.0887 2.1030 2.1170 2.1310 2.1448 2.1585 2.1720 2.1854 2.1987 2.2119 2.2250 2.2379 2.2508

(1.8962)

S – 0.1178 0.1210 0.1242 0.1273 0.1303 0.1333 0.1363 0.1392 0.1421 0.1450 0.1479 0.1507 0.1535 0.1563 0.1591 0.1619 0.1647 0.1674 0.1701 0.1729 0.1756 0.1783 0.1810 0.1837

(0.1146)

V

220.0

– 413.6 417.8 422.0 426.3 430.5 434.7 438.9 443.1 447.3 451.6 455.8 460.1 464.4 468.7 473.0 477.4 481.8 486.2 490.6 495.1 499.6 504.1 508.7 513.3

(409.4)

H

(–34.89°C)

Absolute Pressure, kPa

– 1.9106 1.9278 1.9446 1.9611 1.9772 1.9930 2.0086 2.0239 2.0390 2.0538 2.0685 2.0829 2.0972 2.1113 2.1253 2.1391 2.1528 2.1664 2.1798 2.1931 2.2063 2.2194 2.2324 2.2453

(1.8933)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.1123 0.1154 0.1184 0.1214 0.1243 0.1272 0.1301 0.1329 0.1357 0.1385 0.1412 0.1439 0.1466 0.1493 0.1520 0.1547 0.1573 0.1600 0.1626 0.1652 0.1678 0.1704 0.1730 0.1756

(0.1099)

V – 413.2 417.5 421.7 425.9 430.2 434.4 438.6 442.8 447.1 451.3 455.6 459.9 464.2 468.5 472.9 477.3 481.7 486.1 490.5 495.0 499.5 504.0 508.6 513.2

(409.9)

H

(–33.85°C)

230.0

– 1.9043 1.9216 1.9385 1.9551 1.9713 1.9872 2.0028 2.0182 2.0333 2.0482 2.0629 2.0774 2.0917 2.1058 2.1198 2.1337 2.1474 2.1610 2.1744 2.1878 2.2010 2.2141 2.2271 2.2400

(1.8906)

S –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Temp. °C

778 Appendix 2

–30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60

Temp. °C

90 95 100 105 110 115 120

0.1072 0.1102 0.1132 0.1160 0.1189 0.1216 0.1244 0.1271 0.1298 0.1325 0.1351 0.1377 0.1404 0.1429 0.1455 0.1481 0.1506 0.1532 0.1557

(0.1055)

V

0.2054 0.2083 0.2113 0.2142 0.2171 0.2201 –

412.8 417.1 421.4 425.6 429.9 434.1 438.4 442.6 446.9 451.1 455.4 459.7 464.0 468.4 472.7 477.1 481.5 485.9 490.4

(410.4)

H

1.8981 1.9156 1.9326 1.9493 1.9656 1.9815 1.9972 2.0126 2.0278 2.0428 2.0575 2.0720 2.0864 2.1006 2.1146 2.1285 2.1422 2.1558 2.1693

(1.8880)

S

0.1026 0.1055 0.1083 0.1111 0.1138 0.1165 0.1192 0.1218 0.1244 0.1270 0.1295 0.1321 0.1346 0.1371 0.1395 0.1420 0.1445 0.1469 0.1493

(0.1015)

V

412.4 416.7 421.0 425.3 429.6 433.9 438.1 442.4 446.7 450.9 455.2 459.5 463.9 468.2 472.6 477.0 481.4 485.8 490.3

(410.8)

H

(–31.87°C)

518.0 522.6 527.3 532.0 536.7 541.5 –

(–32.84°C)

0.1955 0.1983 0.2011 0.2039 0.2067 0.2095 – 250.0

2.2694 2.2820 2.2946 2.3071 2.3195 2.3319 –

240.0

518.1 522.7 527.4 532.1 536.8 541.6 –

1.8922 1.9098 1.9269 1.9437 1.9601 1.9761 1.9919 2.0073 2.0226 2.0376 2.0523 2.0669 2.0813 2.0955 2.1096 2.1235 2.1372 2.1509 2.1643

(1.8854)

S

2.2636 2.2763 2.2889 2.3014 2.3138 2.3261 –

0.0983 0.1011 0.1038 0.1065 0.1092 0.1118 0.1144 0.1169 0.1194 0.1219 0.1244 0.1268 0.1292 0.1316 0.1340 0.1364 0.1388 0.1411 0.1435

(0.0977)

V

0.1864 0.1891 0.1918 0.1945 0.1972 0.1999 0.2026

412.0 416.4 420.7 425.0 429.3 433.6 437.9 442.1 446.4 450.7 455.0 459.4 463.7 468.1 472.4 476.8 481.2 485.7 490.1

(411.2)

H

(–30.92°C)

260.0

517.9 522.5 527.2 531.9 536.6 541.4 546.2

1.8864 1.9041 1.9214 1.9382 1.9547 1.9708 1.9867 2.0022 2.0175 2.0325 2.0473 2.0620 2.0764 2.0906 2.1047 2.1186 2.1324 2.1461 2.1596

(1.8830)

S

2.2581 2.2708 2.2834 2.2959 2.3083 2.3207 2.3329

0.0943 0.0970 0.0997 0.1023 0.1049 0.1074 0.1099 0.1123 0.1148 0.1172 0.1196 0.1219 0.1243 0.1266 0.1289 0.1312 0.1335 0.1358 0.1380

(0.0943)

V

0.1782 0.1808 0.1834 0.1860 0.1885 0.1911 0.1936

411.6 416.0 420.4 424.7 429.0 433.3 437.6 441.9 446.2 450.5 454.8 459.2 463.5 467.9 472.3 476.7 481.1 485.6 490.0

(411.6)

H

(–30.01°C)

270.0

517.8 522.4 527.1 531.8 536.6 541.3 546.1

1.8807 1.8986 1.9160 1.9330 1.9495 1.9657 1.9816 1.9972 2.0126 2.0277 2.0425 2.0572 2.0716 2.0859 2.1000 2.1140 2.1278 2.1415 2.1550

(1.8807)

S

2.2528 2.2655 2.2781 2.2906 2.3031 2.3154 2.3277

–30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 (continued)

Temp. °C

90 95 100 105 110 115 120

Appendix 2 779

(0.0910)

0.0932 0.0958 0.0984

–25 –20 –15

V

0.1582 0.1607 0.1632 0.1657 0.1682 0.1707 0.1732 0.1756 0.1781 0.1806 0.1830 0.1855

(0.1055)

Temp. °C

65 70 75 80 85 90 95 100 105 110 115 120

Temp. °C

V

415.6 420.0 424.4

(412.0)

H

1.8933 1.9108 1.9279

(1.8785)

S

0.0897 0.0922 0.0947

(0.0880)

V

415.2 419.7 424.0

(412.4)

H

(–28.25°C)

494.8 499.3 503.8 508.4 513.0 517.6 522.3 526.9 531.6 536.4 541.2 546.0

(410.8)

(–29.12°C)

0.1517 0.1542 0.1566 0.1590 0.1614 0.1638 0.1661 0.1685 0.1709 0.1733 0.1756 0.1780

(0.1015)

H

290.0

2.1826 2.1959 2.2090 2.2220 2.2349 2.2477 2.2604 2.2731 2.2856 2.2980 2.3104 2.3227

(1.8880)

V

280.0

494.9 499.4 503.9 508.5 513.1 517.7 522.3 527.0 531.7 536.5 541.2 546.0

(410.4)

S

(–31.87°C)

(–32.84°C)

H

250.0

240.0

1.8881 1.9057 1.9229

(1.8764)

S

2.1777 2.1910 2.2041 2.2171 2.2300 2.2429 2.2556 2.2682 2.2808 2.2932 2.3056 2.3179

(1.8854)

S

0.0864 0.0889 0.0913

(0.0852)

V

0.1458 0.1481 0.1504 0.1527 0.1551 0.1574 0.1596 0.1619 0.1642 0.1665 0.1688 0.1711

(0.0977)

V

260.0

414.9 419.3 423.7

(412.7)

H

(–27.40°C)

300.0

494.6 499.2 503.7 508.3 512.9 517.5 522.2 526.8 531.6 536.3 541.1 545.9

(411.2)

H

(–30.92°C)

Absolute Pressure, kPa

1.8830 1.9008 1.9180

(1.8743)

S

2.1730 2.1862 2.1994 2.2124 2.2253 2.2382 2.2509 2.2636 2.2761 2.2886 2.3010 2.3133

(1.8830)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

0.0833 0.0857 0.0881

(0.0825)

V

0.1403 0.1425 0.1448 0.1470 0.1492 0.1514 0.1536 0.1558 0.1581 0.1603 0.1624 0.1646

(0.0943)

V

414.5 419.0 423.4

(413.1)

H

(–26.58°C)

310.0

494.5 499.0 503.6 508.2 512.8 517.4 522.1 526.8 531.5 536.2 541.0 545.8

(411.6)

H

(–30.01°C)

270.0

1.8781 1.8959 1.9133

(1.8723)

S

2.1684 2.1817 2.1948 2.2079 2.2208 2.2337 2.2464 2.2591 2.2716 2.2841 2.2965 2.3088

(1.8807)

S

–25 –20 –15

Temp. °C

65 70 75 80 85 90 95 100 105 110 115 120

Temp. °C

780 Appendix 2

–10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

0.1009 0.1033 0.1057 0.1081 0.1105 0.1128 0.1151 0.1174 0.1197 0.1219 0.1242 0.1264 0.1286 0.1308 0.1330 0.1351 0.1373 0.1395 0.1416 0.1438 0.1459 0.1481 0.1502 0.1523 0.1544 0.1566 0.1587 0.1608

428.7 433.0 437.4 441.7 446.0 450.3 454.6 459.0 463.4 467.7 472.1 476.5 481.0 485.4 489.9 494.4 498.9 503.5 508.1 512.7 517.3 522.0 526.7 531.4 536.1 540.9 545.7 550.6

1.9445 1.9608 1.9768 1.9924 2.0078 2.0229 2.0379 2.0526 2.0670 2.0814 2.0955 2.1095 2.1233 2.1370 2.1505 2.1640 2.1772 2.1904 2.2035 2.2164 2.2293 2.2421 2.2547 2.2673 2.2798 2.2922 2.3045 2.3167

0.0971 0.0995 0.1019 0.1042 0.1065 0.1087 0.1110 0.1132 0.1154 0.1176 0.1197 0.1219 0.1240 0.1261 0.1283 0.1304 0.1325 0.1346 0.1366 0.1387 0.1408 0.1429 0.1449 0.1470 0.1490 0.1511 0.1531 0.1552

428.4 432.8 437.1 441.4 445.8 450.1 454.5 458.8 463.2 467.6 472.0 476.4 480.8 485.3 489.8 494.3 498.8 503.4 508.0 512.6 517.2 521.9 526.6 531.3 536.1 540.8 545.7 550.5

1.9396 1.9560 1.9720 1.9877 2.0032 2.0184 2.0333 2.0481 2.0626 2.0769 2.0911 2.1051 2.1190 2.1327 2.1462 2.1597 2.1730 2.1862 2.1993 2.2122 2.2251 2.2379 2.2505 2.2631 2.2756 2.2880 2.3003 2.3126

0.0937 0.0960 0.0983 0.1005 0.1027 0.1049 0.1071 0.1093 0.1114 0.1135 0.1156 0.1177 0.1198 0.1218 0.1239 0.1259 0.1280 0.1300 0.1320 0.1340 0.1360 0.1380 0.1400 0.1420 0.1440 0.1460 0.1480 0.1499

428.1 432.5 436.8 441.2 445.5 449.9 454.3 458.6 463.0 467.4 471.8 476.2 480.7 485.2 489.7 494.2 498.7 503.3 507.9 512.5 517.1 521.8 526.5 531.2 536.0 540.8 545.6 550.4

1.9349 1.9513 1.9674 1.9832 1.9987 2.0140 2.0289 2.0437 2.0583 2.0727 2.0869 2.1009 2.1148 2.1285 2.1421 2.1555 2.1689 2.1821 2.1952 2.2081 2.2210 2.2338 2.2465 2.2591 2.2716 2.2840 2.2963 2.3086

0.0904 0.0927 0.0949 0.0971 0.0992 0.1014 0.1035 0.1056 0.1077 0.1097 0.1117 0.1138 0.1158 0.1178 0.1198 0.1218 0.1237 0.1257 0.1276 0.1296 0.1315 0.1335 0.1354 0.1373 0.1393 0.1412 0.1431 0.1450

427.8 432.2 436.6 441.0 445.3 449.7 454.1 458.4 462.8 467.2 471.7 476.1 480.6 485.0 489.5 494.0 498.6 503.2 507.8 512.4 517.0 521.7 526.4 531.1 535.9 540.7 545.5 550.4

1.9302 1.9468 1.9629 1.9788 1.9944 2.0096 2.0247 2.0395 2.0541 2.0685 2.0827 2.0968 2.1107 2.1244 2.1381 2.1515 2.1649 2.1781 2.1912 2.2042 2.2171 2.2299 2.2426 2.2552 2.2677 2.2801 2.2924 2.3047 (continued)

–10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

Appendix 2 781

(0.0800)

0.0804 0.0828 0.0851 0.0873 0.0896 0.0917 0.0939 0.0960 0.0980 0.1001 0.1021 0.1041 0.1061 0.1081 0.1101 0.1120 0.1140 0.1159 0.1178 0.1198 0.1217 0.1236 0.1255 0.1273

Temp. °C

–25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

V

414.1 418.6 423.1 427.5 431.9 436.3 440.7 445.1 449.5 453.9 458.3 462.7 467.1 471.5 475.9 480.4 484.9 489.4 493.9 498.5 503.1 507.7 512.3 516.9

(413.4)

1.8732 1.8912 1.9087 1.9257 1.9423 1.9586 1.9745 1.9901 2.0055 2.0205 2.0354 2.0500 2.0645 2.0787 2.0928 2.1067 2.1205 2.1341 2.1476 2.1610 2.1742 2.1873 2.2003 2.2132

(1.8703)

S

– 0.0800 0.0823 0.0845 0.0866 0.0888 0.0908 0.0929 0.0949 0.0969 0.0989 0.1009 0.1028 0.1047 0.1066 0.1085 0.1104 0.1123 0.1142 0.1160 0.1179 0.1197 0.1216 0.1234

