thermodynamics - assets - cambridge university...

www.cambridge.org© in this web service Cambridge University Press

Cambridge University Press978-0-521-19570-6 - ThermodynamicsSanford Klein and Gregory NellisFrontmatterMore information

THERMODYNAMICS

This book differs from other thermodynamics texts in its objective, whichis to provide engineers with the concepts, tools, and experience neededto solve practical real-world energy problems. The presentation integratescomputer tools (e.g., EES) with thermodynamic concepts to allow engi-neering students and practicing engineers to solve problems that they wouldotherwise not be able to solve. The use of examples, solved and explained indetail and supported with property diagrams that are drawn to scale, is ubiq-uitous in this textbook. The examples are not trivial drill problems, but rathercomplex and timely real-world problems that are of interest by themselves.As with the presentation, the solutions to these examples are complete anddo not skip steps. Similarly, the book includes numerous end-of-chapterproblems, both in the book and online. Most of these problems are moredetailed than those found in other thermodynamics textbooks. The supple-ments include complete solutions to all exercises, software downloads, andadditional content on selected topics.

Sanford Klein is currently the Bascom Ouweneel Professor of MechanicalEngineering at the University of Wisconsin, Madison. He has been on thefaculty at Wisconsin since 1977. He is the Director of the Solar Energy Lab-oratory and has been involved in many studies of solar and other types ofenergy systems. He is the author or co-author of more than 160 publica-tions relating to the analysis of energy systems. Professor Klein’s currentresearch interests are in solar energy systems and applied thermodynam-ics and heat transfer. In addition, he is actively involved in the develop-ment of engineering computer tools for both instruction and research. Heis the primary author of a modular simulation program (TRNSYS), a solarenergy system design program (F-CHART), a finite element heat transferprogram (FEHT), and the general engineering equation solving program(EES). Professor Klein is a Fellow of the American Society of MechanicalEngineers (ASME); the American Society of Heating, Refrigeration, andAir-Conditioning Engineers (ASHRAE); and the American Solar EnergySociety (ASES).

Gregory Nellis is the Elmer R. and Janet A. Kaiser Professor of MechanicalEngineering at the University of Wisconsin, Madison. He received his M.S.and Ph.D. at the Massachusetts Institute of Technology and is a memberof the ASHRAE, the ASME, the International Institute of Refrigeration(IIR), and the Cryogenic Society of America (CSA). Professor Nellis car-ries out applied research that is related to energy systems with a focus onrefrigeration technology, and he has published more than 40 journal papers.Professor Nellis’s focus has been on graduate and undergraduate education,and he has received the Polygon, Pi Tau Sigma, and Woodburn awards forexcellence in teaching as well as the Boom Award for excellence in cryo-genic research. He is the co-author of Heat Transfer (2009) with SanfordKlein.

http://www.cambridge.org/9780521195706

http://www.cambridge.org




Thermodynamics

SANFORD KLEIN

University of Wisconsin, Madison

GREGORY NELLIS

University of Wisconsin, Madison






cambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, Sao Paulo, Delhi, Tokyo, Mexico City

Cambridge University Press32 Avenue of the Americas, New York, NY 10013-2473, USA

www.cambridge.orgInformation on this title: www.cambridge.org/9780521195706

C© Sanford Klein and Gregory Nellis 2012

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.

First published 2012

Printed in the United States of America

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging in Publication data

Klein, Sanford A., 1950–Thermodynamics / Sanford Klein, Gregory Nellis.

p. cm.Includes bibliographical references and index.ISBN 978-0-521-19570-6 (hardback)1. Thermodynamics. 2. Engineering – Problems, exercises, etc. I. Nellis, Gregory. II. Title.QC311.15.K58 2011536′.7–dc22 2011001982

ISBN 978-0-521-19570-6 Hardback

Additional resources for this publication at www.cambridge.org/kleinandnellis

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-partyInternet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, orwill remain, accurate or appropriate.






CONTENTS

Preface page xv

Acknowledgments xvii

Nomenclature xix

1 BASIC CONCEPTS � 1

1.1 Overview 11.2 Thermodynamic Systems 31.3 States and Properties 4

1.3.1 State of a System 41.3.2 Measurable and Derived Properties 41.3.3 Intensive and Extensive Properties 51.3.4 Internal and External Properties 5

1.4 Balances 61.5 Introduction to EES (Engineering Equation Solver) 81.6 Dimensions and Units 11

1.6.1 The SI and English Unit Systems 11EXAMPLE 1.6-1: WEIGHT ON MARS 141.6.2 Working with Units in EES 14EXAMPLE 1.6-2: POWER REQUIRED BY A VEHICLE 15

1.7 Specific Volume, Pressure, and Temperature 241.7.1 Specific Volume 241.7.2 Pressure 241.7.3 Temperature 26References 28Problems 28

2 THERMODYNAMIC PROPERTIES � 34

2.1 Equilibrium and State Properties 342.2 General Behavior of Fluids 362.3 Property Tables 41

2.3.1 Saturated Liquid and Vapor 41EXAMPLE 2.3-1: PRODUCTION OF A VACUUM BY CONDENSATION 452.3.2 Superheated Vapor 47

Interpolation 492.3.3 Compressed Liquid 50

2.4 EES Fluid Property Data 512.4.1 Thermodynamic Property Functions 51

v






vi Contents

EXAMPLE 2.4-1: THERMOSTATIC EXPANSION VALVE 552.4.2 Arrays and Property Plots 59EXAMPLE 2.4-2: LIQUID OXYGEN TANK 63

