Thermodynamics

THERMODYNAMICSThis book differs from other thermodynamics texts in its objective, whichistoprovideengineerswiththeconcepts, tools, andexperienceneededto solve practical real-world energy problems. The presentation integratescomputertools(e.g., EES)withthermodynamicconceptstoallowengi-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 inthis 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 Kleins 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 nite 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 Nelliss 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.ThermodynamicsSANFORD KLEINUniversity of Wisconsin, MadisonGREGORY NELLISUniversity of Wisconsin, Madisoncambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, S ao Paulo, Delhi, Tokyo, Mexico CityCambridge University Press32 Avenue of the Americas, New York, NY 10013-2473, USAwww.cambridge.orgInformation on this title: www.cambridge.org/9780521195706C Sanford Klein and Gregory Nellis 2012This 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 2012Printed in the United States of AmericaA catalog record for this publication is available from the British Library.Library of Congress Cataloging in Publication dataKlein, Sanford A., 1950Thermodynamics / 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

.7dc22 2011001982ISBN 978-0-521-19570-6 HardbackAdditional resources for this publication at www.cambridge.org/kleinandnellisCambridge 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.CONTENTSPreface page xvAcknowledgments xviiNomenclature xix1 BASIC CONCEPTS r11.1 Overview 11.2 Thermodynamic Systems 31.3 States and Properties 41.3.1 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 51.4 Balances 61.5 Introduction to EES (Engineering Equation Solver) 81.6 Dimensions and Units 111.6.1 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 151.7 Specic Volume, Pressure, and Temperature 241.7.1 Specic Volume 241.7.2 Pressure 241.7.3 Temperature 26References 28Problems 282 THERMODYNAMIC PROPERTIES r342.1 Equilibrium and State Properties 342.2 General Behavior of Fluids 362.3 Property Tables 412.3.1 Saturated Liquid and Vapor 41EXAMPLE 2.3-1: PRODUCTION OF A VACUUM BY CONDENSATION 452.3.2 Superheated Vapor 47Interpolation 492.3.3 Compressed Liquid 502.4 EES Fluid Property Data 512.4.1 Thermodynamic Property Functions 51vvi ContentsEXAMPLE 2.4-1: THERMOSTATIC EXPANSION VALVE 552.4.2 Arrays and Property Plots 59EXAMPLE 2.4-2: LIQUID OXYGEN TANK 632.5 The Ideal Gas Model 69EXAMPLE 2.5-1: THERMALLY-DRIVEN COMPRESSOR 722.6 The Incompressible Substance Model 78EXAMPLE 2.6-1: FIRE EXTINGUISHING SYSTEM 80References 85Problems 853 ENERGY AND ENERGY TRANSPORT r923.1 Conservation of Energy Applied to a Closed System 923.2 Forms of Energy 933.2.1 Kinetic Energy 933.2.2 Potential Energy 943.2.3 Internal Energy 943.3 Specic 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 1073.4 Heat 1103.4.1 Heat Transfer Mechanisms 111EXAMPLE 3.4-1: RUPTURE OF A HELIUM DEWAR 1123.4.2 The Caloric Theory 1153.5 Work 116EXAMPLE 3.5-1: COMPRESSION OF AMMONIA 121EXAMPLE 3.5-2: HELIUM BALLOON 1293.6 What is Energy and How Can you Prove that it is Conserved? 133References 137Problems 1374 GENERAL APPLICATION OF THE FIRST LAW r1514.1 General Statement of the First Law 1514.2 Specic Enthalpy 1554.2.1 Property Tables 1554.2.2 EES Fluid Property Data 1564.2.3 Ideal Gas 1564.2.4 Incompressible Substance 1594.3 Methodology for Solving Thermodynamics Problems 159EXAMPLE 4.3-1: PORTABLE COOLING SYSTEM 1614.4 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 167Contents vii4.4.6 Throttles 1684.4.7 Heat Exchangers 168EXAMPLE 4.4-1: DE-SUPERHEATER IN AN AMMONIA REFRIGERATION SYSTEM 1704.5 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 1875 THE SECOND LAW OF THERMODYNAMICS r2045.1 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 2095.2 Reversible and Irreversible Processes 210EXAMPLE 5.2-1: REVERSIBLE AND IRREVERSIBLE WORK 2145.3 Maximum Thermal Efciency of Heat Engines and Heat Pumps 2175.4 Thermodynamic Temperature Scale 220EXAMPLE 5.4-1: THERMODYNAMIC TEMPERATURE SCALES 2225.5 The Carnot Cycle 225Problems 2326 ENTROPY r2376.1 Entropy, a Property of Matter 2376.2 Fundamental Property Relations 2416.3 Specic Entropy 2436.3.1 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 2496.4 A General Statement of the Second Law of Thermodynamics 249EXAMPLE 6.4-1: ENTROPY GENERATED BY HEATING WATER 2546.5 The Entropy Balance 2576.5.1 Entropy Generation 2576.5.2 Solution Methodology 2606.5.3 Choice of System Boundary 260System Encloses all Irreversible Processes 261EXAMPLE 6.5-1: AIR HEATING SYSTEM 262System Excludes all Irreversible Processes 264EXAMPLE 6.5-2: EMPTYING AN ADIABATIC TANK WITH IDEAL GAS (REVISITED) 2656.6 Efciencies of Thermodynamic Devices 2666.6.1 Turbine Efciency 266EXAMPLE 6.6-1: TURBINE ISENTROPIC EFFICIENCY 267EXAMPLE 6.6-2: TURBINE POLYTROPIC EFFICIENCY 2706.6.2 Compressor Efciency 277viii ContentsEXAMPLE 6.6-3: INTERCOOLED COMPRESSION 2786.6.3 Pump Efciency 287EXAMPLE 6.6-4: SOLAR POWERED LIVESTOCK PUMP 2896.6.4 Nozzle Efciency 292EXAMPLE 6.6-5: JET-POWERED WAGON 2946.6.5 Diffuser Efciency 300EXAMPLE 6.6-6: DIFFUSER IN A GAS TURBINE ENGINE 3026.6.6 Heat Exchanger Effectiveness 305EXAMPLE 6.6-7: ARGON REFRIGERATION CYCLE 308Heat Exchangers with Constant Specic Heat Capacity 312EXAMPLE 6.6-8: ENERGY RECOVERY HEAT EXCHANGER 316References 322Problems 3227 EXERGY r3507.1 Denition of Exergy and Second Law Efciency 3507.2 Exergy of Heat 351EXAMPLE 7.2-1: SECOND LAW EFFICIENCY 3537.3 Exergy of a Flow Stream 355EXAMPLE 7.3-1: HEATING SYSTEM 3587.4 Exergy of a System 361EXAMPLE 7.4-1: COMPRESSED AIR POWER SYSTEM 3647.5 Exergy Balance 367EXAMPLE 7.5-1: EXERGY ANALYSIS OF A COMMERCIAL LAUNDRY FACILITY 3697.6 Relation Between Exergy Destruction and Entropy Generation (E1) 378Problems 3798 POWER CYCLES r3858.1 The Carnot Cycle 3858.2 The Rankine Cycle 3888.2.1 The Ideal Rankine Cycle 388Effect of Boiler Pressure 395Effect of Heat Source Temperature 397Effect of Heat Sink Temperature 3978.2.2 The Non-Ideal Rankine Cycle 3998.2.3 Modications to the Rankine Cycle 405Reheat 405Regeneration 410EXAMPLE 8.2-1: SOLAR TROUGH POWER PLANT 4138.3 The Gas Turbine Cycle 4268.3.1 The Basic Gas Turbine Cycle 427Effect of Air-Fuel Ratio 433Effect of Pressure Ratio and Turbine Inlet Temperature 434Effect of Compressor and Turbine Efciencies 4378.3.2 Modications to the Gas Turbine Cycle 437Reheat and Intercooling 437EXAMPLE 8.3-1: OPTIMAL INTERCOOLING PRESSURE 439Recuperation 442Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).Contents ixEXAMPLE 8.3-2: GAS TURBINE ENGINE FOR SHIP PROPULSION 4438.3.3 The Gas Turbine Engines for Propulsion 452Turbojet Engine 452EXAMPLE 8.3-3: TURBOJET ENGINE 454Turbofan Engine 458EXAMPLE 8.3-4: TURBOFAN ENGINE 460Turboprop Engine 4678.3.4 The Combined Cycle and Cogeneration 4678.4 Reciprocating Internal Combustion Engines 4688.4.1 The Spark-Ignition Reciprocating Internal Combustion Engine 468Spark-Ignition, Four-Stroke Engine Cycle 469Simple Model of Spark-Ignition, Four-Stroke Engine 472Octane Number of Gasoline 477EXAMPLE 8.4-1: POLYTROPIC MODEL WITH RESIDUAL COMBUSTION GAS 479Spark-Ignition, Two-Stroke Internal Combustion Engine 4888.4.2 The Compression-Ignition Reciprocating Internal Combustion Engine 491EXAMPLE 8.4-2: TURBOCHARGED DIESEL ENGINE 4938.5 The Stirling Engine 5018.5.1 The Stirling Engine Cycle 5028.5.2 Simple Model of the Ideal Stirling Engine Cycle (E2) 5048.6 Tradeoffs Between Power and Efciency 5058.6.1 The Heat Transfer Limited Carnot Cycle 5058.6.2 Carnot Cycle using Fluid Streams as the Heat Source and HeatSink (E3) 5118.6.3 Internal Irreversibilities (E4) 5118.6.4 Application to other Cycles 511References 512Problems 5129 REFRIGERATION AND HEAT PUMP CYCLES r5299.1 The Carnot Cycle 5299.2 The Vapor Compression Cycle 5329.2.1 The Ideal Vapor Compression Cycle 532Effect of Refrigeration Temperature 5389.2.2 The Non-Ideal Vapor Compression Cycle 540EXAMPLE 9.2-1: INDUSTRIAL FREEZER 542EXAMPLE 9.2-2: INDUSTRIAL FREEZER DESIGN 5459.2.3 Refrigerants 550Desirable Refrigerant Properties 550Positive Evaporator Gage Pressure 551Moderate Condensing Pressure 551Appropriate Triple Point and Critical Point Temperatures 551High Density/Low Specic Volume at the Compressor Inlet 553High Latent Heat (Specic Enthalpy Change) of Vaporization 553High Dielectric Strength 553Compatibility with Lubricants 553Non-Toxic 554Non-Flammable 554Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).x ContentsInertness and Stability 554Refrigerant Naming Convention 554Ozone Depletion and Global Warming Potential 5569.2.4 Vapor Compression Cycle Modications 557Liquid-Suction Heat Exchanger 559EXAMPLE 9.2-3: REFRIGERATION CYCLE WITH A LIQUID-SUCTION HEATEXCHANGER 560Liquid Overfed Evaporator 564Intercooled Cycle 567Economized Cycle 568Flash-Intercooled Cycle 571EXAMPLE 9.2-4: FLASH INTERCOOLED CYCLE FOR A BLAST FREEZER 571EXAMPLE 9.2-5: CASCADE CYCLE FOR A BLAST FREEZER 5789.3 Heat Pumps 584EXAMPLE 9.3-1: HEATING SEASON PERFORMANCE FACTOR 5889.4 The Absorption Cycle 5989.4.1 The Basic Absorption Cycle 5989.4.2 Absorption Cycle Working Fluids (E6) 6019.5 Recuperative Cryogenic Cooling Cycles 6019.5.1 The Reverse Brayton Cycle 6039.5.2 The Joule-Thomson Cycle 6119.5.3 Liquefaction Cycles (E7) 6149.6 Regenerative Cryogenic Cooling Cycles (E8) 614References 614Problems 61510 PROPERTY RELATIONS FOR PURE FLUIDS r62910.1 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 633Limiting Ideal Gas Behavior 633The Boyle Isotherm 633Critical Point Behavior 63410.1.3 Two-Parameter Equations of State 637The van der Waals Equation of State 637EXAMPLE 10.1-1: APPLICATION OF THE VAN DER WAALS EQUATION OF STATE 641The Dieterici Equation of State 646EXAMPLE 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 651EXAMPLE 10.1-3: PENG-ROBINSON EQUATION OF STATE 65310.1.4 Multiple Parameter Equations of State 65610.2 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 661Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).Contents xi10.3 Derived Thermodynamic Properties 67010.3.1 Maxwells 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 Specic Heat Capacity 68510.4 Methodology for Calculating u, h, and s 688EXAMPLE 10.4-1: CALCULATING THE PROPERTIES OF ISOBUTANE 69210.5 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) 70310.6 Fugacity 70410.6.1 The Fugacity of Gases 706Calculating Fugacity using the RKS and PR Equations of State (E10) 70810.6.2 The Fugacity of Liquids 708References 710Problems 71011 MIXTURES AND MULTI-COMPONENT PHASE EQUILIBRIUM r72111.1 P-v-T Relations for Ideal Gas Mixtures 72111.1.1 Composition Relations 72111.1.2 Mixture Rules for Ideal Gas Mixtures 72311.2 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 73411.3 P-v-T Relations for Non-Ideal Gas Mixtures 73811.3.1 Daltons Rule 73811.3.2 Amagats Rule 73911.3.3 Empirical Mixing Rules 740Kays Rule 740Mixing Rules 741EXAMPLE 11.3-1: SPECIFIC VOLUME OF A GAS MIXTURE 74211.4 Energy and Entropy for Non-Ideal Gas Mixtures 74611.4.1 Enthalpy and Entropy Changes of Mixing 74611.4.2 Enthalpy and Entropy Departures 749Molar Specic Enthalpy and Entropy Departures from a Two-ParameterEquation of State (E11) 75111.4.3 Enthalpy and Entropy for Ideal Solutions 75211.4.4 Enthalpy and Entropy using a Two-Parameter Equation of State 753The RKS Equation of State (E12) 753The Peng-Robinson Equation of State 754EXAMPLE 11.4-1: ANALYSIS OF A COMPRESSOR WITH A GAS MIXTURE 754Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).xii Contents11.4.5 Peng-Robinson Library Functions 764EXAMPLE 11.4-2: ANALYSIS OF A COMPRESSOR WITH A GAS MIXTURE(REVISITED) 76511.5 Multi-Component Phase Equilibrium 76911.5.1 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 77611.6 The Phase Rule 783References 784Problems 78412 PSYCHROMETRICS r79112.1 Psychrometric Denitions 791EXAMPLE 12.1-1: BUILDING AIR CONDITIONING SYSTEM 79512.2 Wet Bulb and Adiabatic Saturation Temperatures 79912.3 The Psychrometric Chart and EES Psychrometric Functions 80212.3.1 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) 81212.4 Psychrometric Processes for Comfort Conditioning 81412.4.1 Humidication Processes 815EXAMPLE 12.4-1: HEATING/HUMIDIFICATION SYSTEM 81612.4.2 Dehumidication Processes 822EXAMPLE 12.4-2: AIR CONDITIONING SYSTEM 82312.4.3 Evaporative Cooling 82712.4.4 Desiccants (E16) 82912.5 Cooling Towers 83012.5.1 Cooling Tower Nomenclature 83112.5.2 Cooling Tower Analysis 832EXAMPLE 12.5-1: ANALYSIS OF A COOLING TOWER 83412.6 Entropy for Psychrometric Mixtures (E17) 838References 838Problems 83813 COMBUSTION r85213.1 Introduction to Combustion 85213.2 Balancing Chemical Reactions 85413.2.1 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 85813.3 Energy Considerations 864Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).Contents xiii13.3.1 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 89413.4 Entropy Considerations 898EXAMPLE 13.4-1: PERFORMANCE OF A GAS TURBINE ENGINE 90113.5 Exergy of Fuels (E18) 907References 907Problems 90814 CHEMICAL EQUILIBRIUM r92214.1 Criterion for Chemical Equilibrium 92214.2 Reaction Coordinates 924EXAMPLE 14.2-1: SIMULTANEOUS CHEMICAL REACTIONS 92714.3 The Law of Mass Action 93114.3.1 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 93914.4 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) 95114.5 Heterogeneous Reactions (E19) 95314.6 Adiabatic Reactions 954EXAMPLE 14.6-1: ADIABATIC COMBUSTION OF HYDROGEN 954EXAMPLE 14.6-2: ADIABATIC COMBUSTION OF ACETYLENE 960Reference 967Problems 96715 STATISTICAL THERMODYNAMICS r97215.1 A Brief Review of Quantum Theory History 97315.1.1 Electromagnetic Radiation 97315.1.2 Extension to Particles 97515.2 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 97915.3 The Equilibrium Distribution 97915.3.1 Macrostates and Thermodynamic Probability 980Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).xiv Contents15.3.2 Identication of the Most Probable Macrostate 98215.3.3 The Signicance of 98515.3.4 Boltzmanns Law 98715.4 Properties and the Partition Function 98915.4.1 Denition 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 99215.5 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 99715.6 Extension to More Complex Particles 99815.7 Heat and Work from a Statistical Thermodynamics Perspective 1001References 1004Problems 100516 COMPRESSIBLE FLOW (E20) r1009Problems 1009AppendicesA: Unit Conversions and Useful Information 1015B: Property Tables for Water 1019C: Property Tables for R134a 1031D: Ideal Gas & Incompressible Substances 1037E: Ideal Gas Properties of Air 1039F: Ideal Gas Properties of Common Combustion Gases 1045G: Numerical Solution to ODEs 1056H: Introduction to Maple (E26) 1057Index 1059Section can be found on the Web site that accompanies this book (www.cambridge.org/kleinandnellis).PREFACEThermodynamics 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 relationshipsthatdescribetheproblem. Thesetofequationsthatleadstoauseful solutiontoaproblem results from application of appropriate balances and rate relations, simpliedwith justied 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 Thermodynamicsis 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 identied, they must be solved. In ourexperience, much of the time and effort required to solve thermodynamics problemsresultsfromlookinguppropertyinformationintablesandsolvingtheappropriateequations. 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 students 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(EngineeringEquationSolver)program. EESeliminatesmuchofthemathematicalcomplexity 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 easilyxvxvi Prefaceobtain 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.Sufcient material is provided for both undergraduate and graduate thermodynamicscourses. The book can be used in a single-semester undergraduate course by appro-priatelyselectingfromtheavailabletopics. Forexample, wetypicallydonotcoverChapter 7 and Chapters 1416 in our single-semester undergraduate course. Topics suchas absorption cycles (9.4), cryogenic cooling cycles (9.56), 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 rst 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 nd 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.Thebookincludesalargecollectionofreal-worldproblemsattheendofeachchapter. 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 rst review that these problems are too complex foruse in a rst 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 lls 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 2011ACKNOWLEDGMENTSThe 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 specically 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, weareindebtedtoCambridgeUniversityPressandinparticularPeterGordon for giving us this opportunity and helping us through the process of bringing ourmanuscript to this nal state.xviiNOMENCLATUREa specic Helmholtz free energy (J/kg)parameter in an equation of stateA area (m2)Helmholtz free energy (J)amplitude of waveAcritical area (m2)Accross-sectional area (m2)Affrontal area (m2)AF air-fuel ratio (-)Assurface area (m2)b parameter in an equation of state (m3/kg)B parameter dened in Eq. (10-71)parameter dened in Eq. (15-106)BPR bypass ratio (-)bwr back work ratio (-)c specic heat capacity (J/kg-K)speed of sound (m/s)speed of light in a vacuum (3108m/s) c molar specic heat of an incompressible substance (J/kmol-K)C number of chemical species in a mixture (-)C capacitance rate (product of mass ow rate and specic heat) (W/K)CDdrag coefcient (-)COP coefcient of performance (-)cPspecic heat capacity at constant pressure (J/kg-K) cPmolar specic heat capacity at constant pressure (J/kmol-K)CRcapacitance ratio (-)CR compression ratio (-)cvspecic heat capacity at constant volume (J/kg-K) cvmolar specic 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,blackbody spectral emissive power (W/m2-m)EER energy efciency rating (Btu/W-hr)ei,jnumber of moles of element j per mole of substance i (-)Ejnumber of moles of element j (kmol)xixxx Nomenclaturef frequency (Hz)fugacity (Pa)partition function (-)fraction of ow (-)F force (N)number of intensive properties (for Gibbs phase rule)

