Principles of Thermodynamics Myron Kaufman Emory University Atlanta, Georgia Marcel Dekker, Inc. New York Basel • TM Copyright ©2001 by Marcel Dekker,Inc. All Rights Reserved. ISBN: 0-8247-0692-7 Thisbookisprinted onacid-free paper Headquarters Marcel Dekker, Inc. 270Madison Avenue, NewYork,NY10016 tel:212-696-9000; fax:212-685-4540 EasternHemisphereDistribution Marcel Dekker AG Hutgasse 4,Postfach 812, CH-4001Basel, Switzerland tel:41-61-260-6300; fax: 41-61-260-6333 WorldWideWeb http:==www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales=Professional Marketing at the headquarters address above. Copyright #2002by Marcel Dekker,Inc.All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means,electronicormechanical,includingphotocopying,microfilming,andrecording,or by any information storage and retrieval system, without permission in writing from the publisher. Current printing(last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED INTHE UNITEDSTATES OFAMERICA UNDERGRADUATECHEMISTRY ASeriesofTextbooks Editedby J.J.LAGOWSKI DepartmentofChemistry TheUniversityofTexasatAustin 1. ModernInorganicChemistry,J.J.Lagowski 2. Modern Chemical Analysis and Instrumentation, Harold F. Walton and Jorge Reyes 3. ProblemsinChemistry,SecondEdition,RevisedandExpanded,HenryO.Daley, Jr.,andRobertF.O'Malley 4. PrinciplesofColloidandSurfaceChemistry,PaulC.Hiemenz 5. PrinciplesofSolutionandSolubility,KozoShinoda,translatedincollaborationwith PaulBecher 6. PhysicalChemistry:AStep-by-StepApproach, M.K.Kemp 7. NumericalMethodsinChemistry,K.JeffreyJohnson 8. Polymer Chemistry: An Introduction, Raymond B. Seymour and Charles E. Carraher,Jr. 9. Principles of Colloid and Surface Chemistry, Second Edition, Revised and Expanded,PaulC.Hiemenz 10. ProblemsinChemistry,SecondEdition,RevisedandExpanded,HenryO.Daley, Jr.,andRobertF.O'Malley 11. Polymer Chemistry: An Introduction, Second Edition, Raymond B. Seymour and CharlesE.Carraher,Jr. 12. Polymer Chemistry: An Introduction, Third Edition, Revised and Expanded, RaymondB.SeymourandCharlesE.Carraher,Jr. 13. Seymour/Carraher’sPolymerChemistry:AnIntroduction,FourthEdition,Revised andExpanded,CharlesE.Carraher,Jr. 14. Seymour/Carraher’s Polymer Chemistry: Fifth Edition, Revised and Expanded, CharlesE.Carraher,Jr. 15. PrinciplesofThermodynamics,MyronKaufman AdditionalVolumesinPreparation Seymour/Carraher’s Polymer Chemistry: Sixth Edition, Revised and Expanded, CharlesE.Carraher,Jr. Dedicated to my beloved brother Stuart, whose brilliant life ended too soon. Preface Once upon a time there were Giants, with names like Joule, Maxwell, Carnot, Clausius, and Thomson (Lord Kelvin). They lived during a time, called the Industrial Revolution, when labor-saving machines were being developed to greatly expand the productive capabilities of humankind. In the never-ending attempts to improve the performance of these machines, the Giants were led to profoundconsiderationsofthefundamentallimitsofenergyconversions.Starting with some simple observations, they developed the science of thermodynamics. This science deals with energy and its capabilities and transformations. Later, Boltzmann—another Giant—connected thermodynamics to the microscopic world of atoms and molecules, while Prigogine extended thermodynamics to deal with non-equilibrium systems. The purpose of Principles of Thermodynamics is to convey the powerful ideasoftheGiantstoadvancedundergraduates,beginninggraduatestudents,and interestedscientificreadersatanappropriatemathematicallevel,enlighteningthis audiencetothewidevarietyofproblemsforwhichathermodynamicperspective isuseful.Inthisvolume,Ihavechosentoexpressthelawsofthermodynamicsin terms of simple principles, self-evident from everyday experience. For example, the second law—the cornerstone of any presentation of thermodynamics—is stated as ‘‘in any real process there is net degradation of energy.’’ I believe this approachismuchmorecomprehensiblethanthatbasedonmachines,usedbythe Giants. v vi Preface Since mathematics is the language of thermodynamics, there are many equations in this book. However, the mathematics used is no more complicated than necessary. Facility with differentiation and integration at the levelof a first- year course in calculus is assumed and a few relationships from multivariable calculus are used repeatedly. All the reader has to know about this subject, however, is presented in Appendix A. Although the mathematically advanced reader can skim over this, it remains as a handy reference for any question that arises on multivariable calculus. PrinciplesofThermodynamicsshouldbeaccessibletoscientificallyliterate persons who are either learning the subject on their own or reviewing the material. At Emory University, this volume forms the basis of the first semester of a one-year sequence in physical chemistry. Problems and questions are included at the end of each chapter. Essentially, the questions test whether the