2.5 The Ideal Gas Model 69EXAMPLE 2.5-1: THERMALLY-DRIVEN COMPRESSOR 72

2.6 The Incompressible Substance Model 78EXAMPLE 2.6-1: FIRE EXTINGUISHING SYSTEM 80References 85Problems 85

3 ENERGY AND ENERGY TRANSPORT � 92

3.1 Conservation of Energy Applied to a Closed System 923.2 Forms of Energy 93

3.2.1 Kinetic Energy 933.2.2 Potential Energy 943.2.3 Internal Energy 94

3.3 Specific Internal Energy 943.3.1 Property Tables 953.3.2 EES Fluid Property Data 96EXAMPLE 3.3-1: HOT STEAM EQUILIBRATING WITH COLD LIQUID WATER 963.3.3 Ideal Gas 1013.3.4 Incompressible Substances 106EXAMPLE 3.3-2: AIR IN A TANK 107

3.4 Heat 1103.4.1 Heat Transfer Mechanisms 111EXAMPLE 3.4-1: RUPTURE OF A HELIUM DEWAR 1123.4.2 The Caloric Theory 115

3.5 Work 116EXAMPLE 3.5-1: COMPRESSION OF AMMONIA 121EXAMPLE 3.5-2: HELIUM BALLOON 129

3.6 What is Energy and How Can you Prove that it is Conserved? 133References 137Problems 137

4 GENERAL APPLICATION OF THE FIRST LAW � 151

4.1 General Statement of the First Law 1514.2 Specific Enthalpy 155

4.2.1 Property Tables 1554.2.2 EES Fluid Property Data 1564.2.3 Ideal Gas 1564.2.4 Incompressible Substance 159

4.3 Methodology for Solving Thermodynamics Problems 159EXAMPLE 4.3-1: PORTABLE COOLING SYSTEM 161

4.4 Thermodynamic Analyses of Steady-State Applications 1634.4.1 Turbines 1634.4.2 Compressors 1654.4.3 Pumps 1664.4.4 Nozzles 1674.4.5 Diffusers 167






Contents vii

4.4.6 Throttles 1684.4.7 Heat Exchangers 168EXAMPLE 4.4-1: DE-SUPERHEATER IN AN AMMONIA REFRIGERATION SYSTEM 170

4.5 Analysis of Open Unsteady Systems 175EXAMPLE 4.5-1: HYDROGEN STORAGE TANK FOR A VEHICLE 176EXAMPLE 4.5-2: EMPTYING AN ADIABATIC TANK FILLED WITH IDEAL GAS 180EXAMPLE 4.5-3: EMPTYING A BUTANE TANK 184Reference 187Problems 187

5 THE SECOND LAW OF THERMODYNAMICS � 204

5.1 The Second Law of Thermodynamics 2045.1.1 Second Law Statements 2075.1.2 Continuous Operation 2075.1.3 Thermal Reservoir 2085.1.4 Equivalence of the Second Law Statements 209

5.2 Reversible and Irreversible Processes 210EXAMPLE 5.2-1: REVERSIBLE AND IRREVERSIBLE WORK 214

5.3 Maximum Thermal Efficiency of Heat Engines and Heat Pumps 2175.4 Thermodynamic Temperature Scale 220

EXAMPLE 5.4-1: THERMODYNAMIC TEMPERATURE SCALES 2225.5 The Carnot Cycle 225

Problems 232

6 ENTROPY � 237

6.1 Entropy, a Property of Matter 2376.2 Fundamental Property Relations 2416.3 Specific Entropy 243

6.3.1 Property Tables 2436.3.2 EES Fluid Property Data 243EXAMPLE 6.3-1: ENTROPY CHANGE DURING A PHASE CHANGE 2446.3.3 Entropy Relations for Ideal Gases 245EXAMPLE 6.3-2: SPECIFIC ENTROPY CHANGE FOR NITROGEN 2476.3.4 Entropy Relations for Incompressible Substances 249

6.4 A General Statement of the Second Law of Thermodynamics 249EXAMPLE 6.4-1: ENTROPY GENERATED BY HEATING WATER 254

6.5 The Entropy Balance 2576.5.1 Entropy Generation 2576.5.2 Solution Methodology 2606.5.3 Choice of System Boundary 260

System Encloses all Irreversible Processes 261EXAMPLE 6.5-1: AIR HEATING SYSTEM 262

System Excludes all Irreversible Processes 264EXAMPLE 6.5-2: EMPTYING AN ADIABATIC TANK WITH IDEAL GAS (REVISITED) 265

6.6 Efficiencies of Thermodynamic Devices 2666.6.1 Turbine Efficiency 266EXAMPLE 6.6-1: TURBINE ISENTROPIC EFFICIENCY 267EXAMPLE 6.6-2: TURBINE POLYTROPIC EFFICIENCY 2706.6.2 Compressor Efficiency 277






viii Contents

EXAMPLE 6.6-3: INTERCOOLED COMPRESSION 2786.6.3 Pump Efficiency 287EXAMPLE 6.6-4: SOLAR POWERED LIVESTOCK PUMP 2896.6.4 Nozzle Efficiency 292EXAMPLE 6.6-5: JET-POWERED WAGON 2946.6.5 Diffuser Efficiency 300EXAMPLE 6.6-6: DIFFUSER IN A GAS TURBINE ENGINE 3026.6.6 Heat Exchanger Effectiveness 305EXAMPLE 6.6-7: ARGON REFRIGERATION CYCLE 308

Heat Exchangers with Constant Specific Heat Capacity 312EXAMPLE 6.6-8: ENERGY RECOVERY HEAT EXCHANGER 316References 322Problems 322

7 EXERGY � 350

7.1 Definition of Exergy and Second Law Efficiency 3507.2 Exergy of Heat 351

EXAMPLE 7.2-1: SECOND LAW EFFICIENCY 3537.3 Exergy of a Flow Stream 355

EXAMPLE 7.3-1: HEATING SYSTEM 3587.4 Exergy of a System 361

EXAMPLE 7.4-1: COMPRESSED AIR POWER SYSTEM 3647.5 Exergy Balance 367

EXAMPLE 7.5-1: EXERGY ANALYSIS OF A COMMERCIAL LAUNDRY FACILITY 3697.6 Relation Between Exergy Destruction and Entropy Generation∗ (E1) 378