(0.0777)

V

– 418.3 422.8 427.2 431.7 436.1 440.5 444.9 449.3 453.7 458.1 462.5 466.9 471.3 475.8 480.3 484.8 489.3 493.8 498.4 502.9 507.5 512.2 516.8

(413.7)

H

(–24.99°C)

(–25.78°C)

H

330.0

320.0

– 1.8866 1.9042 1.9213 1.9380 1.9543 1.9703 1.9860 2.0014 2.0165 2.0314 2.0461 2.0606 2.0749 2.0890 2.1029 2.1167 2.1303 2.1438 2.1572 2.1705 2.1836 2.1966 2.2095

(1.8685)

S

– 0.0774 0.0796 0.0818 0.0839 0.0860 0.0880 0.0900 0.0920 0.0939 0.0958 0.0978 0.0996 0.1015 0.1034 0.1052 0.1071 0.1089 0.1107 0.1125 0.1143 0.1161 0.1179 0.1197

(0.0755)

V

340.0

– 417.9 422.4 426.9 431.4 435.8 440.2 444.6 449.1 453.5 457.9 462.3 466.7 471.2 475.7 480.1 484.6 489.1 493.7 498.3 502.8 507.4 512.1 516.7

(414.0)

H

(–24.23°C)

Absolute Pressure, kPa

– 1.8821 1.8998 1.9170 1.9338 1.9502 1.9662 1.9820 1.9974 2.0126 2.0275 2.0422 2.0567 2.0711 2.0852 2.0992 2.1130 2.1266 2.1402 2.1536 2.1668 2.1800 2.1930 2.2059

(1.8667)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.0750 0.0771 0.0792 0.0813 0.0833 0.0853 0.0873 0.0892 0.0911 0.0930 0.0948 0.0967 0.0985 0.1003 0.1021 0.1039 0.1057 0.1075 0.1092 0.1110 0.1127 0.1145 0.1162

(0.0734)

V

– 417.5 422.1 426.6 431.1 435.5 440.0 444.4 448.8 453.3 457.7 462.1 466.6 471.0 475.5 480.0 484.5 489.0 493.6 498.1 502.7 507.3 512.0 516.6

(414.3)

H

(–23.48°C)

350.0

– 1.8776 1.8955 1.9128 1.9297 1.9461 1.9622 1.9780 1.9935 2.0088 2.0237 2.0385 2.0530 2.0674 2.0815 2.0955 2.1094 2.1230 2.1366 2.1500 2.1633 2.1764 2.1895 2.2024

(1.8649)

S

–25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Temp. °C

782 Appendix 2

(0.0714)

0.0726 0.0748 0.0768 0.0788 0.0808 0.0828 0.0847 0.0866 0.0884 0.0903 0.0921 0.0939 0.0957 0.0974 0.0992 0.1009 0.1027 0.1044

–20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65

V

0.1292 0.1311 0.1330 0.1349 0.1367 0.1386 0.1404 0.1379

Temp. °C

95 100 105 110 115 120 125 130

417.2 421.8 426.3 430.8 435.3 439.7 444.2 448.6 453.1 457.5 462.0 466.4 470.9 475.4 479.9 484.4 488.9 493.4

(414.6)

H

1.8733 1.8912 1.9087 1.9256 1.9422 1.9583 1.9742 1.9897 2.0050 2.0200 2.0348 2.0494 2.0638 2.0780 2.0920 2.1058 2.1195 2.1331

(1.8632)

S

0.0704 0.0725 0.0745 0.0765 0.0785 0.0804 0.0822 0.0841 0.0859 0.0877 0.0895 0.0912 0.0930 0.0947 0.0964 0.0981 0.0998 0.1015

(0.0696)

V

416.8 421.4 426.0 430.5 435.0 439.5 444.0 448.4 452.9 457.3 461.8 466.2 470.7 475.2 479.7 484.2 488.8 493.3

(414.9)

H

(–22.03°C)

521.5 526.2 531.0 535.7 540.5 545.4 550.2 555.0

(–22.75°C)

0.1252 0.1271 0.1289 0.1307 0.1325 0.1343 0.1361 0.1338 370.0

2.2260 2.2387 2.2514 2.2639 2.2763 2.2886 2.3009 2.3094

360.0

521.6 526.3 531.1 535.8 540.6 545.4 550.3 555.1

1.8690 1.8871 1.9046 1.9217 1.9383 1.9545 1.9704 1.9860 2.0014 2.0164 2.0313 2.0459 2.0603 2.0745 2.0885 2.1024 2.1161 2.1297

(1.8615)

S

2.2223 2.2351 2.2477 2.2602 2.2726 2.2850 2.2972 2.3059

0.0683 0.0704 0.0724 0.0743 0.0762 0.0781 0.0799 0.0817 0.0835 0.0853 0.0870 0.0887 0.0904 0.0921 0.0938 0.0954 0.0971 0.0987

(0.0678)

V

0.1215 0.1233 0.1250 0.1268 0.1285 0.1303 0.1321 0.1299

416.4 421.1 425.7 430.2 434.8 439.3 443.7 448.2 452.7 457.1 461.6 466.1 470.6 475.1 479.6 484.1 488.6 493.2

(415.2)

H

(–21.33°C)

380.0

521.4 526.1 530.9 535.7 540.5 545.3 550.1 554.9

1.8648 1.8830 1.9006 1.9178 1.9345 1.9508 1.9668 1.9824 1.9978 2.0129 2.0278 2.0424 2.0568 2.0711 2.0851 2.0990 2.1128 2.1264

(1.8599)

S

2.2187 2.2315 2.2441 2.2566 2.2691 2.2814 2.2937 2.3024

0.0664 0.0684 0.0703 0.0722 0.0741 0.0759 0.0777 0.0795 0.0812 0.0829 0.0846 0.0863 0.0880 0.0896 0.0913 0.0929 0.0945 0.0961

(0.0661)

V

0.1179 0.1197 0.1214 0.1231 0.1248 0.1265 0.1282 –

416.1 420.8 425.4 430.0 434.5 439.0 443.5 448.0 452.5 457.0 461.4 465.9 470.4 474.9 479.4 484.0 488.5 493.1

(415.5)

H

(–20.64°C)

390.0

521.3 526.1 530.8 535.6 540.4 545.2 550.1 –

1.8607 1.8790 1.8968 1.9140 1.9308 1.9472 1.9632 1.9789 1.9943 2.0094 2.0243 2.0390 2.0535 2.0678 2.0818 2.0958 2.1095 2.1231

(1.8583)

S

2.2152 2.2280 2.2406 2.2531 2.2656 2.2780 2.2902 –

–20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 (continued)

Temp. °C

95 100 105 110 115 120 125 130

Appendix 2 783

0.1061 0.1078 0.1095 0.1112 0.1129 0.1146 0.1163 0.1179 0.1196 0.1213 0.1229 0.1246 0.1263

70 75 80 85 90 95 100 105 110 115 120 125 130

(0.0645)

0.0665 0.0684 0.0703

Temp. °C

–15 –10 –5

V

(0.0714)

Temp. °C

V

420.4 425.1 429.7

(415.7)

1.8751 1.8929 1.9103

(1.8568) 0.0621 0.0639 0.0657

(0.0608)

V

419.6 424.3 428.9

(416.4)

H

(–18.34°C)

H

S

497.9 502.5 507.1 511.8 516.5 521.2 525.9 530.6 535.4 540.2 545.0 549.9 554.8

(414.9)

(–19.97°C)

0.1032 0.1048 0.1065 0.1081 0.1098 0.1114 0.1131 0.1147 0.1163 0.1179 0.1196 0.1212 0.1228

(0.0696)

H

425.0

2.1465 2.1598 2.1730 2.1860 2.1990 2.2118 2.2246 2.2372 2.2498 2.2622 2.2746 2.2869 2.2991

(1.8632)

V

400.0

498.0 502.6 507.2 511.9 516.5 521.2 526.0 530.7 535.5 540.3 545.1 550.0 554.9

(414.6)

S

(–22.03°C)

(–22.75°C)

H

370.0

360.0

1.8655 1.8837 1.9012

(1.8531)

S

2.1431 2.1564 2.1696 2.1827 2.1957 2.2085 2.2213 2.2339 2.2465 2.2589 2.2713 2.2836 2.2958

(1.8615)

S

0.0582 0.0599 0.0617

(0.0575)

V

0.1004 0.1020 0.1036 0.1052 0.1068 0.1084 0.1100 0.1116 0.1132 0.1148 0.1164 0.1179 0.1195

(0.0678)

V

380.0

418.7 423.5 428.2

(417.0)

H

(–16.78°C)

450.0

497.8 502.4 507.0 511.7 516.4 521.1 525.8 530.5 535.3 540.1 545.0 549.8 554.7

(415.2)

H

(–21.33°C)

Absolute Pressure, kPa

1.8563 1.8747 1.8925

(1.8496)

S

2.1398 2.1532 2.1664 2.1794 2.1924 2.2053 2.2180 2.2307 2.2433 2.2557 2.2681 2.2804 2.2926

(1.8599)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

0.0546 0.0564 0.0580

(0.0545)

V

0.0977 0.0993 0.1009 0.1024 0.1040 0.1056 0.1071 0.1087 0.1102 0.1118 0.1133 0.1149 0.1164

(0.0661)

V

417.8 422.7 427.5

(417.5)

H

(–15.29°C)

475.0

497.7 502.3 506.9 511.6 516.3 521.0 525.7 530.5 535.2 540.1 544.9 549.8 554.7

(415.5)

H

(–20.64°C)

390.0

1.8474 1.8661 1.8842

(1.8464)

S

2.1366 2.1500 2.1632 2.1763 2.1892 2.2021 2.2149 2.2276 2.2401 2.2526 2.2650 2.2773 2.2895

(1.8583)

S

–15 –10 –5

Temp. °C

70 75 80 85 90 95 100 105 110 115 120 125 130

Temp. °C

784 Appendix 2

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135

0.0721 0.0739 0.0756 0.0774 0.0791 0.0807 0.0824 0.0841 0.0857 0.0873 0.0889 0.0905 0.0921 0.0936 0.0952 0.0967 0.0983 0.0998 0.1013 0.1029 0.1044 0.1059 0.1074 0.1089 0.1104 0.1119 0.1134 0.1149

434.2 438.8 443.3 447.8 452.3 456.8 461.3 465.8 470.3 474.8 479.3 483.8 488.4 493.0 497.6 502.2 506.8 511.5 516.2 520.9 525.6 530.4 535.2 540.0 544.8 549.7 554.6 559.5

1.9271 1.9436 1.9597 1.9754 1.9909 2.0061 2.0210 2.0357 2.0502 2.0645 2.0786 2.0926 2.1064 2.1200 2.1335 2.1468 2.1601 2.1732 2.1862 2.1990 2.2118 2.2245 2.2371 2.2496 2.2620 2.2743 2.2865 2.2986

0.0675 0.0692 0.0708 0.0725 0.0741 0.0757 0.0773 0.0789 0.0804 0.0819 0.0834 0.0849 0.0864 0.0879 0.0894 0.0909 0.0923 0.0938 0.0952 0.0967 0.0981 0.0995 0.1010 0.1024 0.1038 0.1052 0.1066 0.1080

433.6 438.1 442.7 447.2 451.8 456.3 460.8 465.3 469.9 474.4 478.9 483.5 488.1 492.7 497.3 501.9 506.6 511.2 515.9 520.6 525.4 530.2 535.0 539.8 544.6 549.5 554.4 559.3

1.9183 1.9349 1.9512 1.9670 1.9826 1.9979 2.0130 2.0278 2.0423 2.0567 2.0709 2.0849 2.0987 2.1124 2.1259 2.1393 2.1526 2.1657 2.1787 2.1916 2.2044 2.2171 2.2297 2.2422 2.2547 2.2670 2.2792 2.2914

0.0633 0.0650 0.0666 0.0682 0.0697 0.0712 0.0727 0.0742 0.0757 0.0772 0.0786 0.0800 0.0814 0.0829 0.0843 0.0856 0.0870 0.0884 0.0898 0.0912 0.0925 0.0939 0.0952 0.0966 0.0979 0.0993 0.1006 0.1019

432.9 437.5 442.1 446.7 451.3 455.8 460.4 464.9 469.5 474.0 478.6 483.2 487.8 492.4 497.0 501.6 506.3 511.0 515.7 520.4 525.2 529.9 534.7 539.6 544.4 549.3 554.2 559.2

1.9098 1.9266 1.9430 1.9591 1.9748 1.9902 2.0053 2.0202 2.0348 2.0493 2.0635 2.0776 2.0915 2.1052 2.1188 2.1322 2.1455 2.1587 2.1717 2.1846 2.1975 2.2102 2.2228 2.2353 2.2478 2.2601 2.2724 2.2845

0.0597 0.0612 0.0628 0.0643 0.0658 0.0672 0.0687 0.0701 0.0715 0.0729 0.0743 0.0756 0.0770 0.0783 0.0797 0.0810 0.0823 0.0836 0.0849 0.0862 0.0875 0.0888 0.0901 0.0914 0.0926 0.0939 0.0952 0.0965

432.2 436.9 441.5 446.1 450.7 455.3 459.9 464.5 469.1 473.6 478.2 482.8 487.4 492.1 496.7 501.4 506.0 510.7 515.4 520.2 524.9 529.7 534.5 539.4 544.2 549.1 554.0 559.0

1.9017 1.9187 1.9352 1.9514 1.9672 1.9828 1.9980 2.0130 2.0277 2.0422 2.0565 2.0706 2.0846 2.0983 2.1119 2.1254 2.1387 2.1519 2.1650 2.1780 2.1908 2.2036 2.2162 2.2288 2.2412 2.2536 2.2658 2.2780 (continued)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135

Appendix 2 785

(0.0519)

0.0532 0.0548 0.0563 0.0579 0.0593 0.0608 0.0622 0.0636 0.0650 0.0664 0.0677 0.0690 0.0704 0.0717 0.0730 0.0742 0.0755 0.0768 0.0780 0.0793 0.0805 0.0818 0.0830 0.0842

Temp. °C

–10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

V

421.8 426.7 431.5 436.2 440.9 445.6 450.2 454.9 459.5 464.1 468.7 473.3 477.9 482.5 487.1 491.8 496.4 501.1 505.8 510.5 515.2 519.9 524.7 529.5