F force vector (N)fifugacity of pure uid i (Pa)fipartial fugacity of component i in a mixture (Pa)g gravitational acceleration (m/s2)specic Gibbs free energy (J/kg)G Gibbs free energy (J) g molar specic Gibbs free energy (J/kmol)gidegeneracy of energy level i (-)h specic enthalpy (J/kg)Plancks constant (6.6251034J/s)h molar specic enthalpy (J/kmol)H enthalpy (J)H enthalpy ow rate (W)haventhalpy of an air-water vapor mixture per kg dry air (J/kga)hconvconvective heat transfer coefcient (W/m2-K)HC heat of combustion (J/kg)hdepmolar specic enthalpy departure (J/kmol or J/kg)hdep,imolar specic enthalpy departure of component i in a mixture (J/kmol)hfgspecic enthalpy of vaporization (J/kg)hfgmolar specic enthalpy of vaporization (J/kmol)hformmolar specic enthalpy of formation (J/kmol)HHV higher heating value (J/kmol)himolar specic enthalpy of component i in a mixture (J/kmol)HSPF heating season performance factor (Btu/W-hr)hstdstandardized molar specic 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 specic heat capacities, cP/cv (-)Boltzmanns constant (1.38051023J/K)k unit vector in the z-directionK spring constant (N/m)KE kinetic energy (J)kijbinary mixing parameter (-)Kjequilibrium constant for reaction j (-)KPcoefcient of pressure recovery (-)KTisothermal 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 ow rate (kg/s)Nomenclature xxiM the dimension massM Mach number (-)MEP mean effective pressure (Pa)mfimass fraction of component i in a mixture (-)mimass 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)NAAvogadros number (6.0221026kmol1)ninumber of moles of component i in a mixture (kmol)Ninumber of particles in energy level i (-)NTU number of transfer units (-)p momentum (N-s)P pressure (Pa)probability (-)P0standard state pressure or low pressure at which the ideal gas law is valid (Pa)P0dead state pressure (Pa)stagnation pressure (Pa)Patmatmospheric pressure (Pa)Pcritcritical pressure (Pa)Pcrit,effeffective critical (or pseudo-critical) pressure of a mixture (Pa)PE potential energy (J)Pgagegage pressure (Pa)Pipartial pressure of component i in a mixture (Pa)PLF part load factor (-)Prreduced pressure (-)PR pressure ratio (-)Pr,effeffective 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)Q12heat transfer during the process of going from state 1 to state 2 (J)R ideal gas constant (J/kg-K)radius (m)resistance Runivuniversal gas constant (8314.3 J/kmol-K)s specic entropy (J/kg-K) s molar specic entropy (J/kmol-K)S entropy (J/K)S rate of entropy transfer (W/K)saventropy of an airwater vapor mixture per kg dry air (J/kga-K) sdepmolar specic entropy departure (J/kmol-K) sdep,imolar specic entropy departure of pure gas i in a mixture (J/kmol-K)Sgenentropy generation (J/K)Sgenrate of entropy generation (W/K)Smentropy transfer due to mass transfer (J/K)Smrate of entropy transfer due to mass transfer (W/K)xxii Nomenclature simolar specic entropy of component i in a mixture (J/kmol-K)SQentropy transfer due to heat (J/K)SQrate of entropy transfer due to heat (W/K)SEER seasonal energy efciency rating (Btu/W-hr)SFC specic fuel consumption (kg/s-N)SHR sensible heat ratio (-)t the dimension timet time (s)T the dimension temperatureT temperature (K)T0dead state temperature (K)stagnation temperature (K)TBBoyle temperature (K)Tcritcritical temperature (K)Tcrit,effeffective critical (or pseudo-critical) temperature of a mixture (K)Tdpdew-point temperature (K)Trreduced temperature (-)Tr,effeffective reduced (or pseudo-reduced) temperature of a mixture (-)Tr,Breduced Boyle temperature (-)Twbwet bulb temperature (K)th thickness (m)u specic internal energy (J/kg) u molar specic internal energy (J/kmol) uipartial molar specic internal energy of component i in a mixture (J/kmol) ust dstandardized molar internal energy (J/kmol)U internal energy (J)UA conductance (W/K)building heat loss coefcient (W/K)v specic volume (m3/kg) v molar specic volume (m3/kmol) vimolar specic volume of component i in a mixture (m3/kmol)V volume (m3)V volumetric ow rate (m3/s)V velocity (m/s)vavvolume of an airwater vapor mixture per kg dry air (m3/kga)vcritcritical specic volume (m3/kg) vcritcritical molar specic volume (m3/kmol)vcrit,effeffective critical (or pseudo-critical) specic volume of a mixture (m3/kg)Vdispdisplacement rate of a compressor (m3/s)Vivolume of component i in a mixture (m3)Vipartial molar volume of component i in a mixture(m3/kmol)vrreduced specic volume (-)vr,effeffective reduced (or pseudo-reduced) specic volume (-)W work (J)weight (N)W12work transfer during the process of going from state 1 to state 2 (J)Wlostlost work or exergy destruction (J)W work transfer rate, power (W)x qualityposition (m)displacement (m)X exergy (J)Nomenclature xxiiiXdesexergy destroyed (J)Xfexergy associated with a mass transfer (J)ximole fraction of component i in the liquid phase of a mixture (-)XQexergy associated with a heat transfer (J)Xsexergy of a system (J)xfspecic exergy of a owing substance (J/kg)xsspecic exergy of a system (J/kg)Xdesrate of exergy destruction, also called the irreversibility rate (W)Xfrate of exergy ow with mass ow (W)XQrate of exergy ow with heat (W)yimole fraction of component i in a mixture (-)mole fraction of component i in the vapor phase of a mixture (-)z elevation in a gravitational eld (m)Z compressibility factor (-)Zcritcritical compressibility factor (-)zitotal mole fraction of component i in a mixture (-)Zicompressibility factor for component i in a mixture (-)Greek Symbols reduced Helmholtz free energy (-)parameter in the RK or PR equation of state (-) parameter dened in Eq. (15-101) (1/J) uncertainty in some measurementreduced density (-)differential amount change of some property of a systemGojstandard state Gibbs free energy change of reaction (J)hfglatent heat of vaporization (J/kg)

hmixmolar specic enthalpy change of mixing (J/kmol)P pressure drop (Pa) smixmolar specic entropy change of mixing (J/kmol-K)T approach temperature difference (K) vmixmolar specic volume change of mixing (m3/kmol)Vmixvolume change of mixing (m3) Lennard-Jones energy potential (J)emissivity (-)effectiveness of a heat exchanger (-)reaction coordinate or degree of reaction (kmol)ienergy associated with a energy level i (J)jreaction coordinate for reaction j (kmol) fugacity coefcient (-)relative humidity (-) surface tension (N/m) efciency (-)2Second Law efciency (-) wavelength (m)undetermined multiplier number of phases (-) angle (radian) density (kg/m3)xxiv Nomenclature Lennard-Jones length potential (m)Stefan-Boltzmann constant (5.67108W/m2-K4) torque (N-m)inverse reduced temperature (-) viscosity (Pa-s)f,ichemical potential of component i in the liquid phase of a mixture (J/kmol)g,ichemical potential of component i in the vapor phase of a mixture (J/kmol)JTJoule-Thomson coefcient (K/Pa)istoichiometric coefcient for component ii, jstoichiometric coefcient for component i in reaction j constraint function that evaluates to zero angular velocity (rad/s)acentric factor (-)humidity ratio (kgv/kga)effeffective acentric factor of a mixture (-) thermodynamic probability (-)Superscripts quantity evaluated at location of critical areao under conditions where uid behaves as an ideal gas (i.e., at low pressure)Subscriptsa dry airact actualamb ambientas adiabatic saturationatm atmosphericav psychrometric property dened on a per mass of dry air basisavg averageb boundaryboilerblackbodyB Boyle isothermBDC bottom dead centerBE Bose-Einstein modelc compressorC cold uid 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 diffuserdownstream of a normal shockdragdes destroyed within systemdp dew pointec evaporative coolerNomenclature xxvevap evaporatorexp expansion processf saturated liquidfuelfurnaceFD Fermi-Dirac modelg saturated vaporgage gagegen generated within systemgenerator in an absorption cycleH hot uid in a heat exchanger or hot thermal reservoirheat pumpHTCB hot-to-cold blow processhf heat transfer uidhx 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 overallstagnationinitialp pumppistonpropulsiveP related to an isobaric process, at constant pressureassociated with the products of a reactionpure associated with a pure substanceout out, leaving a systemR refrigeration cycleassociated 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 surroundingsxxvi Nomenclaturet turbineat time tT related to an isothermal process, at constant temperatureTDC top dead centerth thermalu upstream of a normal shockv valvewater vaporvol volumetricwb wet bulbx in the x-directiony in the y-directionz in the z-direction spectral as a function of wavelength free-stream uidOther Notes a specic property on molar basisf(A) function of variable AA change in variable AdA differential change in the property AA differential amount of the quantity Auncertainty in the quantity AA rate of transfer of quantity ATHERMODYNAMICS1 Basic Concepts1.1 OverviewThermodynamics is unquestionably the most powerful and most elegant of the engi-neering sciences. Its power arises from the fact that it can be applied to any discipline,technology, application, or process. The origins of thermodynamics can be traced to thedevelopment of the steam engine in the 1700s, and thermodynamic principles do governthe performance of these types of machines. However, the power of thermodynamics liesin its generality. Thermodynamics is used to understand the energy exchanges accom-panying a wide range of mechanical, chemical, and biological processes that bear littleresemblance to the engines that gave birth to the discipline. Thermodynamics has evenbeen used to study the energy exchanges that are involved in nuclear phenomena and ithas been helpful in identifying sub-atomic particles. The elegance of thermodynamics isthe simplicity of its basic postulates. There are two primary laws of thermodynamics,the First Law and the Second Law, and they always apply with no exceptions. No