Problems 379

8 POWER CYCLES � 385

8.1 The Carnot Cycle 3858.2 The Rankine Cycle 388

8.2.1 The Ideal Rankine Cycle 388Effect of Boiler Pressure 395Effect of Heat Source Temperature 397Effect of Heat Sink Temperature 397

8.2.2 The Non-Ideal Rankine Cycle 3998.2.3 Modifications to the Rankine Cycle 405

Reheat 405Regeneration 410

EXAMPLE 8.2-1: SOLAR TROUGH POWER PLANT 4138.3 The Gas Turbine Cycle 426

8.3.1 The Basic Gas Turbine Cycle 427Effect of Air-Fuel Ratio 433Effect of Pressure Ratio and Turbine Inlet Temperature 434Effect of Compressor and Turbine Efficiencies 437

8.3.2 Modifications to the Gas Turbine Cycle 437Reheat and Intercooling 437

EXAMPLE 8.3-1: OPTIMAL INTERCOOLING PRESSURE 439Recuperation 442

∗ Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).






Contents ix

EXAMPLE 8.3-2: GAS TURBINE ENGINE FOR SHIP PROPULSION 4438.3.3 The Gas Turbine Engines for Propulsion 452

Turbojet Engine 452EXAMPLE 8.3-3: TURBOJET ENGINE 454

Turbofan Engine 458EXAMPLE 8.3-4: TURBOFAN ENGINE 460

Turboprop Engine 4678.3.4 The Combined Cycle and Cogeneration 467

8.4 Reciprocating Internal Combustion Engines 4688.4.1 The Spark-Ignition Reciprocating Internal Combustion Engine 468

Spark-Ignition, Four-Stroke Engine Cycle 469Simple Model of Spark-Ignition, Four-Stroke Engine 472Octane Number of Gasoline 477

EXAMPLE 8.4-1: POLYTROPIC MODEL WITH RESIDUAL COMBUSTION GAS 479Spark-Ignition, Two-Stroke Internal Combustion Engine 488

8.4.2 The Compression-Ignition Reciprocating Internal Combustion Engine 491EXAMPLE 8.4-2: TURBOCHARGED DIESEL ENGINE 493

8.5 The Stirling Engine 5018.5.1 The Stirling Engine Cycle 5028.5.2 Simple Model of the Ideal Stirling Engine Cycle∗ (E2) 504

8.6 Tradeoffs Between Power and Efficiency 5058.6.1 The Heat Transfer Limited Carnot Cycle 5058.6.2 Carnot Cycle using Fluid Streams as the Heat Source and Heat

Sink∗ (E3) 5118.6.3 Internal Irreversibilities∗ (E4) 5118.6.4 Application to other Cycles 511References 512Problems 512

9 REFRIGERATION AND HEAT PUMP CYCLES � 529

9.1 The Carnot Cycle 5299.2 The Vapor Compression Cycle 532

9.2.1 The Ideal Vapor Compression Cycle 532Effect of Refrigeration Temperature 538

9.2.2 The Non-Ideal Vapor Compression Cycle 540EXAMPLE 9.2-1: INDUSTRIAL FREEZER 542EXAMPLE 9.2-2: INDUSTRIAL FREEZER DESIGN 5459.2.3 Refrigerants 550

Desirable Refrigerant Properties 550Positive Evaporator Gage Pressure 551Moderate Condensing Pressure 551Appropriate Triple Point and Critical Point Temperatures 551High Density/Low Specific Volume at the Compressor Inlet 553High Latent Heat (Specific Enthalpy Change) of Vaporization 553High Dielectric Strength 553Compatibility with Lubricants 553Non-Toxic 554Non-Flammable 554







x Contents

Inertness and Stability 554Refrigerant Naming Convention 554Ozone Depletion and Global Warming Potential 556

9.2.4 Vapor Compression Cycle Modifications 557Liquid-Suction Heat Exchanger 559

EXAMPLE 9.2-3: REFRIGERATION CYCLE WITH A LIQUID-SUCTION HEATEXCHANGER 560

Liquid Overfed Evaporator 564Intercooled Cycle 567Economized Cycle 568Flash-Intercooled Cycle 571

EXAMPLE 9.2-4: FLASH INTERCOOLED CYCLE FOR A BLAST FREEZER 571EXAMPLE 9.2-5: CASCADE CYCLE FOR A BLAST FREEZER 578

9.3 Heat Pumps 584EXAMPLE 9.3-1: HEATING SEASON PERFORMANCE FACTOR 588

9.4 The Absorption Cycle 5989.4.1 The Basic Absorption Cycle 5989.4.2 Absorption Cycle Working Fluids∗ (E6) 601

9.5 Recuperative Cryogenic Cooling Cycles 6019.5.1 The Reverse Brayton Cycle 6039.5.2 The Joule-Thomson Cycle 6119.5.3 Liquefaction Cycles∗ (E7) 614

9.6 Regenerative Cryogenic Cooling Cycles∗ (E8) 614References 614Problems 615

10 PROPERTY RELATIONS FOR PURE FLUIDS � 629

10.1 Equations of State for Pressure, Volume, and Temperature 62910.1.1 Compressibility Factor and Reduced Properties 63010.1.2 Characteristics of the Equation of State 633

Limiting Ideal Gas Behavior 633The Boyle Isotherm 633Critical Point Behavior 634

10.1.3 Two-Parameter Equations of State 637The van der Waals Equation of State 637

EXAMPLE 10.1-1: APPLICATION OF THE VAN DER WAALS EQUATION OF STATE 641The Dieterici Equation of State 646

EXAMPLE 10.1-2: DIETERICI EQUATION OF STATE 646The Redlich-Kwong Equation of State 649The Redlich-Kwong-Soave (RKS) Equation of State 650The Peng-Robinson (PR) Equation of State 651

EXAMPLE 10.1-3: PENG-ROBINSON EQUATION OF STATE 65310.1.4 Multiple Parameter Equations of State 656