(418.0)

1.8578 1.8761 1.8938 1.9110 1.9277 1.9441 1.9600 1.9757 1.9910 2.0060 2.0209 2.0354 2.0498 2.0640 2.0780 2.0918 2.1054 2.1190 2.1323 2.1456 2.1587 2.1717 2.1845 2.1973

(1.8432)

S

0.0502 0.0518 0.0533 0.0548 0.0562 0.0576 0.0590 0.0604 0.0617 0.0630 0.0643 0.0656 0.0668 0.0681 0.0693 0.0705 0.0718 0.0730 0.0742 0.0754 0.0766 0.0778 0.0789 0.0801

(0.0494)

V

421.0 425.9 430.8 435.6 440.3 445.0 449.7 454.4 459.0 463.6 468.3 472.9 477.5 482.1 486.8 491.4 496.1 500.8 505.5 510.2 515.0 519.7 524.5 529.3

(418.5)

H

(–12.47°C)

(–13.85°C)

H

525.0

500.0

1.8497 1.8683 1.8862 1.9036 1.9205 1.9370 1.9531 1.9688 1.9843 1.9994 2.0143 2.0290 2.0434 2.0576 2.0717 2.0855 2.0992 2.1128 2.1262 2.1394 2.1526 2.1656 2.1785 2.1913

(1.8403)

S

0.0476 0.0491 0.0506 0.0520 0.0534 0.0548 0.0561 0.0574 0.0587 0.0599 0.0612 0.0624 0.0636 0.0648 0.0660 0.0672 0.0684 0.0695 0.0707 0.0718 0.0730 0.0741 0.0752 0.0764

(0.0472)

V

550.0

420.2 425.2 430.1 434.9 439.7 444.5 449.2 453.9 458.5 463.2 467.9 472.5 477.2 481.8 486.5 491.1 495.8 500.5 505.2 510.0 514.7 519.5 524.3 529.1

(419.0)

H

(–11.14°C)

Absolute Pressure, kPa

1.8419 1.8607 1.8789 1.8965 1.9135 1.9302 1.9464 1.9623 1.9778 1.9930 2.0080 2.0227 2.0372 2.0515 2.0656 2.0795 2.0933 2.1069 2.1203 2.1336 2.1468 2.1598 2.1727 2.1855

(1.8375)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.0466 0.0481 0.0495 0.0508 0.0521 0.0534 0.0547 0.0559 0.0571 0.0583 0.0595 0.0607 0.0618 0.0630 0.0641 0.0653 0.0664 0.0675 0.0686 0.0697 0.0708 0.0719 0.0729

(0.0452)

V

– 424.4 429.4 434.3 439.1 443.9 448.7 453.4 458.1 462.8 467.4 472.1 476.8 481.5 486.1 490.8 495.5 500.2 505.0 509.7 514.5 519.2 524.0 528.9

(419.4)

H

(–9.85°C)

575.0

– 1.8533 1.8717 1.8895 1.9068 1.9236 1.9399 1.9559 1.9715 1.9869 2.0019 2.0167 2.0313 2.0456 2.0598 2.0738 2.0876 2.1012 2.1147 2.1280 2.1412 2.1543 2.1672 2.1800

(1.8347)

S

–10 –5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

Temp. °C

786 Appendix 2

(0.0433)

0.0444 0.0458 0.0471 0.0484 0.0497 0.0510 0.0522 0.0534 0.0546 0.0557 0.0569 0.0580 0.0591 0.0602 0.0613 0.0624 0.0635 0.0645

–5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

V

0.0855 0.0867 0.0879 0.0891 0.0903 0.0915 0.0927 –

Temp. °C

110 115 120 125 130 135 140 145

423.6 428.6 433.6 438.5 443.3 448.1 452.9 457.6 462.3 467.0 471.7 476.4 481.1 485.8 490.5 495.2 500.0 504.7

(419.9)

H

1.8461 1.8648 1.8828 1.9002 1.9172 1.9337 1.9498 1.9655 1.9809 1.9961 2.0110 2.0256 2.0400 2.0542 2.0682 2.0820 2.0957 2.1092

(1.8322)

S

0.0423 0.0437 0.0450 0.0463 0.0475 0.0487 0.0499 0.0511 0.0522 0.0533 0.0544 0.0555 0.0566 0.0577 0.0587 0.0598 0.0608 0.0618

(0.0416)

V

422.8 427.9 432.9 437.9 442.8 447.6 452.4 457.2 461.9 466.6 471.3 476.1 480.8 485.5 490.2 494.9 499.7 504.4

(420.3)

H

(–7.40°C)

534.1 539.0 543.9 548.8 553.7 558.6 563.6 568.3

(–8.61°C)

0.0813 0.0825 0.0836 0.0848 0.0859 0.0871 0.0882 0.0815 625.0

2.2100 2.2225 2.2350 2.2474 2.2596 2.2718 2.2840 –

600.0

534.3 539.2 544.0 548.9 553.9 558.8 563.8 –

1.8390 1.8580 1.8762 1.8938 1.9109 1.9276 1.9438 1.9597 1.9752 1.9904 2.0054 2.0201 2.0345 2.0488 2.0629 2.0767 2.0904 2.1040

(1.8297)

S

2.2040 2.2166 2.2290 2.2414 2.2537 2.2660 2.2781 2.2791

0.0404 0.0417 0.0430 0.0442 0.0454 0.0466 0.0478 0.0489 0.0500 0.0511 0.0522 0.0532 0.0543 0.0553 0.0563 0.0574 0.0584 0.0594

(0.0400)

V

0.0775 0.0786 0.0797 0.0808 0.0819 0.0830 0.0841 –

422.0 427.1 432.2 437.2 442.2 447.0 451.9 456.7 461.5 466.2 471.0 475.7 480.4 485.2 489.9 494.6 499.4 504.2

(420.6)

H

(–6.24°C)

650.0

533.9 538.8 543.7 548.6 553.5 558.5 563.5 –

1.8321 1.8513 1.8698 1.8876 1.9049 1.9217 1.9380 1.9540 1.9696 1.9849 2.0000 2.0147 2.0293 2.0436 2.0577 2.0716 2.0854 2.0989

(1.8273)

S

2.1983 2.2109 2.2234 2.2358 2.2481 2.2603 2.2725 –

0.0386 0.0399 0.0411 0.0424 0.0435 0.0447 0.0458 0.0469 0.0480 0.0491 0.0501 0.0511 0.0521 0.0531 0.0541 0.0551 0.0561 0.0570

(0.0385)

V

0.0740 0.0751 0.0762 0.0772 0.0783 0.0793 0.0804 –

421.1 426.4 431.5 436.6 441.6 446.5 451.4 456.2 461.0 465.8 470.6 475.3 480.1 484.8 489.6 494.3 499.1 503.9

(421.0)

H

(–5.10°C)

675.0

533.7 538.6 543.5 548.4 553.3 558.3 563.3 –

1.8253 1.8448 1.8635 1.8815 1.8990 1.9159 1.9324 1.9485 1.9642 1.9796 1.9947 2.0095 2.0241 2.0385 2.0527 2.0666 2.0804 2.0941

(1.8249)

S

2.1928 2.2054 2.2179 2.2303 2.2427 2.2549 2.2671 –

–5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 (continued)

Temp. °C

110 115 120 125 130 135 140 145

Appendix 2 787

0.0656 0.0667 0.0677 0.0688 0.0698 0.0708 0.0719 0.0729 0.0739 0.0749 0.0760 0.0770 0.0780

85 90 95 100 105 110 115 120 125 130 135 140 145

(0.0372)

0.0382 0.0394 0.0406

Temp. °C

0 5 10

V

(0.0433)

Temp. °C

V

425.6 430.8 436.0

(421.4)

H

1.8384 1.8574 1.8756

(1.8227)

S

0.0366 0.0378 0.0390

(0.0359)

V

424.8 430.1 435.3

(421.7)

H

(–2.92°C)

509.2 514.0 518.8 523.6 528.4 533.3 538.2 543.1 548.0 553.0 557.9 562.9 568.0

(420.3)

(–4.00°C)

0.0629 0.0639 0.0649 0.0659 0.0669 0.0679 0.0689 0.0699 0.0709 0.0719 0.0728 0.0738 0.0748

(0.0416)

H

725.0

2.1226 2.1358 2.1489 2.1619 2.1748 2.1875 2.2001 2.2127 2.2251 2.2375 2.2497 2.2619 2.2740

(1.8322)

V

700.0

509.4 514.2 519.0 523.8 528.6 533.5 538.4 543.3 548.2 553.1 558.1 563.1 568.1

(419.9)

S

(–7.40°C)

(–8.61°C)

H

625.0

600.0

1.8322 1.8514 1.8698

(1.8206)

S

2.1174 2.1307 2.1438 2.1568 2.1697 2.1824 2.1951 2.2076 2.2201 2.2325 2.2447 2.2569 2.2690

(1.8297)

S

0.0351 0.0363 0.0375

(0.0347)

V

0.0603 0.0613 0.0623 0.0633 0.0642 0.0652 0.0662 0.0671 0.0681 0.0690 0.0700 0.0709 0.0718

(0.0400)

V

Absolute Pressure, kPa

424.1 429.4 434.6

(422.0)

H

(–1.88°C)

750.0

508.9 513.7 518.5 523.4 528.2 533.1 538.0 542.9 547.8 552.8 557.8 562.8 567.8

(420.6)

H

(–6.24°C)

650.0

1.8260 1.8454 1.8641

(1.8185)

S

2.1124 2.1257 2.1388 2.1518 2.1647 2.1775 2.1902 2.2028 2.2153 2.2277 2.2399 2.2521 2.2642

(1.8273)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

0 0.0336 0.0347

(0.0325)

V

0.0580 0.0590 0.0599 0.0608 0.0618 0.0627 0.0636 0.0646 0.0655 0.0664 0.0673 0.0682 0.0691

(0.0385)

V

427.9 433.3

(422.6)

H

(0.14°C)

800.0

508.7 513.5 518.3 523.1 528.0 532.9 537.8 542.7 547.6 552.6 557.6 562.6 567.6

(421.0)

H

(–5.10°C)

675.0

1.8339 1.8530

(1.8145)

S

2.1075 2.1208 2.1340 2.1471 2.1600 2.1728 2.1855 2.1981 2.2106 2.2230 2.2353 2.2475 2.2596

(1.8249)

S

5 10

Temp. °C

85 90 95 100 105 110 115 120 125 130 135 140 145

Temp. °C

788 Appendix 2

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155

0.0418 0.0429 0.0440 0.0451 0.0461 0.0471 0.0482 0.0492 0.0501 0.0511 0.0521 0.0530 0.0540 0.0549 0.0558 0.0568 0.0577 0.0586 0.0595 0.0604 0.0613 0.0622 0.0631 0.0639 0.0648 0.0657 0.0666 0.0675 –

441.0 446.0 450.9 455.7 460.6 465.4 470.2 475.0 479.7 484.5 489.3 494.0 498.8 503.6 508.4 513.2 518.1 522.9 527.8 532.7 537.6 542.5 547.4 552.4 557.4 562.4 567.5 572.5 –

1.8932 1.9103 1.9269 1.9431 1.9589 1.9744 1.9896 2.0045 2.0192 2.0336 2.0478 2.0618 2.0757 2.0893 2.1028 2.1162 2.1294 2.1425 2.1554 2.1683 2.1810 2.1936 2.2061 2.2185 2.2308 2.2431 2.2552 2.2672 –

0.0401 0.0412 0.0423 0.0433 0.0444 0.0454 0.0464 0.0473 0.0483 0.0492 0.0502 0.0511 0.0520 0.0529 0.0538 0.0547 0.0556 0.0565 0.0573 0.0582 0.0591 0.0600 0.0608 0.0617 0.0625 0.0634 0.0642 0.0651 –

440.4 445.4 450.3 455.3 460.1 465.0 469.8 474.6 479.4 484.2 489.0 493.7 498.5 503.3 508.2 513.0 517.8 522.7 527.6 532.5 537.4 542.3 547.3 552.2 557.2 562.3 567.3 572.4 –

1.8876 1.9048 1.9216 1.9379 1.9538 1.9694 1.9847 1.9996 2.0144 2.0288 2.0431 2.0572 2.0710 2.0847 2.0983 2.1117 2.1249 2.1380 2.1510 2.1638 2.1766 2.1892 2.2017 2.2142 2.2265 2.2387 2.2509 2.2629 –

0.0386 0.0397 0.0407 0.0417 0.0427 0.0437 0.0447 0.0456 0.0465 0.0475 0.0484 0.0493 0.0502 0.0510 0.0519 0.0528 0.0536 0.0545 0.0554 0.0562 0.0570 0.0579 0.0587 0.0595 0.0604 0.0612 0.0620 0.0628 –

439.8 444.8 449.8 454.8 459.7 464.5 469.4 474.2 479.0 483.8 488.6 493.4 498.3 503.1 507.9 512.7 517.6 522.5 527.3 532.2 537.2 542.1 547.1 552.0 557.1 562.1 567.1 572.2 –

1.8821 1.8995 1.9164 1.9328 1.9488 1.9645 1.9798 1.9949 2.0097 2.0242 2.0385 2.0526 2.0666 2.0803 2.0939 2.1073 2.1205 2.1337 2.1467 2.1596 2.1723 2.1850 2.1975 2.2100 2.2223 2.2345 2.2467 2.2588 –

0.0358 0.0368 0.0378 0.0388 0.0398 0.0407 0.0416 0.0425 0.0434 0.0443 0.0451 0.0460 0.0468 0.0477 0.0485 0.0493 0.0501 0.0509 0.0517 0.0525 0.0533 0.0541 0.0549 0.0557 0.0565 0.0573 0.0580 0.0588 0.0596

438.6 443.7 448.8 453.8 458.8 463.7 468.6 473.5 478.3 483.2 488.0 492.8 497.7 502.5 507.4 512.2 517.1 522.0 526.9 531.8 536.8 541.7 546.7 551.7 556.7 561.7 566.8 571.9 577.0