otherengineering science achieves such a broad range of applicability based on such a simpleset of postulates.So, what is thermodynamics? We can begin to answer this question by dissecting theword into its roots: thermo and dynamics. The term thermo originates from a Greekword meaning warm or hot, which is related to temperature. This suggests a conceptthat is related to temperature and referred to as heat. The concept of heat will receivemuch attention in this text. Dynamics suggests motion or movement. Thus the termthermodynamics may be loosely interpreted as heat motion. This interpretation ofthe word reects the origins of the science. Thermodynamics was developed in orderto explain how heat, usually generated from combusting a fuel, can be provided to amachine in order to generate mechanical power or motion. However, as noted above,thermodynamics has since matured into a more general science that can be applied toa wide range of situations, including those for which heat is not involved at all. Theterm thermodynamics is sometimes criticized because the science of thermodynamicsis ordinarily limited to systems that are in equilibrium. Systems in equilibrium are notdynamic. Thisfacthaspromptedsometo suggestthatthesciencewouldbebetternamed thermostatics (Tribus, 1961).Perhaps the best denition of thermodynamics is this: Thermodynamics is the sciencethat studies the conversion of energy from one form to another. This denition capturesthe generality of the science. The denition also introduces a new concept energy.Thermodynamics involves a number of concepts that may be new to you, such as heatand energy, and these terms must each be carefully dened. As you read this, it mayseem that heat and energy are familiar words and therefore no further denition of theseconcepts is necessary. However, the common understanding of these terms differs fromthe formal denitions that are needed in order to apply the laws of thermodynamics.12 Basic ConceptsThe First Law of Thermodynamics states that energy is conserved in all processes(in the absence of nuclear reactions). If energy is conserved (i.e., it is not generated ordestroyed) thenthe amount of energy that is available must be constant. But if the amountof energy is constant then why do we hear on the news that the world is experiencing anenergy shortage? How could we be running out of energy? Why do we receive monthlyenergy bills?The answer to these questions lies in the difference between the term energy as it iscommonly used and the formal, thermodynamic denition of energy. These differencesbetweencommonvernacularandprecisethermodynamicdenitionsareasourceofconfusion. The term energy that is used in everyday conversations should be thought ofas the capacity to do work. This denition is not consistent with the thermodynamicdenitionofenergy, butratherreferstoadifferentthermodynamicconceptthatisreferredtoasexergyandisstudiedinChapter7. Thethermodynamicdenitionofenergy is not as satisfying. Energy is not really something; rather, it is a property ofmatter. We cannot see, smell, taste, hear or feel energy. We can measure it, but onlyindirectly. Hopefully, the thermodynamic concept of energy will become clearer as youprogress through this book.The First Law of Thermodynamics is concerned with the conservation of energy.However, energy has both quantity and quality. The quality of energy is not conservedand the Second Law of Thermodynamics can be interpreted as a system for assigningquality to energy. Although energy is conserved, the quality of energy is always reducedduring energy transformation processes. Lower quality energy is less useful to us in thesense that its capability for doing work has been diminished. The quality of energy iscontinuously degraded by all real processes; this observation can be expressed in layterms as running out of energy.The Second Lawis responsible for the directional nature of all real processes. That is,processes can occur in only one direction and will not spontaneously reverse themselvesbecause doing so would require a spontaneous increase in the quality of energy. TheSecondLawexplainswhyheatowsfromhottocoldandwhyobjectsatdifferenttemperatures will eventually come to the same temperature. The Second Law explainswhy gases mix and things break. It can be used to explain why we age and why timemoves forward. The Second Law of Thermodynamics is likely the most famous law inall of the physical sciences.Our society is now facing some very challenging problems. Some of these problemsarerelatedtothediminishingsupplyofpetroleum, coal, natural gas, andtheothercombustible materials that provide the energy (the common denition rather than thethermodynamic denition) that powers our world. Even if these fuels were inexhaustible(which they are not), combustion of carbon-basedfuels necessarily producescarbondioxide, which has been linked to global warming and other climate change phenomena.What alternatives exist to provide the power that we need? Hydrogen-powered fuel cells,biomass, nuclear power plants, solar and wind energy systems have all been mentionedin the popular media as potential solutions. Which one of these alternatives is actuallybest? What role can each of themplay in terms of displacing our current energy supplies?These are huge questions. The solution to our energy problem will likely be one of thebiggest challenges facing our species this century. In one sense this is alarming, but it isalso very exciting. You are reading this book because you have either a professional orpersonal interest in the subject of thermodynamics. Thermodynamics plays a major rolein addressing these energy-related questions. It is clear that the demand for people whoare well-educated in thermodynamics and capable of applying the discipline to a widerange of problems will only increase.1.2Thermodynamic Systems 3systemFigure 1-1:A system dened to contain allof the air in apiston-cylinder device.1.2 Thermodynamic SystemsEvery thermodynamic analysis begins with the specication of asystem. A system issimply any object, quantity of matter, or region of space that has been selected for study.The system provides the precise specication for the focus of the analysis and enablesthe use of the First and Second Laws of Thermodynamics. Everything that is not part ofthe system is referred to as the surroundings.The specication of a system requires the identication of its boundary, the surfacethat separates the system from its surroundings. The system boundary may correspondto a real surface. For example, Figure 1-1 illustrates a perfectly-sealed piston-cylinderdevice that is lled with air. The dashed blue line indicates the boundary of a system thatis dened so that it contains all of the air within the cylinder. Notice that the boundaryof this system must move as the position of the piston changes.The laws of thermodynamics can be applied to any system and often there will bemore than one logical system choice for a particular problem. For example, Figure 1-2illustrates an air tank that is being lled from an air line. One choice for a system isthe xed region that corresponds to the internal volume of the air tank. An alternativesystem is dened by the dashed blue line in Figure 1-2 so that it contains all of the airthat was initially in the tank. Notice that the boundary of this system must move as thetank is lled.We classify systems according to their interactions with the surroundings. If massdoes not cross the boundary of a systemthen it is referred to as a closed system. Mass doescross the boundary of an open system. An adiabatic system is one in which the boundaryis impermeable to heat, i.e., the energy transfer that normally occurs when a temperaturedifference exists between the system and surroundings. A steady-state system is one inwhich all of the properties of the system do not change with time. An isolated system hasno interaction of any kind with its surroundings.TheFirstandSecondLawsofThermodynamicsapplyregardlessofthesystemchoice. The denition of a system is dictated by convenience. While there is no wrongchoice of system, some system choices simplify the mathematical description of a pro-cess whereas others cause the problem to become impossibly complicated. Your abilityair lineair tanksystemFigure 1-2:A system dened to contain all of the air that is initially in a tank that is being lled.4 Basic Conceptsto select an appropriate system will improve with experience. The rst step in everythermodynamics problem is the selection of a system and this is accomplished by clearlyindicating its boundaries so that it can be carefully analyzed.1.3 States and Properties1.3.1State of a SystemOnce a system has been specied, it is next necessary to specify its state. The state isa description of the system in terms of quantities that will be helpful in describing itsbehavior and its interactions with the surroundings.There are two very different ways to describe a thermodynamic system, referred to asthe microscopic and macroscopic approaches. The microscopic approach recognizes thatthe systemconsists of matter that is composed of countless, discrete particles (molecules).Thesemoleculesoftenbehaveinamannerthatmaybenon-intuitivebasedonoureveryday experience with much larger amounts of matter. The fundamental particlesmove at high velocities and have kinetic energies in three