10.2 Application of Fundamental Property Relations 65710.2.1 The Fundamental Property Relations 65810.2.2 Complete Equations of State 659EXAMPLE 10.2-1: USING A COMPLETE EQUATION OF STATE 660EXAMPLE 10.2-2: THE REDUCED HELMHOLTZ EQUATION OF STATE 661







Contents xi

10.3 Derived Thermodynamic Properties 67010.3.1 Maxwell’s Relations 67010.3.2 Calculus Relations for Partial Derivatives 67210.3.3 Derived Relations for u, h, and s 673EXAMPLE 10.3-1: ISOTHERMAL COMPRESSION PROCESS 67610.3.4 Derived Relations for other Thermodynamic Quantities 681EXAMPLE 10.3-2: SPEED OF SOUND OF CARBON DIOXIDE 68210.3.5 Relations Involving Specific Heat Capacity 685

10.4 Methodology for Calculating u, h, and s 688EXAMPLE 10.4-1: CALCULATING THE PROPERTIES OF ISOBUTANE 692

10.5 Phase Equilibria for Pure Fluids 69710.5.1 Criterion for Phase Equilibrium 69710.5.2 Relations between Properties during a Phase Change 699EXAMPLE 10.5-1: EVALUATING A NEW REFRIGERANT 70110.5.3 Estimating Saturation Properties using an Equation of State∗ (E9) 703

10.6 Fugacity 70410.6.1 The Fugacity of Gases 706

Calculating Fugacity using the RKS and PR Equations of State∗ (E10) 70810.6.2 The Fugacity of Liquids 708References 710Problems 710

11 MIXTURES AND MULTI-COMPONENT PHASE EQUILIBRIUM � 721

11.1 P-v-T Relations for Ideal Gas Mixtures 72111.1.1 Composition Relations 72111.1.2 Mixture Rules for Ideal Gas Mixtures 723

11.2 Energy, Enthalpy, and Entropy for Ideal Gas Mixtures 72611.2.1 Changes in Properties for Ideal Gas Mixtures with Fixed Composition 72811.2.2 Enthalpy and Entropy Change of Mixing 729EXAMPLE 11.2-1: POWER AND EFFICIENCY OF A GAS TURBINE 731EXAMPLE 11.2-2: SEPARATING CO2 FROM THE ATMOSPHERE 734

11.3 P-v-T Relations for Non-Ideal Gas Mixtures 73811.3.1 Dalton’s Rule 73811.3.2 Amagat’s Rule 73911.3.3 Empirical Mixing Rules 740

Kay’s Rule 740Mixing Rules 741

EXAMPLE 11.3-1: SPECIFIC VOLUME OF A GAS MIXTURE 74211.4 Energy and Entropy for Non-Ideal Gas Mixtures 746

11.4.1 Enthalpy and Entropy Changes of Mixing 74611.4.2 Enthalpy and Entropy Departures 749

Molar Specific Enthalpy and Entropy Departures from a Two-ParameterEquation of State∗ (E11) 751

11.4.3 Enthalpy and Entropy for Ideal Solutions 75211.4.4 Enthalpy and Entropy using a Two-Parameter Equation of State 753

The RKS Equation of State∗ (E12) 753The Peng-Robinson Equation of State 754

EXAMPLE 11.4-1: ANALYSIS OF A COMPRESSOR WITH A GAS MIXTURE 754







xii Contents

11.4.5 Peng-Robinson Library Functions 764EXAMPLE 11.4-2: ANALYSIS OF A COMPRESSOR WITH A GAS MIXTURE

(REVISITED) 76511.5 Multi-Component Phase Equilibrium 769

11.5.1 Criterion of Multi-Component Phase Equilibrium∗ (E13) 76911.5.2 Chemical Potentials 76911.5.3 Evaluation of Chemical Potentials for Ideal Gas Mixtures 77111.5.4 Evaluation of Chemical Potentials for Ideal Solutions∗ (E14) 77211.5.5 Evaluation of Chemical Potentials for Liquid Mixtures∗ (E15) 77211.5.6 Applications of Multi-Component Phase Equilibrium 773EXAMPLE 11.5-1: USE OF A MIXTURE IN A REFRIGERATION CYCLE 776

11.6 The Phase Rule 783References 784Problems 784

12 PSYCHROMETRICS � 791

12.1 Psychrometric Definitions 791EXAMPLE 12.1-1: BUILDING AIR CONDITIONING SYSTEM 795

12.2 Wet Bulb and Adiabatic Saturation Temperatures 79912.3 The Psychrometric Chart and EES’ Psychrometric Functions 802

12.3.1 Psychrometric Properties 80212.3.2 The Psychrometric Chart 804EXAMPLE 12.3-1: BUILDING AIR CONDITIONING SYSTEM (REVISITED) 80812.3.3 Psychrometric Properties in EES 810EXAMPLE 12.3-2: BUILDING AIR CONDITIONING SYSTEM (REVISITED AGAIN) 812

12.4 Psychrometric Processes for Comfort Conditioning 81412.4.1 Humidification Processes 815EXAMPLE 12.4-1: HEATING/HUMIDIFICATION SYSTEM 81612.4.2 Dehumidification Processes 822EXAMPLE 12.4-2: AIR CONDITIONING SYSTEM 82312.4.3 Evaporative Cooling 82712.4.4 Desiccants∗ (E16) 829

12.5 Cooling Towers 83012.5.1 Cooling Tower Nomenclature 83112.5.2 Cooling Tower Analysis 832EXAMPLE 12.5-1: ANALYSIS OF A COOLING TOWER 834

12.6 Entropy for Psychrometric Mixtures∗ (E17) 838References 838Problems 838

13 COMBUSTION � 852

13.1 Introduction to Combustion 85213.2 Balancing Chemical Reactions 854

13.2.1 Air as an Oxidizer 85513.2.2 Methods for Quantifying Excess Air 85613.2.3 Psychrometric Issues 857EXAMPLE 13.2-1: COMBUSTION OF A PRODUCER GAS 858