1.8714 1.8891 1.9062 1.9229 1.9392 1.9550 1.9705 1.9857 2.0007 2.0153 2.0297 2.0439 2.0579 2.0718 2.0854 2.0989 2.1122 2.1254 2.1384 2.1514 2.1642 2.1768 2.1894 2.2019 2.2143 2.2266 2.2387 2.2508 2.2629 (continued)

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155

Appendix 2 789

(0.0305)

0.0312 0.0323 0.0333 0.0343 0.0353 0.0362 0.0372 0.0380 0.0389 0.0398 0.0406 0.0415 0.0423 0.0431 0.0439 0.0447 0.0455 0.0463 0.0470 0.0478 0.0486 0.0493 0.0501 0.0508

Temp. °C

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

V

426.4 431.9 437.3 442.6 447.7 452.8 457.8 462.8 467.8 472.7 477.6 482.5 487.4 492.2 497.1 502.0 506.8 511.7 516.6 521.5 526.5 531.4 536.3 541.3

(423.1)

1.8226 1.8422 1.8610 1.8791 1.8965 1.9135 1.9299 1.9460 1.9617 1.9770 1.9921 2.0068 2.0214 2.0357 2.0498 2.0637 2.0774 2.0909 2.1043 2.1175 2.1306 2.1436 2.1565 2.1692

(1.8107)

S

0.0291 0.0301 0.0311 0.0321 0.0330 0.0339 0.0348 0.0357 0.0365 0.0374 0.0382 0.0390 0.0397 0.0405 0.0413 0.0420 0.0428 0.0435 0.0443 0.0450 0.0457 0.0464 0.0472 0.0479

(0.0288)

V

424.9 430.5 436.0 441.4 446.6 451.8 456.9 461.9 467.0 471.9 476.9 481.8 486.7 491.6 496.5 501.4 506.3 511.2 516.1 521.1 526.0 531.0 535.9 540.9

(423.6)

H

(3.90°C)

(2.06°C)

H

900.0

850.0

1.8116 1.8318 1.8510 1.8694 1.8872 1.9044 1.9211 1.9373 1.9532 1.9687 1.9839 1.9988 2.0134 2.0278 2.0420 2.0560 2.0697 2.0834 2.0968 2.1101 2.1232 2.1362 2.1491 2.1619

(1.8071)

S

– 0.0282 0.0291 0.0301 0.0310 0.0319 0.0327 0.0336 0.0344 0.0352 0.0360 0.0367 0.0375 0.0382 0.0389 0.0397 0.0404 0.0411 0.0418 0.0425 0.0432 0.0439 0.0446 0.0452

(0.0273)

V

Absolute Pressure, kPa

– 429.1 434.7 440.2 445.5 450.8 455.9 461.1 466.1 471.1 476.1 481.1 486.1 491.0 495.9 500.9 505.8 510.7 515.7 520.6 525.6 530.5 535.5 540.5

(424.1)

H

(5.66°C)

950.0

– 1.8215 1.8412 1.8600 1.8781 1.8956 1.9125 1.9290 1.9450 1.9607 1.9760 1.9910 2.0058 2.0203 2.0345 2.0486 2.0625 2.0761 2.0896 2.1030 2.1162 2.1292 2.1422 2.1550

(1.8036)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.0264 0.0274 0.0283 0.0292 0.0300 0.0309 0.0317 0.0324 0.0332 0.0340 0.0347 0.0354 0.0361 0.0368 0.0375 0.0382 0.0389 0.0396 0.0402 0.0409 0.0416 0.0422 0.0429

(0.0259)

V

– 427.6 433.4 438.9 444.4 449.7 455.0 460.2 465.3 470.4 475.4 480.4 485.4 490.4 495.3 500.3 505.3 510.2 515.2 520.1 525.1 530.1 535.1 540.1

(424.5)

H

(7.36°C)

1000.0

– 1.8115 1.8316 1.8508 1.8693 1.8870 1.9042 1.9209 1.9371 1.9529 1.9684 1.9836 1.9984 2.0130 2.0274 2.0415 2.0555 2.0692 2.0828 2.0962 2.1094 2.1225 2.1355 2.1484

(1.8004)

S

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Temp. °C

790 Appendix 2

(0.0234)

0.0243 0.0251 0.0260 0.0268 0.0276 0.0284 0.0291 0.0298 0.0305 0.0312 0.0319 0.0325 0.0332 0.0338 0.0345 0.0351 0.0357 0.0363

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

V

0.0516 0.0523 0.0530 0.0538 0.0545 0.0552 0.0560 0.0505

Temp. °C

125 130 135 140 145 150 155 160

430.6 436.4 442.1 447.6 453.0 458.3 463.6 468.8 473.9 479.0 484.1 489.1 494.1 499.2 504.2 509.2 514.2 519.2

(425.2)

H

1.8130 1.8331 1.8523 1.8707 1.8884 1.9055 1.9221 1.9383 1.9541 1.9695 1.9846 1.9994 2.0139 2.0282 2.0423 2.0562 2.0699 2.0834

(1.7942)

S

0.0216 0.0225 0.0233 0.0241 0.0249 0.0256 0.0263 0.0270 0.0276 0.0283 0.0289 0.0296 0.0302 0.0308 0.0314 0.0320 0.0325 0.0331

(0.0214)

V

427.6 433.8 439.7 445.4 451.0 456.5 461.8 467.1 472.4 477.6 482.7 487.8 492.9 498.0 503.1 508.1 513.2 518.2

(425.8)

H

(13.55°C)

545.9 550.9 556.0 561.1 566.1 571.3 576.4 580.9

(10.56°C)

0.0486 0.0493 0.0500 0.0507 0.0514 0.0521 0.0528 0.0479 1200.0

2.1818 2.1943 2.2067 2.2190 2.2312 2.2433 2.2554 2.2536

1100.0

546.3 551.3 556.3 561.4 566.5 571.6 576.7 581.2

1.7948 1.8159 1.8359 1.8550 1.8733 1.8909 1.9079 1.9245 1.9406 1.9563 1.9716 1.9866 2.0014 2.0159 2.0301 2.0441 2.0580 2.0716

(1.7885)

S

2.1745 2.1871 2.1995 2.2119 2.2241 2.2362 2.2483 2.2472

– 0.0203 0.0211 0.0218 0.0226 0.0233 0.0239 0.0246 0.0252 0.0258 0.0264 0.0270 0.0276 0.0282 0.0287 0.0293 0.0298 0.0304

(0.0196)

V

0.0459 0.0466 0.0472 0.0479 0.0486 0.0492 0.0499 –

– 431.0 437.2 443.1 448.9 454.5 460.0 465.5 470.8 476.1 481.3 486.5 491.7 496.9 502.0 507.1 512.2 517.3

(426.3)

H

(16.36°C)

1300.0

545.5 550.6 555.6 560.7 565.8 570.9 576.1 –

– 1.7991 1.8201 1.8399 1.8588 1.8769 1.8944 1.9113 1.9278 1.9438 1.9594 1.9746 1.9896 2.0042 2.0186 2.0328 2.0468 2.0605

(1.7831)

S

2.1677 2.1802 2.1927 2.2051 2.2173 2.2295 2.2416 –

– 0.0183 0.0191 0.0198 0.0206 0.0212 0.0219 0.0225 0.0231 0.0237 0.0243 0.0248 0.0254 0.0259 0.0265 0.0270 0.0275 0.0280

(0.0181)

V

0.0435 0.0441 0.0448 0.0454 0.0461 0.0467 0.0473 –

– 428.0 434.5 440.7 446.7 452.5 458.2 463.8 469.2 474.6 480.0 485.2 490.5 495.7 500.9 506.0 511.2 516.3

(426.7)

H

(19.01°C)

1400.0

545.2 550.2 555.3 560.4 565.5 570.6 575.8 –

– 1.7825 1.8045 1.8251 1.8447 1.8635 1.8814 1.8988 1.9156 1.9319 1.9477 1.9632 1.9784 1.9933 2.0078 2.0222 2.0362 2.0501

(1.7780)

S

2.1611 2.1737 2.1862 2.1986 2.2109 2.2231 2.2352 –

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 (continued)

Temp. °C

125 130 135 140 145 150 155 160

Appendix 2 791

0.0370 0.0376 0.0382 0.0388 0.0394 0.0399 0.0405 0.0411 0.0417 0.0423 0.0429 0.0434 0.0440 0.0375

105 110 115 120 125 130 135 140 145 150 155 160 165 170

(0.0168)

0.0174 0.0181 0.0188

Temp. °C

25 30 35

V

(0.0234)

Temp. °C

V

431.7 438.2 444.5

(427.0)

H

1.7891 1.8107 1.8310

(1.7731)

S

0.0158 0.0166 0.0173

(0.0157)

V

428.8 435.6 442.1

(427.2)

H

1600.0

523.3 528.4 533.4 538.5 543.6 548.7 553.8 559.0 564.1 569.3 574.5 579.7 584.9 589.0

(425.8)

(23.91°C)

0.0337 0.0342 0.0348 0.0354 0.0359 0.0364 0.0370 0.0375 0.0381 0.0386 0.0391 0.0397 0.0402 0.0347

(0.0214)

H

1500.0

2.0968 2.1100 2.1230 2.1360 2.1488 2.1614 2.1740 2.1864 2.1988 2.2110 2.2232 2.2352 2.2472 2.2380

(1.7942)

V

(21.52°C)

524.2 529.2 534.3 539.3 544.4 549.5 554.6 559.7 564.8 569.9 575.1 580.3 585.5 589.6

(425.2)

S

(13.55°C)

(10.56°C)

H

1200.0

1100.0

1.7736 1.7963 1.8176

(1.7684)

S

2.0850 2.0983 2.1115 2.1245 2.1374 2.1501 2.1627 2.1752 2.1876 2.1999 2.2121 2.2242 2.2362 2.2286

(1.7885)

S

– 0.0152 0.0159

(0.0146)

V

0.0309 0.0314 0.0319 0.0325 0.0330 0.0335 0.0340 0.0345 0.0350 0.0355 0.0360 0.0365 0.0370 –

(0.0196)

V

Absolute Pressure, kPa

– 432.9 439.7

(427.4)

H

(26.19°C)

1700.0

522.4 527.5 532.6 537.7 542.8 548.0 553.1 558.3 563.4 568.6 573.8 579.1 584.3 –

(426.3)

H

(16.36°C)

1300.0

– 1.7820 1.8042

(1.7639)

S

2.0741 2.0875 2.1007 2.1138 2.1268 2.1396 2.1523 2.1648 2.1773 2.1896 2.2019 2.2140 2.2261 –

(1.7831)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.0140 0.0147

(0.0137)

V

0.0285 0.0290 0.0295 0.0300 0.0305 0.0309 0.0314 0.0319 0.0324 0.0328 0.0333 0.0338 0.0342 –

(0.0181)

V

– 430.0 437.1

(427.5)

H

(28.36°C)

1800.0

521.5 526.6 531.7 536.9 542.0 547.2 552.4 557.6 562.8 568.0 573.2 578.5 583.7 –

(426.7)

H

(19.01°C)

1400.0

– 1.7676 1.7910

(1.7595)

S

2.0638 2.0773 2.0906 2.1038 2.1168 2.1297 2.1425 2.1551 2.1676 2.1800 2.1923 2.2045 2.2166 –

(1.7780)

S

25 30 35

Temp. °C

105 110 115 120 125 130 135 140 145 150 155 160 165 170

Temp. °C

792 Appendix 2

40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180

0.0195 0.0201 0.0207 0.0213 0.0219 0.0224 0.0229 0.0235 0.0240 0.0245 0.0250 0.0255 0.0260 0.0264 0.0269 0.0274 0.0278 0.0283 0.0287 0.0292 0.0296 0.0301 0.0305 0.0310 0.0314 0.0318 0.0323 0.0327 –

450.5 456.3 462.0 467.6 473.1 478.5 483.9 489.2 494.5 499.7 505.0 510.2 515.3 520.5 525.7 530.9 536.1 541.2 546.4 551.6 556.8 562.1 567.3 572.6 577.8 583.1 588.4 593.7 –

1.8504 1.8689 1.8867 1.9038 1.9205 1.9366 1.9524 1.9678 1.9828 1.9976 2.0120 2.0263 2.0403 2.0541 2.0677 2.0811 2.0944 2.1075 2.1204 2.1332 2.1459 2.1585 2.1709 2.1833 2.1955 2.2077 2.2197 2.2316 –

0.0179 0.0185 0.0191 0.0197 0.0202 0.0208 0.0213 0.0218 0.0223 0.0228 0.0232 0.0237 0.0242 0.0246 0.0251 0.0255 0.0260 0.0264 0.0268 0.0272 0.0277 0.0281 0.0285 0.0289 0.0293 0.0297 0.0302 0.0306 –

448.3 454.4 460.2 465.9 471.5 477.1 482.5 487.9 493.3 498.6 503.9 509.1 514.4 519.6 524.8 530.0 535.2 540.5 545.7 550.9 556.1 561.4 566.6 571.9 577.2 582.5 587.8 593.2 –

1.8376 1.8567 1.8749 1.8925 1.9095 1.9260 1.9420 1.9576 1.9728 1.9878 2.0024 2.0168 2.0309 2.0448 2.0586 2.0721 2.0854 2.0986 2.1116 2.1245 2.1373 2.1499 2.1624 2.1748 2.1871 2.1992 2.2113 2.2233 –

0.0165 0.0172 0.0177 0.0183 0.0188 0.0193 0.0198 0.0203 0.0208 0.0213 0.0217 0.0222 0.0226 0.0230 0.0235 0.0239 0.0243 0.0247 0.0251 0.0255 0.0259 0.0263 0.0267 0.0271 0.0275 0.0279 0.0283 0.0287 0.0291

446.1 452.3 458.4 464.2 470.0 475.6 481.1 486.6 492.0 497.4 502.8 508.1 513.4 518.6 523.9 529.2 534.4 539.6 544.9 550.2 555.4 560.7 566.0 571.3 576.6 581.9 587.2 592.6 598.0

1.8251 1.8447 1.8635 1.8815 1.8989 1.9157 1.9320 1.9478 1.9633 1.9784 1.9932 2.0077 2.0220 2.0360 2.0499 2.0635 2.0769 2.0902 2.1033 2.1162 2.1290 2.1417 2.1543 2.1667 2.1791 2.1913 2.2034 2.2154 2.2274