dimensions. Depending onthe complexity of the molecules, they may also store energy due to their rotation andthe vibration of the bonds connecting the atoms. The particles interact with each otherand with the walls of their container. There are so many particles that it is hopeless toattempt to represent the observed characteristics of a system by describing the behaviorsof each of its individual particles. However, we may be able to formulate a molecularmodel that describes the attractive and repulsive forces between particles and the variousways that a particle can store energy. We cannot directly test the molecular model againstthebehaviorofasinglemolecule. However, wecanapplystatisticsandprobabilitytheory to the molecular model in order to deduce the macroscopic behavior that wouldresult from a large number of particles. Agreement between the calculated statisticalbehavior and the observed macroscopic behavior lends condence in the delity of themodel.The branch of science that describes the state of a system using this microscopicapproach is called Statistical Thermodynamics. Statistical Thermodynamics directly inte-grates the properties of matter with the conservation of energy. It provides a molecularexplanation for the Second Law of Thermodynamics and it allows some physical prop-erties (e.g., the specic heats and entropy of low pressure gases) to be determined moresimply than is possible using any alternative method. Chapter 15 provides an introductionto Statistical Thermodynamics.This text will apply a macroscopic approach to describe thermodynamic systems. Inthe macroscopic approach, the state of the system is described by a relatively small set ofcharacteristics that are called properties. Some of these properties are already familiar toyou, such as mass, temperature, pressure and volume. This macroscopic approach workswell when the system is sufciently large such that it contains many molecules. However,the macroscopic approach would not work well for a system that consists of a rareedgas (i.e., a vacuum with just a few molecules). For example, how would you measure thetemperature of such a system that consists almost entirely of vacuum?1.3.2Measurable and Derived PropertiesThermodynamic properties are classied as being either measurable or derived. Mea-surable properties can be directly measured using an appropriate instrument. Examplesof measurable properties include mass, temperature, pressure, volume, velocity, eleva-tion, specic heat capacities, and composition. Derived properties cannot be directly1.3States and Properties 5measured. Derivedpropertiesincludeinternal energy, enthalpy, entropy, andotherrelated thermodynamic properties that will be dened in this text.It is not always clear whether a property is measurable or derived. For example,temperature is normally considered to be a measurable property. But how does oneactually measure temperature? The common thermometer consists of a precision borewithin a transparent glass enclosure that is lled with a liquid that expands when its tem-perature is increased. By observing the height of the liquid in the bore, we can measurethe volume of the uid and infer the temperature. There are many other ways to measuretemperature. For example, thermistors relate the electrical resistance of a material toits temperature. Thermocouples are junctions between two dissimilar metals that gen-erate a voltage potential that is a function of temperature. In each of these instruments,however, something (e.g., volume, resistance, or voltage) is directly measured and tem-perature is then inferred from this measurement. Although we do not directly measuretemperature, it is still considered to be a measurable property.1.3.3Intensive and Extensive PropertiesThermodynamic properties are also classied as being either intensive or extensive. Inten-sive properties are independent of the amount of mass in the system whereas the valuesof extensive properties depend directly on the amount of mass. Temperature and pres-sure, for example, are intensive properties. If you were told the temperature or pressureof a system and nothing more, you would have no idea of the size of the system. Volumeand energy are extensive properties. The greater the volume of a system, the more massit must have. Extensive properties are linearly related to the system mass.A specic property is dened as the ratio of an extensive property of a system tothe mass of the system. Thus specic volume, v, is the ratio of volume (an extensiveproperty) to mass:v =Vm(1-1)where V is the volume of the system and m is the mass of the system. The inverse ofspecic volume is density: =1v=mV(1-2)Specic volume and density are both intensive properties. We will encounter severalother extensive properties, including internal energy (U), enthalpy (H), and entropy (S).The corresponding specic properties are specic internal energy (u), specic enthalpy(h), and specic entropy (s):u =Um(1-3)h =Hm(1-4)s =Sm(1-5)1.3.4Internal and External PropertiesProperties can also be classied as being eitherinternal orexternal. The value of aninternal property depends on the nature of the matter that composes the system. External6 Basic Conceptsproperties are independent of the nature of the matter within the system. Examplesofexternal propertiesincludethevelocityofthesystem( V)anditselevationinagravitational eld (z). These properties do not depend on whether we are talking abouta system composed of helium or one composed of steel. For example, in Section 3.2.2 wewill see that a system with a mass m= 1 kg that is elevated a distance z = 1 m in Earthsgravitational eld (g = 9.81 m/s2) will have a potential energyPE =m g z = 9.81 Jregardlessofthetypeofmatterthatthesystemiscomposedof. Internalpropertiesdepend on the nature of the matter in the system and, as a consequence, they dependupon each other. That is, internal properties are functionally related to one another.The interdependence of internal properties is of fundamental importance becauseit allows us to completely x the state of a system by specifying only a few internalproperties. The values of other internal properties can be found by employing the rela-tionships that exist between these properties. It will be shown in Chapter 2 that only twointernal intensive properties are required to x the state of a system containing a puresubstance that consists of only one phase (i.e., solid, liquid, or vapor). For example, if thetemperature and pressure of water vapor are specied, then the density, specic internalenergy, and specic enthalpy all have xed values. Any other intensive property of thewater vapor could also be determined. It is only necessary to know the temperature andpressure of a single phase pure substance in order to determine the specic heat capacityat constant pressure, the magnetic moment, the surface tension, the speed of sound, theelectrical resistivity, and many other properties.You likely have already employed a property relationship in your chemistry classby using the absolute temperature (T) and absolute pressure (P) of a gas in order tocalculate its specic volume (v) using the ideal gas law:v =RTP(1-6)where the parameter R is the ideal gas constant. The ideal gas law will be discussed inSection 2.5. It does not apply under all conditions. The accuracy of Eq. (1-6) is reducedas the pressure is increased or as the temperature is decreased. Under some conditions,the ideal gas law may not be sufciently accurate to be of any use at all. However, thiscomplication does not change the fact that the specic volume is xed at some value (i.e.,it is not an independent variable) when the temperature and pressure are specied. Ifthe ideal gas law is not applicable, a more complicated relation between specic volume,temperature and pressure may be needed, as discussed in Chapter 10. The properties ofmany substances have been measured and the relationships between internal propertiescan be expressed using tables, charts, equations, and computer programs, as describedin Chapter 2.1.4 BalancesBalances are the basic tool of engineering. Once a system has been carefully dened,itispossibletoapplyabalancetothesystem. Abalanceissimplyamathematicalstatement of what we know to be true. Any number of quantities can be balanced forany arbitrary system. The general balance equation, written for a nite period of timeand some arbitrary quantity is:In +Generated = Out +Destroyed +Stored (1-7)where In is the amount entering the system by crossing its boundary, Generated is theamount generated within the system, Out is the amount leaving the system by crossingits boundary, Destroyed is the amount destroyed within the system, and Stored is the1.4Balances 7amount stored in the system (i.e., the change in the quantity during the period of time).A balance can also be written on a rate basis, in which case the rate of each of the termsin Eq. (1-7) must be balanced at a particular instant in time. It is important to emphasizethat the balance provided by Eq. (1-7) makes no sense until you have carefully deneda system and its boundaries.Every month, most of us dene a system that is referred to as our household andcarry out a money balance on this system:Din+ Dgen = Dout+ Ddes+D (1-8)where D indicates the amount of money. The variable Din is the amount of money thatenters your household (from wages and other forms