13.3 Energy Considerations 864







Contents xiii

13.3.1 Enthalpy of Formation 86413.3.2 Heating Values 866EXAMPLE 13.3-1: HEATING VALUE OF A PRODUCER GAS 87113.3.3 Enthalpy and Internal Energy as a Function of Temperature 873EXAMPLE 13.3-2: PROPANE HEATER 87513.3.4 Use of EES for Determining Properties 879EXAMPLE 13.3-3: FURNACE EFFICIENCY 88213.3.5 Adiabatic Reactions 889EXAMPLE 13.3-4: DETERMINATION OF THE EXPLOSION PRESSURE OF METHANE 894

13.4 Entropy Considerations 898EXAMPLE 13.4-1: PERFORMANCE OF A GAS TURBINE ENGINE 901

13.5 Exergy of Fuels∗ (E18) 907References 907Problems 908

14 CHEMICAL EQUILIBRIUM � 922

14.1 Criterion for Chemical Equilibrium 92214.2 Reaction Coordinates 924

EXAMPLE 14.2-1: SIMULTANEOUS CHEMICAL REACTIONS 92714.3 The Law of Mass Action 931

14.3.1 The Criterion of Equilibrium in terms of Chemical Potentials 93114.3.2 Chemical Potentials for an Ideal Gas Mixture 93314.3.3 Equilibrium Constant and the Law of Mass Action for Ideal Gas Mixtures 933EXAMPLE 14.3-1: REFORMATION OF METHANE 93514.3.4 Equilibrium Constant and the Law of Mass Action for an Ideal Solution 938EXAMPLE 14.3-2: AMMONIA SYNTHESIS 939

14.4 Alternative Methods for Chemical Equilibrium Problems 94314.4.1 Direct Minimization of Gibbs Free Energy 944EXAMPLE 14.4-1: REFORMATION OF METHANE (REVISITED) 94514.4.2 Lagrange Method of Undetermined Multipliers 949EXAMPLE 14.4-2: REFORMATION OF METHANE (REVISITED AGAIN) 951

14.5 Heterogeneous Reactions∗ (E19) 95314.6 Adiabatic Reactions 954

EXAMPLE 14.6-1: ADIABATIC COMBUSTION OF HYDROGEN 954EXAMPLE 14.6-2: ADIABATIC COMBUSTION OF ACETYLENE 960Reference 967Problems 967

15 STATISTICAL THERMODYNAMICS � 972

15.1 A Brief Review of Quantum Theory History 97315.1.1 Electromagnetic Radiation 97315.1.2 Extension to Particles 975

15.2 The Wave Equation and Degeneracy for a Monatomic Ideal Gas 97615.2.1 Probability of Finding a Particle 97615.2.2 Application of a Wave Equation 97615.2.3 Degeneracy 979

15.3 The Equilibrium Distribution 97915.3.1 Macrostates and Thermodynamic Probability 980







xiv Contents

15.3.2 Identification of the Most Probable Macrostate 98215.3.3 The Significance of β 98515.3.4 Boltzmann’s Law 987

15.4 Properties and the Partition Function 98915.4.1 Definition of the Partition Function 98915.4.2 Internal Energy from the Partition Function 99015.4.3 Entropy from the Partition Function 99115.4.4 Pressure from the Partition Function 992

15.5 Partition Function for an Monatomic Ideal Gas 99315.5.1 Pressure for a Monatomic Ideal Gas 99415.5.2 Internal Energy for a Monatomic Ideal Gas 99515.5.3 Entropy for a Monatomic Ideal Gas 995EXAMPLE 15.5-1: CALCULATION OF ABSOLUTE ENTROPY VALUES 997

15.6 Extension to More Complex Particles 99815.7 Heat and Work from a Statistical Thermodynamics Perspective 1001

References 1004Problems 1005

16 COMPRESSIBLE FLOW∗ (E20) � 1009

Problems 1009

Appendices

A: Unit Conversions and Useful Information 1015

B: Property Tables for Water 1019

C: Property Tables for R134a 1031

D: Ideal Gas & Incompressible Substances 1037

E: Ideal Gas Properties of Air 1039

F: Ideal Gas Properties of Common Combustion Gases 1045

G: Numerical Solution to ODEs 1056

H: Introduction to Maple∗ (E26) 1057

Index 1059







PREFACE

Thermodynamics is a mature science. Many excellent engineering textbooks have beenwritten on the subject, which leads to the question: Why yet another textbook on classicalthermodynamics? There is a simple answer to this question: this book is different. Theobjective of this book is to provide engineers with the concepts, tools, and experienceneeded to solve practical real-world energy problems. With this in mind, the focus of thiseffort has been to integrate a computer tool with thermodynamic concepts in order toallow engineering students and practicing engineers to tackle problems that they wouldotherwise not be able to solve.

It is generally acknowledged that students need to solve problems in order to inte-grate concepts and skills. The effort required to solve a thermodynamics problem canbe broken into two parts. First, it is necessary to identify the fundamental relationshipsthat describe the problem. The set of equations that leads to a useful solution to aproblem results from application of appropriate balances and rate relations, simplifiedwith justified assumptions. Identifying the necessary equations is the conceptual part ofthe problem, and no computer program can provide this capability in general. Properapplication of the First and Second Laws of Thermodynamics is at the heart of thisprocess. The ability to identify the appropriate equations does not come easily to mostthermodynamics students. This is an area in which problem-solving experience is helpful.A distinguishing feature of this textbook is that it presents detailed examples and discus-sion that explain how to apply thermodynamics concepts identify a set of equations thatwill provide solutions to non-trivial problems.