0.0153 0.0159 0.0165 0.0170 0.0175 0.0180 0.0185 0.0190 0.0195 0.0199 0.0203 0.0208 0.0212 0.0216 0.0220 0.0224 0.0228 0.0232 0.0236 0.0240 0.0244 0.0248 0.0251 0.0255 0.0259 0.0263 0.0266 0.0270 0.0274

443.8 450.3 456.5 462.5 468.3 474.1 479.7 485.3 490.8 496.3 501.7 507.0 512.4 517.7 523.0 528.3 533.6 538.8 544.1 549.4 554.7 560.0 565.3 570.6 575.9 581.3 586.6 592.0 597.4

1.8126 1.8330 1.8523 1.8708 1.8886 1.9057 1.9223 1.9384 1.9541 1.9694 1.9844 1.9990 2.0134 2.0276 2.0415 2.0553 2.0688 2.0821 2.0953 2.1083 2.1212 2.1340 2.1466 2.1591 2.1714 2.1837 2.1959 2.2079 2.2199 (continued)

40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180

Appendix 2 793

(0.0129)

0.0136 0.0142 0.0148 0.0154 0.0159 0.0164 0.0169 0.0174 0.0178 0.0183 0.0187 0.0191 0.0195 0.0199 0.0203 0.0207 0.0211 0.0215 0.0219 0.0223 0.0226 0.0230 0.0234 0.0237

Temp. °C

35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150

V

434.4 441.4 448.1 454.5 460.7 466.7 472.5 478.3 484.0 489.5 495.1 500.5 506.0 511.3 516.7 522.1 527.4 532.7 538.0 543.3 548.7 554.0 559.3 564.6

(427.6)

1.7776 1.8003 1.8214 1.8414 1.8603 1.8785 1.8960 1.9128 1.9292 1.9451 1.9607 1.9758 1.9907 2.0052 2.0195 2.0335 2.0474 2.0610 2.0744 2.0877 2.1008 2.1137 2.1265 2.1392

(1.7553)

S

0.0125 0.0132 0.0138 0.0143 0.0149 0.0154 0.0158 0.0163 0.0167 0.0172 0.0176 0.0180 0.0184 0.0188 0.0192 0.0196 0.0199 0.0203 0.0207 0.0210 0.0214 0.0218 0.0221 0.0225

(0.0122)

V

431.5 438.9 445.9 452.5 458.8 465.0 471.0 476.8 482.6 488.3 493.9 499.4 504.9 510.3 515.7 521.1 526.5 531.9 537.2 542.6 547.9 553.2 558.6 563.9

(427.6)

H

(32.46°C)

(30.45°C)

H

2000.0

1900.0

1.7641 1.7879 1.8099 1.8305 1.8500 1.8686 1.8865 1.9037 1.9203 1.9365 1.9522 1.9676 1.9826 1.9973 2.0117 2.0259 2.0398 2.0535 2.0670 2.0804 2.0935 2.1066 2.1194 2.1321

(1.7511)

S

– 0.0114 0.0120 0.0126 0.0131 0.0136 0.0140 0.0145 0.0149 0.0153 0.0157 0.0161 0.0165 0.0169 0.0172 0.0176 0.0179 0.0183 0.0186 0.0189 0.0193 0.0196 0.0199 0.0202

(0.0109)

V

Absolute Pressure, kPa

– 433.5 441.1 448.2 455.0 461.4 467.7 473.8 479.8 485.6 491.4 497.1 502.7 508.2 513.8 519.2 524.7 530.1 535.6 541.0 546.4 551.8 557.2 562.6

(427.4)

H

(36.26°C)

2200.0

– 1.7627 1.7868 1.8090 1.8297 1.8493 1.8680 1.8859 1.9032 1.9199 1.9360 1.9518 1.9671 1.9821 1.9968 2.0112 2.0254 2.0393 2.0530 2.0665 2.0799 2.0930 2.1060 2.1188

(1.7430)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– 0.0098 0.0105 0.0110 0.0116 0.0120 0.0125 0.0129 0.0134 0.0137 0.0141 0.0145 0.0149 0.0152 0.0156 0.0159 0.0162 0.0166 0.0169 0.0172 0.0175 0.0178 0.0181 0.0184

(0.0098)

V

– 427.3 435.8 443.6 450.8 457.7 464.3 470.7 476.9 482.9 488.8 494.7 500.4 506.1 511.7 517.3 522.9 528.4 533.9 539.4 544.8 550.3 555.7 561.2

(427.0)

H

(39.81°C)

2400.0

– 1.7363 1.7632 1.7874 1.8096 1.8305 1.8501 1.8688 1.8867 1.9040 1.9206 1.9368 1.9525 1.9679 1.9828 1.9975 2.0119 2.0260 2.0399 2.0536 2.0671 2.0804 2.0935 2.1065

(1.7352)

S

35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150

Temp. °C

794 Appendix 2

(0.0089)

0.0091 0.0097 0.0103 0.0107 0.0112 0.0116 0.0120 0.0124 0.0128 0.0131 0.0135 0.0138 0.0142 0.0145 0.0148 0.0151 0.0154 0.0157

45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130

V

0.0241 0.0244 0.0248 0.0251 0.0255 0.0258 0.0262 –

Temp. °C

155 160 165 170 175 180 185 190

429.9 438.5 446.4 453.7 460.7 467.4 473.8 480.1 486.2 492.2 498.1 503.9 509.7 515.4 521.0 526.6 532.2 537.7

(426.4)

H

1.7384 1.7653 1.7894 1.8117 1.8325 1.8521 1.8707 1.8886 1.9058 1.9224 1.9386 1.9542 1.9695 1.9845 1.9991 2.0135 2.0276 2.0414

(1.7275)

S

– 0.0086 0.0091 0.0096 0.0101 0.0105 0.0109 0.0113 0.0116 0.0120 0.0123 0.0126 0.0130 0.0133 0.0136 0.0139 0.0142 0.0144

(0.0081)

V

– 432.9 441.5 449.5 456.9 463.9 470.7 477.2 483.5 489.7 495.7 501.7 507.6 513.4 519.1 524.8 530.5 536.1

(425.7)

H

(46.28°C)

569.3 574.7 580.1 585.5 590.9 596.3 601.7 –

(43.14°C)

0.0228 0.0231 0.0235 0.0238 0.0242 0.0245 0.0248 – 2800.0

2.1517 2.1642 2.1765 2.1887 2.2008 2.2128 2.2247 –

2600.0

570.0 575.3 580.7 586.0 591.4 596.9 602.3 –

– 1.7422 1.7688 1.7928 1.8149 1.8355 1.8551 1.8736 1.8914 1.9085 1.9251 1.9412 1.9568 1.9720 1.9869 2.0015 2.0158 2.0299

(1.7199)

S

2.1447 2.1572 2.1696 2.1818 2.1939 2.2060 2.2179 –

– 0.0075 0.0081 0.0086 0.0091 0.0095 0.0099 0.0103 0.0106 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0128 0.0131 0.0133

(0.0074)

V

0.0206 0.0209 0.0212 0.0215 0.0218 0.0221 0.0224 0.0227

– 426.4 436.2 444.9 452.8 460.3 467.4 474.1 480.7 487.1 493.3 499.4 505.4 511.3 517.2 523.0 528.7 534.4

(424.8)

H

(49.26°C)

3000.0

568.0 573.4 578.8 584.2 589.7 595.2 600.6 606.1

– 1.7172 1.7472 1.7735 1.7972 1.8191 1.8396 1.8589 1.8774 1.8951 1.9121 1.9286 1.9445 1.9601 1.9752 1.9901 2.0046 2.0188

(1.7123)

S

2.1315 2.1441 2.1566 2.1689 2.1811 2.1932 2.2052 2.2171

– – 0.0071 0.0077 0.0082 0.0086 0.0090 0.0094 0.0097 0.0101 0.0104 0.0107 0.0110 0.0113 0.0116 0.0118 0.0121 0.0124

(0.0068)

V

0.0187 0.0190 0.0193 0.0196 0.0199 0.0202 0.0205 0.0207

– – 430.1 439.8 448.4 456.4 463.9 471.0 477.8 484.4 490.8 497.1 503.2 509.3 515.2 521.1 526.9 532.7

(423.8)

H

(52.09°C)

3200.0

566.6 572.1 577.6 583.0 588.5 594.0 599.5 605.0

– – 1.7242 1.7534 1.7791 1.8025 1.8241 1.8444 1.8636 1.8818 1.8994 1.9163 1.9327 1.9485 1.9640 1.9791 1.9938 2.0083

(1.7047)

S

2.1193 2.1319 2.1445 2.1569 2.1692 2.1814 2.1935 2.2054

45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 (continued)

Temp. °C

155 160 165 170 175 180 185 190

Appendix 2 795

0.0160 0.0163 0.0166 0.0169 0.0171 0.0174 0.0177 0.0180 0.0182 0.0185 0.0188 0.0190 0.0193 – –

135 140 145 150 155 160 165 170 175 180 185 190 195 200 205

(0.0062)

0.0062 0.0068 0.0074

Temp. °C

55 60 65

V

(0.0089)

Temp. °C

V

423.1 434.1 443.7

(422.6)

H

1.6987 1.7321 1.7604

(1.6971)

S

– 0.0060 0.0066

(0.0057)

V

– 427.7 438.4

(421.2)

H

3600.0

541.7 547.3 552.8 558.4 564.0 569.5 575.1 580.6 586.2 591.7 597.3 602.9 608.5 614.1 –

(425.7)

(57.36°C)

0.0147 0.0150 0.0153 0.0155 0.0158 0.0161 0.0163 0.0166 0.0168 0.0171 0.0173 0.0176 0.0178 0.0181 –

(0.0081)

H

3400.0

2.0551 2.0685 2.0818 2.0948 2.1078 2.1205 2.1332 2.1457 2.1581 2.1703 2.1825 2.1945 2.2065 – –

(1.7275)

V

(54.78°C)

543.3 548.8 554.3 559.8 565.3 570.8 576.3 581.8 587.3 592.9 598.4 604.0 609.5 – –

(426.4)

S

(46.28°C)

(43.14°C)

H

2800.0

2600.0

– 1.7089 1.7408

(1.6893)

S

2.0437 2.0573 2.0707 2.0839 2.0969 2.1098 2.1225 2.1351 2.1476 2.1599 2.1722 2.1843 2.1963 2.2082 –

(1.7199)

S

– 0.0053 0.0059

(0.0052)

V

0.0136 0.0139 0.0141 0.0144 0.0146 0.0149 0.0151 0.0154 0.0156 0.0159 0.0161 0.0163 0.0166 0.0168 –

(0.0074)

V

Absolute Pressure, kPa

– 420.1 432.5

(419.7)

H

(59.84°C)

3800.0

540.1 545.7 551.4 557.0 562.6 568.2 573.8 579.4 585.0 590.6 596.2 601.8 607.4 613.0 –

(424.8)

H

(49.26°C)

3000.0

– 1.6827 1.7195

(1.6813)

S

2.0328 2.0466 2.0601 2.0735 2.0866 2.0996 2.1125 2.1252 2.1377 2.1501 2.1624 2.1746 2.1867 2.1987 –

(1.7123)

S

Suva® 410A Superheated Vapor–Constant Pressure Tables (Saturated Vapor Properties in Parentheses)

TABLE A.19 (SI) (Continued)

– – 0.0052

(0.0048)

V

0.0126 0.0129 0.0131 0.0134 0.0136 0.0139 0.0141 0.0143 0.0145 0.0148 0.0150 0.0152 0.0155 0.0157 0.0159

(0.0068)

V

– – 425.6

(417.9)

H

(62.21°C)

4000.0

538.5 544.2 549.9 555.6 561.2 566.9 572.5 578.1 583.8 589.4 595.0 600.7 606.3 612.0 617.7

(423.8)

H

(52.09°C)

3200.0

– – 1.6959

(1.6730)

S

2.0224 2.0364 2.0500 2.0635 2.0768 2.0899 2.1029 2.1157 2.1283 2.1408 2.1532 2.1655 2.1776 2.1896 2.2016

(1.7047)

S

55 60 65

Temp. °C

135 140 145 150 155 160 165 170 175 180 185 190 195 200 205

Temp. °C

796 Appendix 2

0.0078 0.0082 0.0086 0.0089 0.0093 0.0096 0.0099 0.0102 0.0105 0.0107 0.0110 0.0113 0.0115 0.0118 0.0120 0.0122 0.0125 0.0127 0.0129 0.0132 0.0134 0.0136 0.0138 0.0140 0.0143 0.0145 0.0147 0.0149 – –

452.2 460.2 467.6 474.8 481.6 488.2 494.7 501.0 507.1 513.2 519.2 525.1 531.0 536.8 542.6 548.4 554.1 559.8 565.5 571.2 576.9 582.6 588.2 593.9 599.6 605.3 611.0 616.7 – –

1.7856 1.8086 1.8299 1.8499 1.8688 1.8869 1.9043 1.9211 1.9373 1.9531 1.9684 1.9834 1.9981 2.0124 2.0265 2.0404 2.0540 2.0674 2.0807 2.0937 2.1066 2.1193 2.1319 2.1444 2.1567 2.1689 2.1810 2.1930 – –

0.0071 0.0075 0.0079 0.0082 0.0086 0.0089 0.0092 0.0095 0.0097 0.0100 0.0103 0.0105 0.0108 0.0110 0.0112 0.0115 0.0117 0.0119 0.0121 0.0123 0.0126 0.0128 0.0130 0.0132 0.0134 0.0136 0.0138 0.0140 0.0142 –

447.8 456.2 464.1 471.6 478.7 485.5 492.2 498.6 505.0 511.2 517.3 523.3 529.3 535.2 541.0 546.9 552.7 558.4 564.2 569.9 575.6 581.4 587.1 592.8 598.5 604.2 609.9 615.7 621.4 –

1.7682 1.7928 1.8153 1.8362 1.8559 1.8747 1.8926 1.9098 1.9264 1.9425 1.9581 1.9734 1.9882 2.0028 2.0171 2.0311 2.0449 2.0584 2.0718 2.0849 2.0979 2.1108 2.1234 2.1360 2.1484 2.1607 2.1728 2.1849 2.1968 –

Note: H = enthalpy in kJ/kg; S = entropy in kJ/(kg) (K); V = volume in m3/kg.