of income), Ddesis the amountof money that is destroyed,Doutis the amount of money that leaves your household(expenses), and Dgen is the amount of money that is created in your household. The termD in Eq. (1-8) is the amount of money stored in your household, i.e., the change in theamount of money contained within your household during the time period of interest. Apositive value of D indicates that you managed to save some money during the monthwhile a negative value indicates that you had to dip into your savings. For most of us, Ddeswill be zero every month as we do not often literally burn up or destroy currency. Also,Dgen will be zero as we cannot (legally) generate money. Thus, balancing our monthlynances will result in the following equation:Din = Dout+D (1-9)Equation (1-9) shows that, at least on a personal level, money is a conserved quantity;that is, it is neither destroyed nor produced. Other quantities are not conserved. Forexample, we could dene a system around the borders of the United States and balancepeople for a year:Pin+ Pgen =Pout+ Pdes+P (1-10)In Eq. (1-10), Pinis the number of people that enter the U.S. by crossing its borders(immigration) and Pout is the number of people leaving the U.S. by crossing its borders(emigration). The quantityP is the change in the population of the U.S. during theyear (i.e., the number of people at the end of the year less the number of people at thebeginning of the year). People are, as you know, not a conserved quantity; they are bothdestroyed and generated. The quantity Pdes is the number of people that die and Pgenis the number of babies born within the borders of the U.S during the year. Equation(1-10) must be satised as it is simply a mathematical statement of what we know to betrue.Mass is a conservedquantity since it cannot be generatedor destroyed(inthe absenceof nuclear reactions). Therefore, a mass balance on a system for a nite period of timeleads to:min = mout+m (1-11)where min is the amount of mass that enters the system by crossing its boundary andmout is the amount of mass that leaves the system by crossing its boundary. Note that thequantities min and mout must be zero for a closed system. The quantity mis the amountof mass stored in the system; this is the mass in the system at the end of time period lessthe mass in the system at the beginning of the time period. A mass balance written on arate basis at a particular instant in time is: min = mout+ dmdt(1-12)8 Basic Conceptswhere minand moutaretheratesatwhichmassisenteringandleavingthesystem,respectively, by crossing its boundaries, anddmdtis the rate of change in the mass of thesystem.The laws of thermodynamics can be expressed most concisely in the formof balances.The First Law of Thermodynamics (which is introduced in Chapter 3) states that energyis a conserved quantity. For any system you care to dene, energy cannot be destroyedor generated. Energy can ow into or out of a system (in various ways) and it can bestored in a system (in various forms). However, energy is never generated or destroyedin a system.TheSecondLawof Thermodynamics states that thethermodynamicpropertyentropy(whichisintroducedinChapter6)isnot aconservedquantity; entropyisalways generated and never destroyed. The Second Law suggests that the entropy ofthe universe is always increasing and it provides directionality to all processes. Any realprocess will result in the generation of entropy. Therefore, in order for the process torun in reverse (i.e., all inows become outows, outows become inows, etc.) it wouldbe necessary to destroy entropy. Because it is not possible to destroy entropy, no realprocess is reversible. A theoretical process that results in no entropy generation isoften referred to as a reversible process and provides a useful limit to the behavior ofreal processes.1.5 Introduction to EES (Engineering Equation Solver)Thermodynamicsandrelatedthermal sciencecourses(e.g., uiddynamicsandheattransfer) focus on providing a mathematical description of physical phenomena (i.e., anengineering model). An engineering model increases our understanding of the underly-ing physics. Properly formulated, the model can be used in place of the actual physicalsystem in order to do mathematical experiments that can be conducted more quicklyand with less cost than their physical counterparts. A good model is predictive. Themodel thereforeallowsthebehaviorof asystemtobeexploredat conditionsthatwould be difcult or impossible to achieve and it provides resolved information thatwouldbehardtomeasureintheactualphysicalsystem. Coupledwithoptimizationtechniques, a model can be used to improve equipment designs and therefore allowus to obtain a desired result at less expense or more quickly or with less effect on theenvironment.An engineering model will consist of a set of algebraic and/or differential equationsthat may be challenging to solve. In general, the more faithfully a mathematical modelrepresents a physical behavior, the more equations are required and the more compli-cated the model becomes. At one extreme, the model can require so much computationaleffort that it may be easier to conduct experiments using the actual physical system. Atthe other extreme, the model can be too simplistic. Although the equations are easyto solve, the model does not accurately represent the physics and therefore is not veryuseful. A useful model is a compromise between these extremes.Engineering Equation Solver (EES) is a computer program that has been devel-oped in order to numerically solve the type of algebraic and differential equations thattypically appear in models of thermodynamic systems. EES can check the dimensionaland unit consistency of the equations in order to catch many common programmingerrors. In addition, EES provides built-in functions for the thermodynamic and trans-port properties of many engineering uids. EES provides the capability to carry outparametric studies and generate high-quality plots; it can do optimization, provide linearand non-linear regression, and automate uncertainty analyses. The combination of equa-tion solving capability with access to engineering property data makes EES a powerful1.5Introduction to EES (Engineering Equation Solver) 9Equations WindowFigure 1-3:Two non-linear equations entered in the EES Equations window.tool for modeling thermal-uid systems and it is used extensively in industry. EES willbe used throughout this textbook.An introduction to EES is presented in this section. If you have already becomefamiliar with EES and are comfortable entering and solving equations then you can skipthis section. The EES program is probably installed on your departmental computersystem. If not, you can use the limited academic version that can be downloaded fromwww.fchart.com or www.cambridge.org/kleinandnellis. To start EES from the WindowsFile Manager or fromExplorer, double-click on the EES program icon or on any le thatwas created by EES. EES begins by displaying a splash screen that shows the registrationinformation, the version number and other information. Click the OK button in orderto dismiss the splash screen.You will next see the Equations window. The Equations windowis where the mathe-matical equations that constitute your model are entered. EES is capable of solving largesets of non-linear, coupled algebraic and differential equations. Enter the following twoequations on separate lines in the Equations window:x ln (x) = y3(1-13)x =1y(1-14)Equations (1-13) and (1-14) have no physical signicance. However, they are non-linearand coupled (i.e., they must be solved simultaneously) and, as a result, they would bedifcult to solve by hand. Note that the equations are entered in the Equations windowin the same manner that you would enter text into a word processor. However, there aresome rules that must be followed in order for EES to understand your input.1. Variable names must start with a letter and may consist of any keyboard characterexcept () | / + {}: or;. The maximum length of a variable name is 30 characters.2. EES is not case-sensitive. That is, upper and lower case letters are not distinguishedfrom one another. The variable X and the variable x are identical as far as EES isconcerned.3. Blank lines and spaces are ignored.4. In general, each equation must be entered on a separate line. However, multipleequations may be entered on one line if they are separated by a semi-colon (;).5. The caret symbol () and are both used to indicate the mathematical operation ofraising a number to a power. For example, y3can be entered as y3 or y3.6. EES uses the standard order of operations that is used by most other computerlanguages.After you have entered Eqs. (1-13) and (1-14), the Equations window should appear asshown in Figure 1-3.It is always important to annotate the equations in the Equations window so thatyouandotherswholookatyourmodel (e.g., yourthermodynamicsprofessor)canunderstand what each equation is intended to do. Annotation can be accomplished inEES by adding comments in the Equations window. Comments can be enclosed withincurly braces {} or within double quotation marks , as shown in Figure 1-4. It is good10 Basic ConceptsEquations Windowthis is a comment{this is also a comment}Figure 1-4:Equations window with equations and comments.practice to enter the comments immediately to the right of each