Once the appropriate equations have been identified, they must be solved. In ourexperience, much of the time and effort required to solve thermodynamics problemsresults from looking up property information in tables and solving the appropriateequations. Though necessary for obtaining a solution, these tasks contribute little tothe learning process. For example, once the student is familiar with the use of propertytables, further use of the tables does not contribute to the student’s grasp of the subject –nor does doing the tedious algebra that is required to solve a large set of equations.Practical problems that focus on real engineering issues tend to be more interesting tostudents, but also more mathematically complex. The time and effort required to doproblems without computing tools may actually detract from learning the subject matterby forcing the student to focus on the mathematical complexity of the problem ratherthan on the underlying concepts.

The motivation for writing this book is a result of our experience in teaching mechan-ical engineering thermodynamics in a manner that is tightly integrated with the EES(Engineering Equation Solver) program. EES eliminates much of the mathematicalcomplexity involved in solving thermodynamics problems by providing a large bank ofhigh-accuracy property data and the capability to solve large sets of simultaneous alge-braic and differential equations. EES also provides the capability to check equations forunit consistency; do parametric studies; produce high-quality plots; and apply numeri-cal integration, optimization, and uncertainty analyses. Using EES, students can easily

xv






xvi Preface

obtain solutions to interesting practical problems that involve nonlinear and implicit setsof equations. They can quickly display the results of these calculations in plots. They canconduct design studies by varying the inputs or constraints and by applying optimizationmethods. EES is a powerful tool that can be of great advantage for solving thermody-namics problems. However, like all tools, some training and experience are needed touse it effectively. The presentation in this book teaches readers by example how to useEES most effectively, with more advanced features introduced in a sequential mannerthroughout the text.

A review of the table of contents shows that the topics and order of presentation aresimilar to those provided in current mechanical engineering thermodynamics textbooks.Sufficient material is provided for both undergraduate and graduate thermodynamicscourses. The book can be used in a single-semester undergraduate course by appro-priately selecting from the available topics. For example, we typically do not coverChapter 7 and Chapters 14–16 in our single-semester undergraduate course. Topics suchas absorption cycles (9.4), cryogenic cooling cycles (9.5–6), desiccants (12.4.4), exergyrelations for psychrometrics (12.6), and fuels (13.5) are also usually not included in ourundergraduate courses. The reason that this book can be used for a first course (despiteits expanded content) while remaining an effective graduate-level textbook is that allconcepts and methods are presented in detail, starting at the beginning without skippingsteps. You will not find many occurrences of the clause, “it can be shown that . . . ” inthis textbook. The use of examples, solved and explained in detail and supported withproperty diagrams that are drawn to scale, is ubiquitous in this textbook. The examplesare not trivial drill problems, but rather complex and timely real-world problems thatare of interest by themselves. As with the presentation, the solutions to these examplesare complete and do not skip steps.

The book includes a large collection of real-world problems at the end of eachchapter. A larger selection of problems is provided on the Web site associated withthis textbook (www.cambridge.org/kleinandnellis). Most of the problems provided withthis book are more detailed than those provided in currently popular thermodynamicstextbooks. It may appear upon first review that these problems are too complex foruse in a first course in thermodynamics. Our experience, however, is that the organizedapproach to problem solving presented in this textbook, combined with the use of EES,allows undergraduates to successfully solve these more detailed problems. Indeed, wehave found that students are more interested in the course because the problems arechallenging and relevant. Complete solutions to all problems are provided to instructors.

This book is unusual in its linking of thermodynamic concepts with detailed instruc-tions for using a powerful equation-solving computer tool that eliminates much of thetedious effort that is otherwise needed to solve thermodynamics problems. It fills anobvious void that we have encountered in teaching both undergraduate and graduatethermodynamics courses. The text and the EES program were developed over manyyears from our experiences teaching the undergraduate and graduate thermodynamicscourses at the University of Wisconsin. It our hope that this text will be a lifelong resourcefor practicing engineers.

Sanford KleinGregory NellisJune 2011






ACKNOWLEDGMENTS

The development of this book has taken several years and a substantial effort. Thishas only been possible due to the collegial and supportive atmosphere that makes theMechanical Engineering Department at the University of Wisconsin such a unique andimpressive place. In particular, we would like to acknowledge Doug Reindl and JohnPfotenhauer for their encouragement throughout the process.

Several years of undergraduate and graduate students and faculty have used ourinitial drafts of this manuscript. These students have had to endure carrying multiplevolumes of poorly bound paper with no index and many typographical errors. Theirfeedback has been invaluable to the development of the book.

More than two decades of students and faculty have contributed to the continuousdevelopment of the EES program. This program was initially developed specifically foruse in undergraduate thermodynamics classes but it has expanded to the point where itis now a commercial program that is widely used in the HVAC&R and other industries.The suggestions and feedback of users at the University of Wisconsin, other universities,and various companies have driven the development of EES to the useful tool that it istoday.

Preparing this book has necessarily reduced the time that we have been able to spendwith our families. We are grateful to them for allowing us this indulgence. In particular,we wish to thank Jan Klein and Jill, Jacob, Spencer, and Sharon Nellis. We could nothave completed this book without their continuous support.

Finally, we are indebted to Cambridge University Press and in particular PeterGordon for giving us this opportunity and helping us through the process of bringing ourmanuscript to this final state.

xvii






NOMENCLATURE

a specific Helmholtz free energy (J/kg)parameter in an equation of state

A area (m2)Helmholtz free energy (J)amplitude of wave

A∗ critical area (m2)Ac cross-sectional area (m2)Af frontal area (m2)AF air-fuel ratio (-)As surface area (m2)b parameter in an equation of state (m3/kg)B parameter defined in Eq. (10-71)

parameter defined in Eq. (15-106)BPR bypass ratio (-)bwr back work ratio (-)c specific heat capacity (J/kg-K)

speed of sound (m/s)speed of light in a vacuum (3×108 m/s)

c molar specific heat of an incompressible substance (J/kmol-K)C number of chemical species in a mixture (-)C capacitance rate (product of mass flow rate and specific heat) (W/K)CD drag coefficient (-)COP coefficient of performance (-)cP specific heat capacity at constant pressure (J/kg-K)cP molar specific heat capacity at constant pressure (J/kmol-K)CR capacitance ratio (-)CR compression ratio (-)cv specific heat capacity at constant volume (J/kg-K)cv molar specific heat capacity at constant volume (J/kmol-K)D diameter (m)d⇀x differential displacement vector (m)E energy (J)

voltage (Volt)number of elements (-)