70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215

0.0064 0.0068 0.0072 0.0076 0.0079 0.0082 0.0085 0.0088 0.0091 0.0093 0.0096 0.0098 0.0101 0.0103 0.0105 0.0108 0.0110 0.0112 0.0114 0.0116 0.0118 0.0120 0.0122 0.0124 0.0126 0.0128 0.0130 0.0132 0.0134 –

442.8 452.0 460.4 468.3 475.7 482.8 489.6 496.3 502.7 509.1 515.3 521.4 527.5 533.5 539.4 545.3 551.2 557.0 562.8 568.6 574.4 580.1 585.9 591.6 597.4 603.1 608.9 614.6 620.4 –

1.7500 1.7766 1.8005 1.8225 1.8431 1.8625 1.8810 1.8987 1.9157 1.9321 1.9481 1.9636 1.9787 1.9935 2.0079 2.0221 2.0360 2.0497 2.0632 2.0765 2.0896 2.1025 2.1153 2.1279 2.1404 2.1527 2.1649 2.1771 2.1891 –

0.0058 0.0062 0.0066 0.0070 0.0073 0.0076 0.0079 0.0082 0.0085 0.0087 0.0090 0.0092 0.0095 0.0097 0.0099 0.0101 0.0103 0.0106 0.0108 0.0110 0.0112 0.0114 0.0116 0.0117 0.0119 0.0121 0.0123 0.0125 0.0127 0.0129

437.4 447.4 456.5 464.7 472.5 479.9 487.0 493.8 500.5 506.9 513.3 519.5 525.7 531.8 537.8 543.8 549.7 555.6 561.4 567.3 573.1 578.9 584.7 590.5 596.3 602.1 607.8 613.6 619.4 625.2

1.7305 1.7596 1.7853 1.8086 1.8302 1.8504 1.8695 1.8877 1.9051 1.9220 1.9382 1.9540 1.9694 1.9844 1.9990 2.0134 2.0275 2.0413 2.0549 2.0683 2.0815 2.0946 2.1074 2.1201 2.1327 2.1451 2.1574 2.1696 2.1816 2.1936

70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215

Appendix 2 797

Pressure (MPa)

100

0.5

150

200

80

90

50

70

250

10

20

40

o

30

40

30

20

10

350

60

Enthalpy (kJ/kg)

300

50

350

Temperature = 0 C

300

400 04 0.0 0.005 6 0.00

400

450

500

450

500

Source: Thermodynamic Properties of DuPont Suva 410A Refrigerant. With permission of E. I. Du Pont de Nemours and Co.

0.006

0.01 0.008

0.02

0.04

0.06

0.1 0.08

0.2

id

te d

liqu

0.7

0.4

0.1

0.8

0.6

0.9

1 0.8

Pressure–Enthalpy Diagram (Sl Units)

0.2

1.0

2

0.3

1.1

DuPont TM Suva 410A

1.2

ura

Sat

0.6

ity =

DuPont Fluorochemicals

1.5

0.5

250

0.6

1.6

4

0.4

1.3

0.7

1.7 E

Qual

1.4

0.8

-K ntro py

= 1.8

kJ/kg

1.9

0.9

2.0

vapor Saturate d

2.1 80 70 60 2.2 50 40 30 20 2.3

200

2.4

150

2.5

100

0.040 0.050 0.060

0.030

0.020

0.015

0.008 0.010

550

0.30

0.20

0.15

0.10

550

8.0

4.0 5.0 6.0

3.0

2.0

1.5

0.80 1.0

0.40 0.50 Volume = 0.60

2.7

6

2.6

600

/kg

10 0 10 20 30 40 o = 50 C Temperature 60 70 80 90 100 110 120 130 140 150 160 170 180 8

600

2.

Enthalpy (kJ/kg)

Pressure (MPa) 0.006

0.01 0.008

0.02

0.04

0.06

0.1 0.08

0.2

0.4

0.6

1 0.8

2

4

6

798 Appendix 2

799

Appendix 2

TABLE A.20 Thermodynamic Properties of Air at Low Pressure T, °R

h, Btu/lb

pr

u, Btu/lb

vr

200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060

47.67 52.46 57.25 62.03 66.82 71.61 76.40 81.18 85.97 90.75 95.53 100.32 105.11 109.90 114.69 119.48 124.27 129.06 133.86 138.66 143.47 148.28 153.09 157.92 162.73 167.56 172.39 177.23 182.08 186.94 191.81 196.69 201.56 206.46 211.35 216.26 221.18 226.11 231.06 236.02 240.98 245.97 250.95 255.96

0.04320 0.06026 0.08165 0.10797 0.13986 0.17795 0.22290 0.27545 0.3363 0.4061 0.4858 0.5760 0.6776 0.7913 0.9182 1.0590 1.2147 1.3860 1.5742 1.7800 2.005 2.249 2.514 2.801 3.111 3.446 3.806 4.193 4.607 5.051 5.526 6.033 6.573 7.149 7.761 8.411 9.102 9.834 10.610 11.430 12.298 13.215 14.182 15.203

33.96 37.38 40.80 44.21 47.63 51.04 54.46 57.87 61.29 64.70 68.11 71.52 74.93 78.36 81.77 85.20 88.62 92.04 95.47 98.90 102.34 105.78 109.21 112.67 116.12 119.58 123.04 126.51 129.99 133.47 136.97 140.47 143.98 147.50 151.02 154.57 158.12 161.68 165.26 168.83 172.43 176.04 179.66 183.29

1714.9 1352.5 1088.8 892.0 741.6 624.5 531.8 457.2 396.6 346.6 305.0 270.1 240.6 215.33 193.65 174.90 158.58 144.32 131.78 120.70 110.88 102.12 94.30 87.27 80.96 75.25 70.07 65.38 61.10 57.20 53.63 50.35 47.34 44.57 42.01 39.64 37.44 35.41 33.52 31.76 30.12 28.59 27.17 25.82

ϕ Btu/lb. °R 0.36303 0.38584 0.40666 0.42582 0.44356 0.46007 0.47550 0.49002 0.50369 0.51663 0.52890 0.54058 0.55172 0.56235 0.57255 0.58233 0.59173 0.60078 0.60950 0.61793 0.62607 0.63395 0.64159 0.64902 0.65621 0.66321 0.67002 0.67665 0.68312 0.68942 0.69558 0.70160 0.70747 0.71323 0.71886 0.72438 0.72979 0.73509 0.74030 0.74540 0.75042 0.75536 0.76019 0.76496 (continued)

800

Appendix 2

TABLE A.20 (Continued) Thermodynamic Properties of Air at Low Pressure T, °R

h, Btu/lb

pr

u, Btu/lb

vr

1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940

260.97 265.99 271.03 276.08 281.14 286.21 291.30 296.41 301.52 306.65 311.79 316.94 322.11 327.29 332.48 337.68 342.90 348.14 353.37 358.63 363.89 369.17 374.47 379.77 385.08 390.40 395.74 401.09 406.45 411.82 417.20 422.59 428.00 433.41 438.83 444.26 449.71 455.17 460.63 466.12 471.60 477.09 482.60 488.12

16.278 17.413 18.604 19.858 21.18 22.56 24.01 25.53 27.13 28.80 30.55 32.39 34.31 36.31 38.41 40.59 42.88 45.26 47.75 50.34 53.04 55.86 58.78 61.83 65.00 68.30 71.73 75.29 78.99 82.83 86.82 90.95 95.24 99.69 104.30 109.08 114.03 119.16 124.47 129.95 135.64 141.51 147.59 153.87

186.93 190.58 194.25 197.94 201.63 205.33 209.05 212.78 216.53 220.28 224.05 227.83 231.63 235.43 239.25 243.08 246.93 250.79 254.66 258.54 262.44 266.34 270.26 274.20 278.13 282.09 286.06 290.04 294.03 298.02 302.04 306.06 310.09 314.13 318.18 322.24 326.32 330.40 334.50 338.61 342.73 346.85 350.98 355.12

24.58 23.40 22.30 21.27 20.293 19.377 18.514 17.700 16.932 16.205 15.518 14.868 14.253 13.670 13.118 12.593 12.095 11.622 11.172 10.743 10.336 9.948 9.578 9.226 8.890 8.569 8.263 7.971 7.691 7.424 7.168 6.924 6.690 6.465 6.251 6.045 5.847 5.658 5.476 5.302 5.134 4.974 4.819 4.670

ϕ Btu/lb. °R 0.76964 0.77426 0.77880 0.78326 0.78767 0.79201 0.79628 0.80050 0.80466 0.80876 0.81280 0.81680 0.82075 0.82464 0.82848 0.83229 0.83604 0.83975 0.84341 0.84704 0.85062 0.85416 0.85767 0.86113 0.86456 0.86794 0.87130 0.87462 0.87791 0.88116 0.88439 0.88758 0.89074 0.89387 0.89697 0.90003 0.90308 0.90609 0.90908 0.91203 0.91497 0.91788 0.92076 0.92362 (continued)

801

Appendix 2

TABLE A.20 (Continued) Thermodynamic Properties of Air at Low Pressure T, °R

h, Btu/lb

pr

u, Btu/lb

vr

ϕ Btu/lb. °R

1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400

493.64 499.17 504.71 510.26 515.82 521.39 526.97 532.55 538.15 543.74 549.35 554.97 560.59 566.23 571.86 577.51 583.16 588.82 594.49 600.16 605.84 611.53 617.22

160.37 167.07 174.00 181.16 188.54 196.16 204.02 212.1 220.5 229.1 238.0 247.2 256.6 266.3 276.3 286.6 297.2 308.1 319.4 330.9 342.8 355.0 367.6

359.28 363.43 367.61 371.79 375.98 380.18 384.39 388.60 392.83 397.05 401.29 405.53 409.78 414.05 418.31 422.59 426.87 431.16 435.46 439.76 444.07 448.38 452.70

4.527 4.390 4.258 4.130 4.008 3.890 3.777 3.667 3.561 3.460 3.362 3.267 3.176 3.088 3.003 2.921 2.841 2.765 2.691 2.619 2.550 2.483 2.419

0.92645 0.92926 0.93205 0.93481 0.93756 0.94026 0.94296 0.94564 0.94829 0.95092 0.95352 0.95611 0.95868 0.96123 0.96376 0.96626 0.96876 0.97123 0.97369 0.97611 0.97853 0.98092 0.98331

Source: Abridged from Table 1 in Joseph H. Keenan and Joseph Kaye: Gas Tables. 1948. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

TABLE A.21 Properties of Some Gases at Low Pressure Products of Combustion, 400% Theoretical Air Temp °R 537 600 700 800 900 1000 1100 1200 1300 1400 1500

Products of Combustion, 200% Theoretical Air

Nitrogen

Oxygen

h

φ

h

φ

h

φ

h

φ

3746.8 4191.9 4901.7 5617.5 6340.3 7072.1 7812.9 8563.4 9324.1 10095.0 10875.6

46.318 47.101 48.195 49.150 50.002 50.773 51.479 52.132 52.741 53.312 53.851

3774.9 4226.3 4947.7 5676.3 6413.0 7159.8 7916.4 8683.6 9461.7 10250.7 11050.2

46.300 47.094 48.207 49.179 50.047 50.833 51.555 52.222 52.845 53.430 53.981

3729.5 4167.9 4864.9 5564.4 6268.1 6977.9 7695.0 8420.0 9153.9 9896.9 10648.9

45.755 46.514 47.588 48.522 49.352 50.099 50.783 51.413 52.001 52.551 53.071

3725.1 4168.3 4879.3 5602.0 6337.9 7087.5 7850.4 8625.8 9412.9 10210.4 11017.1

48.986 49.762 50.858 51.821 52.688 53.477 54.204 54.879 55.508 56.099 56.656 (continued)

802

Appendix 2

TABLE A.21 (Continued) Properties of Some Gases at Low Pressure Products of Combustion, 400% Theoretical Air Temp °R 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300

Products of Combustion, 200% Theoretical Air

Nitrogen

Oxygen

h

φ

h

φ

h

φ

h

φ

11665.6 12464.3 13271.7 14087.2 14910.3 15740.5 16577.1 17419.8 18268.0 19121.4 19979.7 20842.8 21709.8 22581.4 23456.6 24335.5 25217.8 26102.9 26991.4

54.360 54.844 55.306 55.747 56.169 56.574 56.964 57.338 57.699 58.048 58.384 58.710 59.026 59.331 59.628 59.916 60.196 60.469 60.734

11859.6 12678.6 13507.0 14344.1 15189.3 16042.4 16902.5 17769.3 18642.1 19520.7 20404.6 21293.8 22187.5 23086.0 23988.5 24895.3 25805.6 26719.2 27636.4 28556.8 29479.9 30406.0 31334.8 32266.2

54.504 55.000 55.473 55.926 56.360 56.777 57.177 57.562 57.933 58.292 58.639 58.974 59.300 59.615 59.921 60.218 60.507 60.789 61.063 61.329 61.590 61.843 62.091 62.333

11409.7 12178.9 12956.3 13741.6 14534.4 15334.0 16139.8 16951.2 17767.9 18589.5 19415.8 20246.4 21081.1 21919.5 22761.5 23606.8 24455.0 25306.0 26159.7 27015.9 27874.4 28735.1 29597.9 30462.8 31329.4 32198.0 33068.1 33939.9 34813.1 35687.8 36563.8 37441.1 38319.5 39199.1 40079.8 40961.6 41844.4 42728.3

53.561 54.028 54.472 54.896 55.303 55.694 56.068 56.429 56.777 57.112 57.436 57.750 58.053 58.348 58.632 58.910 59.179 59.442 59.697 59.944 60.186 60.422 60.652 60.877 61.097 61.310 61.520 61.726 61.927 62.123 62.316 62.504 62.689 62.870 63.049 63.223 63.395 63.563

11832.5 12655.6 13485.8 14322.1 15164.0 16010.9 16862.6 17718.8 18579.2 19443.4 20311.4 21182.9 22057.8 22936.1 23817.7 24702.5 25590.5 26481.6 27375.9 28273.3 29173.9 30077.5 30984.1 31893.6 32806.1 33721.6 34639.9 35561.1 36485.0 37411.8 38341.4 39273.6 40208.6 41146.1 42086.3 43029.1 43974.3 44922.2

57.182 57.680 58.155 58.607 59.039 59.451 59.848 60.228 60.594 60.946 61.287 61.616 61.934 62.242 62.540 62.831 63.113 63.386 63.654 63.914 64.168 64.415 64.657 64.893 65.123 65.350 65.571 65.788 66.000 66.208 66.413 66.613 66.809 67.003 67.193 67.380 67.562 67.743

Source: Abridged from Tables 4, 7, 11, 13, 15, 17, 19, and 21 in Joseph H. Keenan and Joseph Kaye: Gas Tables. 1948. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. T dT cp0 , Btu/lb. mole °R; ϕ is essentially equal to the absolute entropy at Note: h = enthalpy Btu/lb mole; φ = T T =0 1 atm pressure, Btu/lb. mole °R.