equation; this process isfacilitated by pressing the tab key. Information within comments is ignored by EES andcomments may span as many lines as needed. EES will display the comments in blue.It is sometimes difcult to interpret equations that have been entered in text for-mat in the Equations window, particularly when many nested sets of parentheses oroperations are employed. Therefore, EES provides a Formatted Equations window thatdisplays the equations that are entered in the Equations window using a mathematicalnotation. Select Formatted Equations from the Windows menu in order to access theFormatted Equations window (Figure 1-5). Notice that the comments that are enteredin the Equations window within quotes are also displayed in the Formatted Equationswindow whereas comments entered in curly braces are not displayed. Normally, com-ments within quotes are used to document the equations whereas curly braces are usedto comment out text that you do not wish EES to use at this time. Commentingout a set of equations is a convenient way to remove these equations temporarily. Toaccomplish this, highlight the equation(s) to be removed and right-click. Select Com-ment {} from the pop-up menu that appears. To re-instate the equation(s), highlightthem again, right-click, and select Undo Comment {}.The equations in the Formatted Equations window can be copied and pasted, forexample into a report documenting the model. Highlight the equation(s) of interest andright-click on the selection. Notice that it is possible to copy the equation as a picturethat can be pasted into a word processor. The Professional version of EES can also copythe equation as a LaTeX object or a MathTypeR equation.Select Solve from the Calculate menu. A dialog window will appear indicating theprogress of the solution. Click the Continue button when the calculations are completedin order to display the Solution window that contains the solution to the set of equations(Figure 1-6). EES can solve thousands of equations very quickly, which makes it a verypowerful tool.The Equations window allows a free form input. As you can see in Figure 1-4, thepositionofvariableswithintheequationdoesnotmatteranditisnotnecessarytoisolate the unknown variable on the left side of an equal sign, as is required in formalprogramming languages. This capability is convenient because in many problems, it isnot possible to isolate the unknown variable. Also, the order in which the equationsareentereddoesnotmatter. Beforetheequationsaresolved, EESwill(internally)rearrange them into an order that leads to the most efcient solution process, regardlessFormatted Equationsthis is a commentFigure 1-5:Equations displayed in the Formatted Equations window.1.6Dimensions and Units 11SolutionUnit Settings: SI K Pa J mass rad Figure 1-6:Solution window.of the order that they are entered in the Equations window. Although EES allows youto enter equations in any order, it is still recommended that you enter your equationsin an organized manner that progresses logically from the known information to thedesired results. Also, it is best to enter and solve a few equations at a time, rather thanentering all of the equations needed to solve a problem at once. This strategy allowsyou to efciently debug your program because problems are naturally isolated to thelast group of equations that were entered. These best practices for using EES will bedemonstrated in the example problems presented throughout this textbook.1.6 Dimensions and UnitsMost of the variables used in models of thermodynamic processes and systems representphysical quantities and therefore they are dimensional. It is necessary to know both thevalue of the variable as well as its associated units. Calculation errors that result fromincorrectly converting between units are common and frustrating. Careful attention tounitsisessential. Thissectionreviewsthedimensionsandunitsofthefundamentalquantities used in thermodynamic analyses. One of the most basic and powerful featuresof the EES program is its ability to keep track of units, convert between units, and checkequations for unit consistency.1.6.1The SI and English Unit SystemsDimensions are the fundamental measures of a physical quantity. Dimensions are cat-egorized as being either primary or secondary. Primary dimensions for the quantitiesencountered in most thermodynamic models are usually chosen to be mass, length, time,and temperature, although other choices are equally valid. Secondary dimensions arecombinations of the primary dimensions and result from denitions or physical laws.Examples of secondary dimensions are length/time for velocity and mass-length/time2for force. Note that in this text, when dealing with units, the dash symbol (-) will indicatemultiplication on one side of the divisor. Therefore, the unit N-m/kg should be read asNmkgand the unit J/kg-K should be read asJkgK. This convention is consistent with howunits are entered in the EES program.The scale for a dimension is its units. Many different units can be used to expressa primary dimension. For example, the possible units for the dimension length includeinches, feet, yards, miles, meters, centimeters, furlongs, and many others. Secondarydimensions can also be expressed in many different units. Energy, for example, is a sec-ondary dimensionthat is expressedinterms of primary dimensions as mass-length2/time2.The units of energy include ft-lbf, Btu (British thermal units), calories, Joules, and manyothers.Units are commonly categorized as belonging to the English or SI (Systems Interna-tional) unit system. A list of the standard units used for the primary dimensions in eachsystem is provided in Table 1-1. Some secondary dimensions and their typical units ineach system are provided in Table 1-2.12 Basic ConceptsTable 1-1: Standard units for primary dimensions in the SI and English unit systems.SI Unit System English Unit SystemPhysical Quantity Unit Symbol Unit Symbolmass (M) kilogram kg pound-mass lbmlength (L) meter m foot fttime (t) second s second stemperature (T) Kelvin K Rankine Rdegree CelsiusC degree FahrenheitFWhy is there more than one unit for each dimension? There is no single answerto this question. Convenience certainly provides one explanation. It is possible but notconvenient to express the distance between New York and California in inches or feet,but miles is a more convenient measure. Different societies have historically adopteddifferent units for the same dimension and these conventions tend to persist for a longtime.Inat least onecase, theprimaryunits associatedwithasecondarydimensionremained undiscovered until after the dimension itself had already achieved widespreaduse. Heat and work were for a long time considered to be unrelated quantities. The sci-ence of calorimetry was developed to measure heat and used as its fundamental unit theBritish Thermal Unit (Btu) or calorie. Work was understood to be a separate quantitythat resulted in lifting a weight; therefore, the unit of work was taken to be ft-lbf. Jouledemonstrated in the late 1800s that many of the effects produced by heat could also beproduced by work. At that time it became clear that heat and work both refer to thetransfer of energy and therefore could share a common unit.Whatever the reasons, physical quantities can be expressed using many differentunits and this fact introduces the possibility for unit conversion errors. The practicingengineermustbeabletodealwithandconvertbetweenavarietyofunitsandunitsystems. Instrumentswillreportmeasurementsinavarietyofunits. Forexample, avacuumgage may report pressure measurements inunits of torr while a water manometerwill naturally lead to a pressure measurement in units of inches of water. Engineers mustcommunicate the results of their analyses to a variety of audiences, some of whom aremost comfortable thinking in terms of a specic set of units. For example, cooling powerTable 1-2: Units of some secondary dimensions in the SI and English unit systems.SI Unit System English Unit SystemPhysical Quantity Dimensions Unit Symbol Unit Symbolforce M-L/t2Newton N pound-force lbfenergy M-L2/t2Joule J British Thermal Unit Btupower M-L2/t3Watt (J/s) W horsepower hppressure M/L-t2Pascal (N/m2) Pa pound/inch2psibar bar atmosphere atm1.6Dimensions and Units 13should be reported to a refrigeration engineer in the U.S. in units of tons. An automotiveengineer in the U.S. would be most comfortable understanding output power in units ofhorsepower.In the real world, the inputs to an engineering analysis will be provided in a varietyof units (often in mixed units, some SI and some English) and the results of the analysisshould be reported in whatever units are most appropriate. However, it is not necessaryto carry out the analysis in an arbitrary set of units. In fact, there is a strong argument forworking a problem entirely in the SI system of units that is listed in Table 1-1. This unitsystem is dened so that it is completely self-consistent; that is, no unit conversions arerequired when working in the standard SI unit system. For example, the SI unit of energy(the Joule) is equal to the product of the SI units of force (the Newton) and distance (themeter):1 J = 1 N-m (1-15)The SI unit of force (the Newton) is related to the SI units of mass, distance and time(kg, m, and s, respectively) according to:1 N = 1 