E rate of energy transfer (W)E intensity of radiation (W/m2)Eb,λ blackbody spectral emissive power (W/m2-μm)EER energy efficiency rating (Btu/W-hr)ei,j number of moles of element j per mole of substance i (-)Ej number of moles of element j (kmol)

xix






xx Nomenclature

f frequency (Hz)fugacity (Pa)partition function (-)fraction of flow (-)

F force (N)number of intensive properties (for Gibbs phase rule)

⇀

F force vector (N)fi fugacity of pure fluid i (Pa)f i partial fugacity of component i in a mixture (Pa)g gravitational acceleration (m/s2)

specific Gibbs free energy (J/kg)G Gibbs free energy (J)g molar specific Gibbs free energy (J/kmol)gi degeneracy of energy level i (-)h specific enthalpy (J/kg)

Planck’s constant (6.625×10−34 J/s)h molar specific enthalpy (J/kmol)H enthalpy (J)H enthalpy flow rate (W)hav enthalpy of an air-water vapor mixture per kg dry air (J/kga)hconv convective heat transfer coefficient (W/m2-K)HC heat of combustion (J/kg)hdep molar specific enthalpy departure (J/kmol or J/kg)hdep,i molar specific enthalpy departure of component i in a mixture (J/kmol)hfg specific enthalpy of vaporization (J/kg)hfg molar specific enthalpy of vaporization (J/kmol)hform molar specific enthalpy of formation (J/kmol)HHV higher heating value (J/kmol)hi molar specific enthalpy of component i in a mixture (J/kmol)HSPF heating season performance factor (Btu/W-hr)hstd standardized molar specific enthalpy (J/kmol)HV heating value (J/kmol)i current (Amp)i unit vector in the x-directionI moment of inertia (kg-m2)j unit vector in the y-directionk thermal conductivity (W/m-K)

ratio of specific heat capacities, cP/cv (-)Boltzmann’s constant (1.3805×10−23 J/K)

k unit vector in the z-directionK spring constant (N/m)KE kinetic energy (J)kij binary mixing parameter (-)Kj equilibrium constant for reaction j (-)KP coefficient of pressure recovery (-)KT isothermal compressibility (1/Pa)L the dimension lengthL distance or length (m)LHV lower heating value (J/kmol or J/kg)m mass (kg)

parameter in the RKS and PR equations of state (-)m mass flow rate (kg/s)






Nomenclature xxi

M the dimension massM Mach number (-)MEP mean effective pressure (Pa)mfi mass fraction of component i in a mixture (-)mi mass of component i in a mixture (kg)MW molar mass (kg/kmol)n number of moles (kmol)

polytropic exponent (-)quantum number (-)

N number of particles (-)number (-)engine speed (rpm)

NA Avogadro’s number (6.022×1026 kmol−1)ni number of moles of component i in a mixture (kmol)Ni number of particles in energy level i (-)NTU number of transfer units (-)p momentum (N-s)P pressure (Pa)

probability (-)P0 standard state pressure or low pressure at which the ideal gas law is valid (Pa)P0 dead state pressure (Pa)

stagnation pressure (Pa)Patm atmospheric pressure (Pa)Pcrit critical pressure (Pa)Pcrit,eff effective critical (or pseudo-critical) pressure of a mixture (Pa)PE potential energy (J)Pgage gage pressure (Pa)Pi partial pressure of component i in a mixture (Pa)PLF part load factor (-)Pr reduced pressure (-)PR pressure ratio (-)Pr,eff effective reduced (or pseudo-reduced) pressure of a mixture (-)Q heat transfer (J)

molar quality (-)Q heat transfer rate (W)Q′′ heat transfer rate per unit area (W/m2)Q1→2 heat transfer during the process of going from state 1 to state 2 (J)R ideal gas constant (J/kg-K)

radius (m)resistance �

Runiv universal gas constant (8314.3 J/kmol-K)s specific entropy (J/kg-K)s molar specific entropy (J/kmol-K)S entropy (J/K)S rate of entropy transfer (W/K)sav entropy of an air–water vapor mixture per kg dry air (J/kga-K)sdep molar specific entropy departure (J/kmol-K)sdep,i molar specific entropy departure of pure gas i in a mixture (J/kmol-K)Sgen entropy generation (J/K)Sgen rate of entropy generation (W/K)Sm entropy transfer due to mass transfer (J/K)Sm rate of entropy transfer due to mass transfer (W/K)






xxii Nomenclature

si molar specific entropy of component i in a mixture (J/kmol-K)SQ entropy transfer due to heat (J/K)SQ rate of entropy transfer due to heat (W/K)SEER seasonal energy efficiency rating (Btu/W-hr)SFC specific fuel consumption (kg/s-N)SHR sensible heat ratio (-)t the dimension timet time (s)T the dimension temperatureT temperature (K)T0 dead state temperature (K)

stagnation temperature (K)TB Boyle temperature (K)Tcrit critical temperature (K)Tcrit,eff effective critical (or pseudo-critical) temperature of a mixture (K)Tdp dew-point temperature (K)Tr reduced temperature (-)Tr,eff effective reduced (or pseudo-reduced) temperature of a mixture (-)Tr,B reduced Boyle temperature (-)Twb wet bulb temperature (K)th thickness (m)u specific internal energy (J/kg)u molar specific internal energy (J/kmol)ui partial molar specific internal energy of component i in a mixture (J/kmol)ustd standardized molar internal energy (J/kmol)U internal energy (J)UA conductance (W/K)