∫

803

Appendix 2

TABLE A.21 (SI) Properties of Some Gases at Low Pressure Water Vapor Temp °R 537 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300

Carbon Dioxide

h

φ

h

φ

4258.3 4764.7 5575.4 6396.9 7230.9 8078.9 8942.0 9820.4 10714.5 11624.8 12551.4 13494.9 14455.4 15433.0 16427.5 17439.0 18466.9 19510.8 20570.6 21645.7 22735.4 23839.5 24957.2 26088.0 27231.2 28386.3 29552.8 30730.2 31918.2 33116.0 34323.5 35540.1 36765.4 37998.9 39240.2 40489.1 41745.4 43008.4 44278.0

45.079 45.970 47.219 48.316 49.298 50.191 51.013 51.777 52.494 53.168 53.808 54.418 54.999 55.559 56.097 56.617 57.119 57.605 58.077 58.535 58.980 59.414 59.837 60.248 60.650 61.043 61.426 61.801 62.167 62.526 62.876 63.221 63.557 63.887 64.210 64.528 64.839 65.144 65.444

4030.2 4600.9 5552.0 6552.9 7597.6 8682.1 9802.6 10955.3 12136.9 13344.7 14576.0 15829.0 17101.4 18391.5 19697.8 21018.7 22352.7 23699.0 25056.3 26424.0 27801.2 29187.1 30581.2 31982.8 33391.5 34806.6 36227.9 37654.7 39086.7 40523.6 41965.2 43411.0 44860.6 46314.0 47771.0 49231.4 50695.1 52162.0 53632.1

51.032 52.038 53.503 54.839 56.070 57.212 58.281 59.283 60.229 61.124 61.974 62.783 63.555 64.292 64.999 65.676 66.327 66.953 67.557 68.139 68.702 69.245 69.771 70.282 70.776 71.255 71.722 72.175 72.616 73.045 73.462 73.870 74.267 74.655 75.033 75.404 75.765 76.119 76.464

Hydrogen

Carbon Monoxide

h

φ

h

3640.3 4075.6 4770.2 5467.1 6165.3 6864.5 7564.6 8265.8 8968.7 9673.8 10381.5 11092.5 11807.4 12526.8 13250.9 13980.1 14714.5 15454.4 16199.8 16950.6 17707.3 18469.7 19237.8 20011.8 20791.5 21576.9 22367.7 23164.1 23965.5 24771.9 25582.9 26398.5 27218.5 28042.8 28871.1 29703.5 30539.8 31379.8 32223.5

31.194 31.959 33.031 33.961 34.784 35.520 36.188 36.798 37.360 37.883 38.372 38.830 39.264 39.675 40.067 40.441 40.799 41.143 41.475 41.794 42.104 42.403 42.692 42.973 43.247 43.514 43.773 44.026 44.273 44.513 44.748 44.978 45.203 45.423 45.638 45.849 46.056 46.257 46.456

3729.5 3168.0 4866.0 5568.2 6276.4 6992.2 7716.8 8450.8 9194.6 9948.1 10711.1 11483.4 12264.3 13053.2 13849.8 14653.2 15463.3 16279.4 17101.0 17927.4 18758.8 19594.3 20434.0 21277.2 22123.8 22973.4 23826.0 24681.2 25539.0 26399.3 27261.8 28126.6 28993.5 29862.3 30732.9 31605.2 32479.1 33354.4 34231.2

φ 47.272 48.044 49.120 50.058 50.892 51.646 52.337 52.976 53.571 54.129 54.655 55.154 55.628 56.078 56.509 56.922 57.317 57.696 58.062 58.414 58.754 59.081 59.398 59.705 60.002 60.290 60.569 60.841 61.105 61.362 61.612 61.855 62.093 62.325 62.551 62.772 62.988 63.198 63.405 (continued)

804

Appendix 2

TABLE A.21 (SI) (Continued) Properties of Some Gases at Low Pressure Water Vapor

Hydrogen

Carbon Monoxide

φ

h

φ

h

φ

h

φ

45553.9 46835.9 48123.6 49416.9 50715.5 52019.0 53327.4 54640.3 55957.4 57278.7

65.738 66.028 66.312 66.591 66.866 67.135 67.401 67.662 67.918 68.172

55105.1 56581.0 58059.7 59541.1 61024.9 62511.3 64000.0 65490.9 66984.0 68479.1

76.803 77.135 77.460 77.779 78.091 78.398 78.698 78.994 79.284 79.569

33070.9 33921.6 34775.7 35633.0 36493.4 37356.9 38223.3 39092.8 39965.1 40840.2

46.651 46.842 47.030 47.215 47.396 47.574 47.749 47.921 48.090 48.257

35109.2 35988.6 36869.3 37751.0 38633.9 39517.8 40402.7 41288.6 42175.5 43063.2

63.607 63.805 63.998 64.188 64.374 64.556 64.735 64.910 65.082 65.252

Temp °R 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300

Carbon Dioxide

h

TABLE A.22 Normal Total Emissivity of Various Surfaces Surfaces a. Metals and Their Oxides Aluminum: Highly polished plate, 98.3% pure Polished plate Rough plate Oxidized at 1110°F Al-surfaced roofing Al-treated surfaces, heated at 1110°F Copper Steel Brass: Highly polished: 73.2% Cu, 26.7% Zn, by weight 62.4% Cu, 36.8% Zn, 0.4% Pb, 0.3% Al, by weight 82.9% Cu, 17.0% Zn, by weight Hard-rolled, polished, but direction of polishing visible But somewhat attacked But traces of stearin from polish left on Polished:

°F

є

440, 1070 73 78 390, 1110 110

0.039, 0.057 0.040 0.055 0.11, 0.19 0.216

390, 1110 390, 1110

0.18, 0.19 0.52, 0.57

476, 674 494, 710 530 70 73 75 100, 600

0.028, 0.031 0.0388, 0.037 0.030 0.038 0.043 0.053 0.096, 0.096 (continued)

805

Appendix 2

TABLE A.22 (Continued) Normal Total Emissivity of Various Surfaces Surfaces Rolled plate: Natural surface Rubbed with coarse emery Dull plate Oxidized by heating at 1110°F Chromium: See Nickel alloys for Ni–Cr steels Copper: Carefully polished electrolytic Cu Commercial, emeried, polished, but pits remaining Scraped shiny, but not mirrorlike Polished Plate heated at 1110°F Cuprous oxide Plate, heated for a long time, covered with thick oxide layer Molten copper Gold: Pure, highly polished Iron and steel: Metallic surfaces (or very thin oxide layer): Electrolytic iron, highly polished Polished iron Iron freshly emeried Cast iron, polished Wrought iron, highly polished Cast iron, newly turned Polished steel casting Ground sheet steel Smooth sheet iron Cast iron, turned on lathe Oxidized surfaces: Iron plate, pickled, then rusted red Then completely rusted Rolled sheet steel Oxidized iron Cast iron, oxidized at 1100°F Steel oxidized at 1100°F Smooth, oxidized electrolytic iron Iron oxide Rough ingot iron Sheet steel, strong rough oxide layer Dense shiny oxide layer Cast plate: Smooth Rough

°F

є

72 72 120, 660 390, 1110

0.06 0.20 0.22 0.61, 0.59

176 66 72 242 390, 1110 1470, 2010 77 1970, 2300

0.018 0.030 0.072 0.023 0.57, 0.57 0.66, 0.54 0.78 0.16, 0.13

440, 1160

0.018, 0.035

350, 440 800, 1880 68 392 100, 480 72 1420, 1900 1720, 2010 1650, 1900 1620, 1810

0.052, 0.074 0.144, 0.377 0.242 0.21 0.28 0.435 0.52, 0.56 0.55, 0.61 0.55, 0.60 0.60, 0.70

68 67 70 212 390, 1110 390, 1110 260, 980 930, 2190 1700, 2040 75 75

0.612 0.685 0.657 0.736 0.64, 0.78 0.79, 0.79 0.78, 0.82 0.85, 0.89 0.87, 0.95 0.80 0.82

73 73

0.80 0.82 (continued)

806

Appendix 2

TABLE A.22 (Continued) Normal Total Emissivity of Various Surfaces Surfaces Cast iron, rough, strongly oxidized Wrought iron, dull-oxidized Steel plate, rough High-temperature alloy steels; see Nickel alloys Molten metals: Molten cast iron Molten mild steel Lead: Pure (99.96%) unoxidized Gray oxidized Oxidized at 390°F Mercury, pure clean Molybdenum filament Ni-Cu alloy, oxidized at 1110°F Nickel: Electroplated on polished iron, then polished Technically pure (98.9% Ni by weight, +Mn), polished Electroplated on pickled iron, not polished Wire Plate, oxidized by heating at 1110°F Nickel oxide Nickel alloys: Cr-Ni alloy (18–32% Ni, 55–68% Cu, 20% Zn by weight), gray oxidized Alloy steel (8% Ni, 18% Cr); light silvery, rough, brown after heating Same, after 24 h heating at 980°F Alloy (20% Ni, 25% Cr), brown, splotched, oxidized from service Alloy (60% Ni, 12% Cr), smooth, black, firm adhesive oxide coat from service Platinum: Pure, polished plate Strip Filament Wire Silver: Polished, pure Polished Steel, see Iron Tantalum filament Tin, bright, tinned iron sheet Tungsten: Filament, aged Filament

°F

є

100, 480 70, 680 100, 700

0.95 0.94 0.94, 0.97

2370, 2550 2910, 3270

0.29, 0.29 0.28, 0.28

260, 440 75 390 32, 212 1340, 4700 390, 1110

0.057, 0.075 0.281 0.63 0.09, 0.12 0.096, 0.292 0.41, 0.46

74 440, 710 68 368, 1844 390, 1110 1200, 2290

0.045 0.07, 0.087 0.11 0.096, 0.186 0.37, 0.48 0.59, 0.86

125, 1894 70 420, 914

0.64, 0.76 0.262 0.44, 0.36

420, 980 420, 980

0.62, 0.73 0.90, 0.97

520, 1045

0.89, 0.82

440, 1160 1700, 2960 80, 2240 440, 2510

0.054, 0.104 0.12, 0.17 0.036, 0.192 0.073, 0.182

440, 1160 100, 700

0.0198, 0.0324 0.0221, 0.0312

2420, 4580 76

0.193, 0.31 0.043, 0.064

80, 6000 6000

0.032, 0.35 0.39 (continued)

807

Appendix 2

TABLE A.22 (Continued) Normal Total Emissivity of Various Surfaces Surfaces Zinc: Commercial, 99.1% pure, polished Oxidized by heating at 750°F Galvanized sheet iron: Fairly bright Gray, oxidized

°F

є

440, 620 750

0.045, 0.053 0.11

82 75

0.228 0.276

b. Refractories, Building Materials, Paints, and Miscellaneous Asbestos board 74 Asbestos paper 100, 700 Brick: Red, rough, but no gross irregularities 70 Silica unglazed, rough 1832 Silica glazed, rough 2012 Grog brick, glazed 2012 See Refractory materials, below Carbon: T-carbon, 0.9% ash 260, 1160 Carbon filament 1900, 2560 Candle soot 206, 520 Lampblack: Water–glass coating 209, 362 Water–glass coating 260, 440 Thin layer on iron plate 69 Thick coat 68 0.003 in. or thicker 100, 700 Enamel, white, fused on iron 66 Glass, smooth 72 Gypsum, 0.02 in. thick or smooth on blackened plate 70 Marble, light gray, polished 72 Oak, planed 70 Oil layers on polished nickel (lubricating oil): Polished surface alone 68 +0.001 in. oil 68 +0.002 in. oil 68 +0.005 in. oil 68 +∞ 68 Oil layers on aluminum foil (linseed oil): Aluminum foil 212 +1 coat oil 212 +2 coats oil 212 Paints, lacquers, varnishes: Snow-white enamel varnish on rough iron plate 73 Black shiny lacquer, sprayed on iron 76 Black shiny shellac on tinned iron sheet 70

0.96 0.93, 0.945 0.93 0.80 0.85 0.75

0.81, 0.79 0.526 0.952 0.959, 0.947 0.957, 0.952 0.927 0.967 0.945 0.897 0.937 0.903 0.931 0.895 0.045 0.27 0.46 0.72 0.82 0.087 0.561 0.574 0.906 0.875 0.821 (continued)

808

Appendix 2

TABLE A.22 (Continued) Normal Total Emissivity of Various Surfaces Surfaces Black-matte shellac Black lacquer Flat black lacquer White lacquer Oil paints, 16 different, all colors Aluminum paints and lacquers: 10% Al, 22% lacquer body, on rough or smooth surface 26% Al, 27% lacquer body, on rough or smooth surface Other aluminum paints, varying age and Al content Aluminum lacquer, varnish binder, on rough plate Aluminum paint, after heating to 620°F Paper, thin: Pasted on tinned iron plate Pasted on rough iron plate Pasted on black lacquered plate Plaster, rough, lime Porcelain, glazed Quartz, rough, fused Refractory materials, 40 different Poor radiators

°F

є

170, 295 100, 200 100, 200 100, 200 212

0.91 0.80, 0.95 0.96, 0.98 0.80, 0.95 0.92, 0.96

212 212 212 70 300, 600

0.52 0.30 0.27, 0.67 0.39 0.35

66 66 66 50, 190 72 70 1110, 1830

0.924 0.929 0.944 0.91 0.924 0.932

69

0.65, 0.75 0.70 0.80, 0.85 0.85, 0.90 0.91

74 76 74 32, 212

0.945 0.859 0.900 0.95, 0.963

Good radiators Roofing paper Rubber: Hard, glossy plate Soft, gray, rough (reclaimed) Serpentine, polished Water

Source: A. I. Brown and S. M. Marco, Introduction to Heat Transfer, 3rd ed., McGraw-Hill Book Company, New York, 1958, pp. 54–58. With permission.