kg-ms2(1-16)The same self-consistency is not evident in the English unit system. The unit of energyin the English system (the British Thermal Unit or Btu) is related to the English units offorce and distance according to:1 Btu = 778.17 lbf-ft (1-17)The English unit of force is related to the English units of mass, distance, and timeaccording to:1 lbf = 32.174 lbm-fts2(1-18)The differences between Eqs. (1-15) and (1-16) and Eqs. (1-17) and (1-18) clearly illus-trate the self-consistency of the SI unit system and the need for unit conversions whenworking in the English unit system. Appendix A contains tables of many common unitconversions.The units of each variable are self-evident in the SI unit system. It is not necessaryto constantly worry about applying the correct unit conversion to each equation duringthe development of a model. As a result, if you are working in the SI unit system andyou check the units of your equations then you are actually carrying out a more powerfuland complete check on your equations; you are establishing their dimensional (as wellas their unit) consistency.It is up to the engineer to establish a procedure for dealing with units that worksfor him or her, and it is not the objective of this text to be prescriptive in this regard.Certainly there are many strategies that work. However, in this book we will consistentlyadopt the following procedure. Inputs to the problem reported in arbitrary units will beconverted to the base SI system listed in Table 1-1 and Table 1-2 (i.e., kg, m, s, K, N, J,etc.). The calculations required to solve the problem will be carried out using the base SIsystem and unit checking will be rigorously applied in order to establish the dimensionalconsistencyofeachequation. TheresultswillbeconvertedfromtheSIsysteminto14 Basic ConceptsEXAMPLE1.6-1:WEIGHTONMARSwhatever units are requested or are logical and convenient. With this approach in mind,the tables in Appendix A are presented so that it is easy to convert from arbitrary unitsto their SI equivalent and back.EXAMPLE 1.6-1: WEIGHT ON MARSThe gravitational acceleration on the surface of Mars is g =12.5 ft/s2, which is about38% of the gravitational acceleration on earths surface.a) What is the weight on Mars of an astronaut with a mass of m = 175 lbm?The inputs to the problem, g and m, are converted to base SI units using the con-versions found in Appendix A.g =12.5fts2____0.30480mft= 3.81ms2m=175 lbm____0.45359kglbm= 79.38 kgThe weight of the astronaut is computed according to:W = mg =79.38 kg3.81 ms2____N-s2kg-m = 302.4 NNotice that the computed weight of the astronaut is automatically expressed in theSIunitforforce,theNewton.Nounitconversionisrequiredbecausetheinputswere converted to SI units. If the weight of the astronaut is required in other, non-SIunits (e.g., lbf) then the SI result is converted according to:W =302.4 N____lbf4.4482 N =67.98 lbfThis example illustrates the strategy of converting inputs to the SI system, carryingout the calculations required for the problemin the SI unit system, and then convert-ing the results to appropriate, non-SI units if necessary. This example was trivial.However, as the problems become more complex, this approach is an effective wayof avoiding unit conversion errors.1.6.2Working with Units in EESIt is possible to assign both a value and a unit to each of the variables that are usedinanEESprogram. EEShasbeenprogrammedtocheckthedimensionalandunitconsistency of the equations. In order to apply this capability, it is necessary to enter theunits of all variables that are used in the analysis. We will demonstrate howthis is done inExample 1.6-2.1.6Dimensions and Units 15EXAMPLE1.6-2:POWERREQUIREDBYAVEHICLEEXAMPLE 1.6-2: POWER REQUIRED BY A VEHICLEThetwomajorforcesopposingthemotionof avehicleonalevel roadaretherollingresistanceofthetires(Fr)andtheaerodynamicdragonthecar(Fd).Therolling resistance is the product of the dimensionless rolling resistance coefcient,f = 0.02, and the force exerted by the vehicle on the road (i.e., its weight, W).Fr = f W (1)The aerodynamic drag is expressed in terms of a dimensionless drag coefcient(Cd) according to:Fd = Af Cd12V 2(2)where Af is the frontal area of the vehicle, = 0.075 lbm/ft3is the density of air andVis the speed of the vehicle. The Toyota Prius has a drag coefcient of Cd = 0.29,a frontal area of Af = 21.2 ft2and a curb weight of W= 2930 lbf.a) Determine the power required by a Prius (in hp) traveling at a velocity ofV=65 mph.It is good form to put the problem inputs at the top of the Equations window.Each input is entered and immediately annotated. Well start with the density ofair.rho=0.075 [lbm/ft3] density of airNotethat theunitsof thenumerical constant, 0.075, areenteredinsquarebrackets immediately after the constant is typed in EES. If the EES code is solved atthis point (select Solve from the Calculate menu) you will see that the units of thevariable rho are indicated next to its value in the Solutions window (Figure 1). The symbol in the unit designation for rho is used to raise a unit to a power. EES willalso accept the unit lbm/ft3, but the symbol helps EES recognize that the 3 shouldbe a superscript in the formatted output. Also note that the unit for pound-mass isrepresented in EES as eitherlb_m orlbm. The underscore causes EES to recognizethat the m should be a subscript, but either designation is acceptable.SolutionUnit Settings: SI K Pa J mass rad[lbm/ft3] Figure 1:Solution window.The unit designations that are recognized by EES can be viewed by selectingUnit Conversion Info from the Options menu. Select the dimension from the list onthe left and EES will display the dened units associated with that dimension inthe list on the right, as shown in Figure 2 for the dimension mass.As discussed in Section 1.6.1, the inputs to the problem should be convertedtoSIunits.EESprovidesthefunctionconvert inordertoeasilyconvertfromone16 Basic ConceptsEXAMPLE1.6-2:POWERREQUIREDBYAVEHICLElbmkgMassUnit Conversion InformationFigure 2:Unit Conversion Information dialog.unit to another without resorting to the use of tables of unit conversion factors (likethoseincludedinAppendixA).Theconvertfunctionacceptstwoarguments.Therst argument indicates the unit(s) that you wish to convert from, and the secondargument is the unit(s) that you wish to convert to. Both sets of units must have thesame dimensions (i.e., they must be dimensionally consistent). So, for example, theconversion factor that is required to convert from feet to meters is obtained fromtheEEScodeconvert(ft,m). AccordingtoAppendixA, thefunctionconvert(ft,m) willreturn the conversion factor 0.30480 m/ft. In our case, we wish to convert the densityof air from the English units that it was provided in, lbm/ft3, to SI units, kg/m3. WecandothisconversionbyrevisingtheinformationintheEquationswindowasfollows:rho=0.075 [lbm/ft3]*convert(lbm/ft3,kg/m3) density of airSelect Solve from the Equations menu (or press the F2 key, the shortcut for Solve)and you will see the Solution window (Figure 3).SolutionUnit Settings: SI K Pa J mass rad[lbm/ft3]Figure 3:Solution window.Notice the warning message indicating that EES has detected a unit problem.EEScheckstheunitsofyourequationseachtimeyousolve. YoucanhaveEEScheck units at any time by selecting Check Units from the Calculate menu (or bypressing F8). A window will appear that provides a list of all of the equations that1.6Dimensions and Units 17EXAMPLE1.6-2:POWERREQUIREDBYAVEHICLEcontain unit errors as well as some description of the unit inconsistency that wasdetected (Figure 4).Check UnitsThe units of rho [lbm/ft^3] and 0.075 * 16.0184635 [(lbm/ft^3) * ((kg/m^3)/(lbm/ft^3))] differ by a factor of 16.02.Figure 4:Check Units dialog.The units of the variablerho were previously set to lbm/ft3; these units are nolonger consistent with the equation that is used to specify the variable. This is mostevident by examining the Formatted Equations window (Figure 5).Formatted Equations[lbm/ft3] density of airFigure 5:Formatted Equations window.Figure 5 shows that the units of the variable rho are clearly kg/m3and thereforethe units assigned to this variable should be updated to reect the unit conversionthat was carried out. There are several ways to set the units of a variable. One wayistohighlightthevariableintheEquationswindowandright-clickonit;selectVariable Info from the pop-up menu that appears (Figure 6).rhoEquations Window[lbm/ft^3] density of airVariable Info Shift+Ctrl+VFigure 6:Setting the units of a variable from the Equations window.A dialog box will appear that allows you to set the units of the variable rho, asshown in Figure 7.18 Basic ConceptsEXAMPLE1.6-2:POWERREQUIREDBYAVEHICLErhoFigure 7:Variable information dialog for the variable rho.WhentheEESprogramissolved, theunitsofthevariablerhoareindicatedbesideitsvalueintheSolutionwindow. Anotherwayof settingtheunitsof avariable is by right-clicking on the variable in the Solution window; a dialog willappear that allows you to set many of the characteristics of the variable includingits units, as shown in Figure 8. = 1.201 [lbm/ft3]SolutionFormat Selected VariablesUnit Setting: SI K Pa J mass radFigure 8:Setting units from the Solution window.Noticethatinadditiontotheunits, theformatusedtodisplaythevariablecan be adjusted in the dialog shown in Figure 8. By default, all variables are set toAuto