building heat loss coefficient (W/K)v specific volume (m3/kg)v molar specific volume (m3/kmol)vi molar specific volume of component i in a mixture (m3/kmol)V volume (m3)V volumetric flow rate (m3/s)V velocity (m/s)vav volume of an air–water vapor mixture per kg dry air (m3/kga)vcrit critical specific volume (m3/kg)vcrit critical molar specific volume (m3/kmol)vcrit,eff effective critical (or pseudo-critical) specific volume of a mixture (m3/kg)Vdisp displacement rate of a compressor (m3/s)Vi volume of component i in a mixture (m3)Vi partial molar volume of component i in a mixture(m3/kmol)vr reduced specific volume (-)vr,eff effective reduced (or pseudo-reduced) specific volume (-)W work (J)

weight (N)W1→2 work transfer during the process of going from state 1 to state 2 (J)Wlost “lost” work or exergy destruction (J)W work transfer rate, power (W)x quality

position (m)displacement (m)

X exergy (J)






Nomenclature xxiii

Xdes exergy destroyed (J)Xf exergy associated with a mass transfer (J)xi mole fraction of component i in the liquid phase of a mixture (-)XQ exergy associated with a heat transfer (J)Xs exergy of a system (J)x f specific exergy of a flowing substance (J/kg)xs specific exergy of a system (J/kg)Xdes rate of exergy destruction, also called the irreversibility rate (W)Xf rate of exergy flow with mass flow (W)XQ rate of exergy flow with heat (W)yi mole fraction of component i in a mixture (-)

mole fraction of component i in the vapor phase of a mixture (-)z elevation in a gravitational field (m)Z compressibility factor (-)Zcrit critical compressibility factor (-)zi total mole fraction of component i in a mixture (-)Zi compressibility factor for component i in a mixture (-)

Greek Symbols

α reduced Helmholtz free energy (-)parameter in the RK or PR equation of state (-)

β parameter defined in Eq. (15-101) (1/J)δ uncertainty in some measurement

reduced density (-)differential amount

� change of some property of a system�Go

j standard state Gibbs free energy change of reaction (J)�hfg latent heat of vaporization (J/kg)�hmix molar specific enthalpy change of mixing (J/kmol)�P pressure drop (Pa)�smix molar specific entropy change of mixing (J/kmol-K)�T approach temperature difference (K)�vmix molar specific volume change of mixing (m3/kmol)�Vmix volume change of mixing (m3)ε Lennard-Jones energy potential (J)

emissivity (-)effectiveness of a heat exchanger (-)reaction coordinate or degree of reaction (kmol)

εi energy associated with a energy level i (J)ε j reaction coordinate for reaction j (kmol)φ fugacity coefficient (-)

relative humidity (-)γ surface tension (N/m)η efficiency (-)η2 Second Law efficiency (-)λ wavelength (μm)

undetermined multiplier number of phases (-)θ angle (radian)ρ density (kg/m3)






xxiv Nomenclature

σ Lennard-Jones length potential (m)Stefan-Boltzmann constant (5.67×10−8 W/m2-K4)

τ torque (N-m)inverse reduced temperature (-)

μ viscosity (Pa-s)μf,i chemical potential of component i in the liquid phase of a mixture (J/kmol)μg,i chemical potential of component i in the vapor phase of a mixture (J/kmol)μJT Joule-Thomson coefficient (K/Pa)νi stoichiometric coefficient for component iνi, j stoichiometric coefficient for component i in reaction jψ constraint function that evaluates to zeroω angular velocity (rad/s)

acentric factor (-)humidity ratio (kgv/kga)

ωeff effective acentric factor of a mixture (-)� thermodynamic probability (-)

Superscripts

∗ quantity evaluated at location of critical areao under conditions where fluid behaves as an ideal gas (i.e., at low pressure)

Subscripts

a dry airact actualamb ambientas adiabatic saturationatm atmosphericav psychrometric property defined on a per mass of dry air basisavg averageb boundary

boilerblackbody

B Boyle isothermBDC bottom dead centerBE Bose-Einstein modelc compressorC cold fluid in a heat exchanger or cold thermal reservoircomp compression processcond condensercrit critical, related to the critical pointCTHB cold-to-hot blow processcv associated with a control volumecyl cylinderd diffuser

downstream of a normal shockdrag

des destroyed within systemdp dew pointec evaporative cooler






Nomenclature xxv

evap evaporatorexp expansion processf saturated liquid

fuelfurnace

FD Fermi-Dirac modelg saturated vaporgage gagegen generated within system

generator in an absorption cycleH hot fluid in a heat exchanger or hot thermal reservoir

heat pumpHTCB hot-to-cold blow processhf heat transfer fluidhx heat exchangeri the ith component in a mixtureIC based on incompressible modelin in, entering a systemini initial, at time = 0load refrigeration or building loadmax maximum or maximum possiblemin minimum or minimum possiblemix associated with a mixturemp maximum powerMB Maxwell-Boltzmann modeln nozzlenet net outputnom nominal valueo overall

stagnationinitial

p pumppistonpropulsive

P related to an isobaric process, at constant pressureassociated with the products of a reaction

pure associated with a pure substanceout out, leaving a systemR refrigeration cycle

associated with the reactants of a reactionRankine Rankine cycler reducedref referenceres residual componentrev reversiblerh reheat cycle or reheaters associated with a reversible devicesat saturatedsc subcoolsh superheatsur surroundings






xxvi Nomenclature

t turbineat time t

T related to an isothermal process, at constant temperatureTDC top dead centerth thermalu upstream of a normal shockv valve

water vaporvol volumetricwb wet bulbx in the x-directiony in the y-directionz in the z-directionλ spectral – as a function of wavelength∞ free-stream fluid

Other Notes

a specific property on molar basisf(A) function of variable A�A change in variable AdA differential change in the property AδA differential amount of the quantity A

uncertainty in the quantity AA rate of transfer of quantity A






THERMODYNAMICS




thermodynamics - assets - cambridge university...

Documents