0.60

25

30

30

12.5

35

40

45

50

55

60

80 75 65 70 Dry Bulb Temperature Degrees F.

5

Source: Courtesy of General Electric.

20

25

40

d an

p w70

13.

0

10

20

30

35

45

50

55

60

lb bu et 65 W

de

75

80

85

0

85

14.

0.00

0.10

10

12

14

28

30

32

34

36

38

48 46

90

90

95

10% midity ve hu Relati

% 20

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

0 120 115 110 105 100 Copyright, 1942, General Electric Company

Wet bulb line s

% 30

air dry

40

50

60

70

16

18

20

22

24

26

40

ir

42

44

50

52

58

5

80

90

100

110

120

130

140

150

160

Barometric Pressure 14.696 Lb. per Sq.in.

PSYCHROMETRIC CHART

54

56

14.

0.20

0.30

0.40

0.50

170

180

Weight of Water Vapor in One Pound of Dry Air Grains

190

200

210

220

230

240

.p Btu Tot al H eat–

0.70

Pressure of Water Vapor Lb. per Sq.in.

ry A of D er P oun d

250

Psychrometric Chart for Air–Water Vapor Mixtures

oi nt

s

re

ra tu te m pe

100 % 90% 80% 70%

60% 50 %

of Lb. per 15.0 . t f Cu

40 %

TABLE A.23

Appendix 2 809

13. 0

A

R

NORMAL TEMPERATURE SEA LEVEL BAROMETRIC PRESSURE: 101.325 kPa COPYRIGHT 1992

ASHRAE PSYCHROMETRIC CHART NO. 1

5

40

10

50

g

j/k

(k

15

Sa

n

tio

a ur

t

60

0.0

) da

0

1.

t

em

e

ur

at

r pe

70

20

°C

80

%

50 %

40

20

%

lative

8

0.8

10 4

0.8

30

10% re

%

30

ity

30

re,

atu

per

tem

humid

ulb

t-b

We

0.8

0.8 6

15

0.82

0

0.78

DRY-BULB TEMPERATURE ( C)

20

25

20

25

90

°c

40

air

16

18

20

22

24

26

28

30

50

2

4

6

8

10

12

14

HUMIDITY RATIO w, g w /kgda

Source: ASHRAE Handbook, Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc., 2005. With permission.

10

EN

TH

L A

PY

h

4 2. 0. 0 1. 0

5. 0 2.0

0

0

H3 H

1.0

30

0.9

dry

5

0.5

ENTHALPY = h HUMIDITY RATIO w

2.5

ram

30

0

SENSIBLE HEAT = TOTAL HEAT

2. 0

per g kilo

0

4. 0

0. 4

0.

1. 2.05 4. 0

100

4

20

5. 0

0. 2

1.0 0. 8 0. 7 0.6 0.5

0. 1

10.0

3

AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC

E

H

A

S

%

Psychrometric Chart for Air–Water Vapor Mixtures

0.2

%

0.5

90

me

%

olu tre

80

2V me

%

0.9 ic cub

70

0.9

60

TABLE A.23 (SI)

810 Appendix 2

References American Iron and Steel Institute. AISI Metric Practice Guide: SI Units and Conversion Factors for the Steel Industry. Washington, DC: AISI, 1975. American Society of Heating, Refrigerating, and Air-Conditioning Engineers. ASHRAE Guide and Data Book, latest ed. New York: ASHRAE. American Society of Mechanical Engineers. ASME Orientation and Guide for Use of SI (Metric) Units, 5th ed. New York: ASME, 1974. American Society of Mechanical Engineers. ASME Text Booklet: SI Units in Strength of Materials. New York: ASME, 1975. American Society of Mechanical Engineers. ASME Steam Tables, 6th ed. New York: ASME, 1993. American Solar Energy Society, 2400 Central Avenue, Suite G-l, Boulder, CO 80301. American Wind Energy Association, 122 C Street, Suite 380, Washington, DC 20001. Annamalai, K., I. Puri, and M. Jog. Advanced Engineering Thermodynamics, 2nd ed. Boca Raton, FL: CRC Press, 2011. Baker, H. D., E. A. Ryder, and H. N. Baker. Temperature Measurement in Engineering. New York: John Wiley & Sons, Inc., 1961. Benedict, R. P. Fundamentals of Temperature, Pressure, and Flow Measurements. New York: John Wiley & Sons, Inc., 1969. Bluestein, M. “Nature’s Carnot Engine: The Hurricane,” Proc. of ASME International Mechanical Engineering Conf., IMECE2006-13359, November, 2006. Cengel, Y. A. Heat Transfer: A Practical Approach. New York: McGraw-Hill Companies, 1998. Clifford, G. E. Modern Heating and Ventilating Systems Design. Upper Saddle River, NJ: Regents/ Prentice Hall, 1993. Dodge, B. F., Chemical Engineering Thermodynamics. New York: McGraw-Hill Book Company, 1944. Durham, F. P., Thermodynamics, 2nd ed., Upper Saddle River, NJ: Prentice Hall, Inc., 1959, p. 43. Electric Power Research Institute, 3412 Hillview Avenue, Palo Alto, CA 95160. Fagenbaum, J. “The Stirling: A ‘Hot’ Engine for the 80’s?” Mechanical Engineering, Vol. 105, No. 5, May 1983, pp. 18–29. Fermi, E. Thermodynamics. New York: Dover Publications, 1956, p. 11. Ferris, E. A. Modern Steam Generating Equipment. New York: Combustion Engineering Inc., 1960. Granet, I. “Heat Transfer Performance Curves,” Chemical Engineering, March 1955, pp. 187–190. Granet, I. “Heat Transfer to Subsaturated Water, Dry Air and Hydrogen in Turbulent Flow Inside a Tube,” Journal of the American Society of Naval Engineers, Vol. 69, No. 4, November 1957, pp. 787–794. Granet, I. “The Coefficient of Radiant Heat Transfer,” Design News, September 29, 1970. Granet, I. “Natural Convection Heat Transfer Aids,” Design News, March 20, 1972. Hatsopoulos, G. N., and J. H. Keenan. “A Single Axiom for Classical Thermodynamics,” ASME Paper 61-WA-100, 1961. Howell, J. R., and R. O. Buckius. Fundamentals of Engineering Thermodynamics, 2nd ed. New York: McGraw-Hill Book Company, 1987. Howell, J. R., and R. O. Buckius. Fundamentals of Engineering Thermodynamics, 2nd ed. New York: McGraw-Hill Book Company, 1992, p. 284. Huang, F. F. Engineering Thermodynamics: Fundamentals and Applications. New York: Macmillan Publishing Co., Inc., 1992. International Electronic Research Corporation. Thermal Management Guide. Burbank, CA: IERC, 1990. Irvine, T. E., and J. P. Hartnett. Steam and Gas Tables with Computer Equations. New York: Hemisphere Publishing Corp., 1984. Janna, W. S. Introduction to Fluid Mechanics, 3rd ed. Boston, MA: PWS-Kent Publishing Company, 1993. 811

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Jones, C. “A Survey of Curtiss–Wright’s 1958–1971 Rotary Combustion Engine Technological Developments,” Paper 720468. Detroit, MI: Society of Automotive Engineers National Automobile Engineering Meeting, May 1972. Jordan, R. C., and G. B. Priester. Refrigeration and Air Conditioning, 2nd ed. Upper Saddle River, NJ: Prentice Hall, Inc., 1956. Keenan, J. H. Thermodynamics. New York: John Wiley & Sons, Inc., 1941, p. 58. Keenan, J. H., and J. Kaye. Gas Tables. New York: John Wiley & Sons, Inc., 1948. Keenan, J. H., F. G. Keyes, P. G. Hill, and J. G. Moore. Steam Tables–Thermodynamic Properties of Water Including Vapor, Liquid, and Solid Phases. New York: John Wiley & Sons, Inc., 1969. Also by the same authors and under the same title (SI Units), 1978. Kreith, F., and R. Bezdek. “Can Industry Afford Solar Energy?” Mechanical Engineering, Vol. 105, No. 3, March 1983, pp. 35–41. Kreith, F., and M. S. Bohn. Principles of Heat Transfer, 5th ed. St. Paul, MN: West Publishing Co., 1993. Liley, P. E. 2000 Solved Problems in Mechanical Engineering Thermodynamics. New York: McGraw-Hill Book Co., 1989. McAdams, W. H. Heat Transmission, 3rd ed. New York: McGraw-Hill Book Company, 1954. McQuiston, F. C., and J. D. Parker. Heating, Ventilating, and Air-Conditioning, 4th ed. New York: John Wiley & Sons, Inc., 1994. Moebius Research, Inc. Heat Pump Manual, 2nd ed. Palo Alto, CA: Electric Power Research Institute, 1997. Moran, M. J., and H. N. Shapiro. Fundamentals of Engineering Thermodynamics, 2nd ed. New York: John Wiley & Sons, Inc., 1992. Naef, F. E., and D. N. Burwell. “Mini-OTEC Results,” 7th Energy Technology Conference. Obert, E. F. Concepts of Thermodynamics. New York: McGraw-Hill Book Company, 1960, p. 59. Pita, E. G. Air Conditioning Principles and Systems, 3rd ed. Upper Saddle River, NJ: Pearson Education, Inc., 1998. Potter, M. C., and C. W. Sommerton. Theory and Problems of Engineering Thermodynamics. New York: McGraw-Hill, Inc., 1993. Power magazine special reports: B. G. A. Skrotzki, “Steam Turbines,” June 1962; B. G. A. Skrotzki, “Gas Turbines,” December 1963; R. J. Bender, “Steam Generation,” June 1964; R. K. Evans, “Nuclear Power Reactors,” March 1965; R. G. Schweiger, “Heat Exchangers,” June 1970. Rathakrishnan, E. Elements of Heat Transfer. Boca Raton, FL: CRC Press, 2012. Renewal Products Co. How an Internal Combustion Engine Works. Fairless Hills, PA: The Company, 1960. Reynolds, W. C. Thermodynamic Properties in SI (Graphs, Tables and Computational Equations for 40 Substances). Stanford, CA: Department of Mechanical Engineering, Stanford University, 1979. Rohsenow, W. M., and H. Y. Choi. Heat, Mass and Momentum Transfer. Upper Saddle River, NJ: Prentice Hall, Inc., 1961. Severns, W. H., and J. F. Fellows. Air Conditioning and Refrigeration. New York: John Wiley & Sons, Inc., 1958. Shapiro, A. H. The Dynamics and Thermodynamics of Fluid Flow, Vol. 1. New York: The Ronald Press Company, 1953. Shavit, A., and C. Gutfinger. Thermodynamics: From Concepts to Applications, 2nd ed. Boca Raton, FL: CRC Press, 2009. Steinberg, D. S. Cooling Techniques for Electronic Equipment, 2nd ed. New York: John Wiley & Sons, Inc., 1991. Stoecker, W. F., and J. W. Jones. Refrigeration and Air Conditioning, 2nd ed. New York: McGraw-Hill Book Company, 1982. Stultz, S. C., and J. B. Kitto, eds. Steam: Its Generation and Use. Barberton, OH: The Babcock and Wilcox Company, 1992. Todd, J. P., and H. B. Ellis. An Introduction to Thermodynamics for Engineering Technologists. New York: John Wiley & Sons, Inc., 1981. U.S. Atomic Energy Commission. Power Reactors. Washington, DC: USAEC. Technical Information Service, May 1958.

References

813

Van Wylen, G. J., and R. E. Sonntag. Fundamentals of Classical Thermodynamics, 2nd ed. New York: John Wiley & Sons, Inc., 1973; SI version, 1976. Waxberg, H. Economic Study of Advanced Steam Conditions. New York: Ebasco Services, Inc., June 1981. Wolfe, H. C. ed. Temperature, Its Measurement and Control in Science and Industry. New York: Reinhold Publishing, 1955. Wood, D. B. Applications of Thermodynamics, 2nd ed. Reading, MA: Addison-Wesley Publishing Co., Inc., 1982. Zemansky, M. W. Heat and Thermodynamics, 4th ed. New York: McGraw-Hill Book Company, 1957, p. 59.

MECHANICAL ENGINEERING

Eighth Edition

Thermodynamics and Heat Power “The authors have adopted simple yet engaging ways to present and discuss complex concepts of thermodynamics. Solved illustrative problems are discreetly placed following the explanation of each new concept. The concepts have been introduced from the basic principles and progressively taken to the advanced level.” —Mohammad Hossain, Ph.D., York Technical College, Rock Hill, South Carolina, USA

Building on the last edition, (dedicated to exploring alternatives to coal- and oil-based energy conversion methods and published more than ten years ago), Thermodynamics and Heat Power, Eighth Edition updates the status of existing direct energy conversion methods as described in the previous work. Offering a systems approach to the analysis of energy conversion methods, this text focuses on the fundamentals involved in thermodynamics, and further explores concepts in the areas of ideal gas flow, engine analysis, air conditioning, and heat transfer. It examines energy, heat, and work in relation to thermodynamics, and also explores the properties of temperature and pressures. The book emphasizes practical mechanical systems and incorporates problems at the end of the chapters to advance the application of the material. What’s New in the Eighth Edition: • An emphasis on a systems approach to problems • More discussion of the types of heat and of entropy • Added explanations for understanding pound mass and the mole • Analysis of steady-flow gas processes, replacing the compressible flow section • The concept of paddle work to illustrate how frictional effects can be analyzed • A clearer discussion of the psychrometric chart and its usage in analyzing air conditioning systems • Updates of the status of direct energy conversion systems • A description of how the cooling tower is utilized in high-rise buildings • Practical automotive engine analysis • Expanded Brayton cycle analysis including intercooling, reheat, and regeneration and their effect on gas turbine efficiency • A description of fins and how they improve heat transfer rates • Added illustrative problems and new homework problems • Availability of a publisher’s website for fluid properties and other reference materials • Properties of the latest in commercial refrigerants This text presents an understanding of basic concepts on the subject of thermodynamics and is a definitive resource for undergraduate students in engineering programs, most specifically, students studying engineering technology. K23231

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