students understand thematerial,and theproblemstest whether theycanusethe derived results. More difficult problems are indicated by an asterisk. Some problems, marked with an M, involve numerical calculations that are most easily performed with the use of a computer program such as Mathcad or Mathematica. A brief survey of some of these numerical methods is included in Appendix B, for cases in which the programs are unavailable or cumbersome to use. Thermodynamics deals with relations between properties of materials and changes of these properties during processes. Some knowledge of specific properties is thus necessary before beginning a discussion of thermodynamics. ThisisthepurposeofChapter1,whichdealswithsomeofthepropertiesofgases andothermaterials.InChapter2,afterdefiningtermsandintroducingthezeroth and the first law, conservation of energy is applied to a number of processes. In Chapter 3, the quality of energy is used as the basis for introducing entropy and the second law, which determines the direction of spontaneous processes and equilibrium. In Chapter 4, entropy is placed on an absolute basis with the third law, which involves low-temperature systems. The advantages of analyzing processes using free-energy functions are then introduced. Chapter 5 gives a microscopic-world explanation of the second law, and uses Boltzmann’s definition of entropy to derive some elementary statistical mechanics relationships. These are used to develop the kinetic theory of gases andderiveformulasforthermodynamicfunctionsbasedonmicroscopicpartition functions.Theseformulasareappliedtoidealgases, simplepolymer mechanics, and the classical approximation to rotations and vibrations of molecules. In Chapters 6, 7, and 8, the thermodynamic framework is successively applied to phase transformations of single-component systems, chemical reac- tions, and ideal solutions. Included are discussions of the thermodynamics of open systems, the phase rule, and colligative properties. Chapter 9 gives the framework for discussing nonideal multicomponent systems and describes a Preface vii variety of phase diagrams of such systems. In Chapter 10, the discussion is extended to ionized systems, including galvanic cells. Chapter 11 deals with surfaceeffectsinbothsingle-andmulticomponentsystems,includingadsorption. Finally,inChapter12thethermodynamicsofopensystemsisappliedtosystems at steady state undergoing dissipative process. Although several applications of this material are considered, the aim is to give the reader the tools needed to approachtheextensiveliteratureonthissubject.ThematerialinChapter12isnot coveredinthephysicalchemistrysequence,butisassignedasoutsidereadingfor outstanding students. Principles of Thermodynamics is both compact and rigorous; almost all results are ‘‘derived.’’ Most of all, this book tries to convey the beauty of one of the most impressive triumphs of the human mind—the application of deductive reasoningfromafewsimplepostulates,resultinginthedevelopmentofamyriad of relationships useful in just about every branch of science. ManythanksaregiventoProfessorC.G.TrowbridgeofEmoryUniversity and Professor Wentao Zhu of Tsinghua University, Beijing, for reading parts of themanuscript.Morethananyone,Ithankmywife,June,forherencouragement and understanding throughout the protracted period it took to write this book. Myron Kaufman Contents Preface v 1 Introduction and Background 1 1.1 Introduction 2 1.2 The Ideal Gas 4 1.3 Thermal Expansion Coefficient and Isothermal Compressibility 6 1.4 A Simple Model of the Ideal Gas 8 1.5 Real Gases: The van der Waals Equation 12 1.6 Real Gases: Other Equations 15 1.7 Condensation and the Critical Point 19 1.8 Gas Mixtures 24 1.9 Equations of State of Condensed Phases 26 1.10 Pressure Variations in Fluids 30 Questions 31 Problems 32 Notes 34 2 Thermodynamics: The Zeroth and First Laws 36 2.1 The Nature of Thermodynamics 37 ix x Contents 2.2 Systems 37 2.3 Equilibrium 38 2.4 Properties 39 2.5 Processes 40 2.6 Heat and the Zeroth Law of Thermodynamics 40 2.7 Work 43 2.8 Internal Energy 49 2.9 The First Law 49 2.10 Heat Capacities 51 2.11 The Joule Process 58 2.12 The Joule-Thomson Process 59 2.13 Reversible Adiabatic Expansion of an Ideal Gas 62 2.14 A Simple Heat Engine 64 Questions 67 Problems 69 Notes 70 3 The Second Law of Thermodynamics 71 3.1 The Second Law 71 3.2 Entropy Changes in Some Simple Processes 79 3.3 Heat Diagrams 84 3.4 General Analysis of Thermal Devices 85 Questions 88 Problems 90 Notes 92 4 The Third Law and Free Energies 93 4.1 Absolute Zero and the Third Lawof Thermodynamics 94 4.2 Absolute Entropies 97 4.3 Helmholtz and Gibbs Free Energies 98 4.4 Partial Derivatives of Energy-like Quantities 101 4.5 Heat Capacities 106 4.6 Generalization to Additional Displacements 106 4.7 Standard States 107 4.8 Entropy of Mixing of Ideal Gases 109 4.9 Thermodynamics of Stretching Rubbers 110 Questions 112 Problems 114 Notes 116