Table Of ContentHardy ffirs.tex Printer-03/26/2014 8:22A.M. Pageii
Thermodynamics and
Statistical Mechanics
Thermodynamics and
Statistical Mechanics
An Integrated Approach
ROBERT J. HARDY and CHRISTIAN BINEK
Department of Physics, University of
Nebraska-Lincoln, USA
Thiseditionfirstpublished2014
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LibraryofCongressCataloging-in-PublicationData
Hardy,RobertJ.,1935-author.
Thermodynamicsandstatisticalmechanics:anintegratedapproach/ProfessorRobertJ.HardyandProfessorChristianBinek.
pagescm
Includesindex.
ISBN978-1-118-50101-6(cloth)–ISBN978-1-118-50100-9(pbk.) 1.Thermodynamics–Textbooks. 2.Statistical
mechanics–Textbooks. I.Binek,Christian,author. II.Title.
QC311.H32732014
536′.7–dc23
2013039738
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:9781118501016
Setin10/12ptTimesLTStdbyLaserwordsPrivateLimited,Chennai,India
12014
Hardy ftoc.tex V3-03/20/2014 1:24P.M. Pagev
Contents
Preface xiii
PartI ElementsofThermalPhysics 1
1. Fundamentals 3
1.1 PVT Systems 3
1.2 EquilibriumStates 6
1.3 ProcessesandHeat 10
1.4 Temperature 12
1.5 SizeDependence 13
1.6 HeatCapacityandSpecificHeat 14
Problems 17
2. FirstLawofThermodynamics 19
2.1 Work 19
2.2 Heat 21
2.3 TheFirstLaw 21
2.4 Applications 22
Problems 26
3. PropertiesandPartialDerivatives 27
3.1 Conventions 27
3.2 EquilibriumProperties 28
3.3 RelationshipsbetweenProperties 34
3.4 SeriesExpansions 40
3.5 Summary 41
Problems 42
4. ProcessesinGases 45
4.1 IdealGases 45
4.2 TemperatureChangewithElevation 48
4.3 CyclicProcesses 50
4.4 HeatEngines 52
Problems 58
5. PhaseTransitions 61
5.1 Solids,Liquids,andGases 61
5.2 LatentHeats 65
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vi Contents
5.3 VanderWaalsModel 67
5.4 ClassificationofPhaseTransitions 70
Problems 72
6. ReversibleandIrreversibleProcesses 75
6.1 IdealizationandReversibility 75
6.2 NonequilibriumProcessesandIrreversibility 76
6.3 ElectricalSystems 79
6.4 HeatConduction 82
Problems 86
PartII FoundationsofThermodynamics 89
7. SecondLawofThermodynamics 91
7.1 Energy,Heat,andReversibility 91
7.2 CyclicProcesses 93
7.3 SecondLawofThermodynamics 95
7.4 CarnotCycles 98
7.5 AbsoluteTemperature 100
7.6 Applications 103
Problems 107
8. TemperatureScalesandAbsoluteZero 109
8.1 TemperatureScales 109
8.2 UniformScalesandAbsoluteZero 111
8.3 OtherTemperatureScales 114
Problems 115
9. StateSpaceandDifferentials 117
9.1 Spaces 117
9.2 Differentials 121
9.3 ExactVersusInexactDifferentials 123
9.4 IntegratingDifferentials 127
9.5 DifferentialsinThermodynamics 129
9.6 DiscussionandSummary 134
Problems 136
10. Entropy 139
10.1 DefinitionofEntropy 139
10.2 Clausius’Theorem 142
10.3 EntropyPrinciple 145
10.4 EntropyandIrreversibility 148
10.5 UsefulEnergy 151
10.6 TheThirdLaw 155
10.7 UnattainabilityofAbsoluteZero 156
Problems 158
Appendix10.A.EntropyStatementoftheSecondLaw 158
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Contents vii
11. ConsequencesofExistenceofEntropy 165
11.1 DifferentialsofEntropyandEnergy 165
11.2 IdealGases 167
11.3 RelationshipsBetweenC ,C ,B ,B ,andα 170
V P T S V
11.4 Clapeyron’sEquation 172
11.5 MaximumEntropy,Equilibrium,andStability 174
11.6 Mixing 178
Problems 184
12. ThermodynamicPotentials 185
12.1 InternalEnergy 185
12.2 FreeEnergies 186
12.3 PropertiesFromPotentials 188
12.4 SystemsinContactwithaHeatReservoir 193
12.5 MinimumFreeEnergy 194
Problems 197
Appendix12.A.DerivativesofPotentials 197
13. PhaseTransitionsandOpenSystems 201
13.1 Two-PhaseEquilibrium 201
13.2 ChemicalPotential 206
13.3 Multi-ComponentSystems 211
13.4 GibbsPhaseRule 214
13.5 ChemicalReactions 215
Problems 217
14. DielectricandMagneticSystems 219
14.1 Dielectrics 219
14.2 MagneticMaterials 224
14.3 CriticalPhenomena 229
Problems 233
PartIII Statistical Thermodynamics 235
15. MolecularModels 237
15.1 MicroscopicDescriptions 237
15.2 GasPressure 238
15.3 EquipartitionofEnergy 243
15.4 InternalEnergyofSolids 246
15.5 InactiveDegreesofFreedom 247
15.6 MicroscopicSignificanceofHeat 248
Problems 253
16. KineticTheoryofGases 255
16.1 VelocityDistribution 255
16.2 Combinatorics 256
16.3 MethodofUndeterminedMultipliers 258
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16.4 MaxwellDistribution 260
16.5 Mean-Free-Path 265
Problems 267
Appendix16.A.QuantumDistributions 267
17. MicroscopicSignificanceofEntropy 273
17.1 BoltzmannEntropy 273
17.2 IdealGas 274
17.3 StatisticalInterpretation 278
17.4 ThermodynamicProperties 279
17.5 BoltzmannFactors 284
Problems 286
Appendix17.A.EvaluationofI 286
3N
PartIV StatisticalMechanicsI 289
18. Ensembles 291
18.1 ProbabilitiesandAverages 291
18.2 Two-LevelSystems 293
18.3 InformationTheory 295
18.4 EquilibriumEnsembles 298
18.5 CanonicalThermodynamics 302
18.6 CompositeSystems 305
Problems 308
Appendix18.A.UniquenessTheorem 308
19. PartitionFunction 311
19.1 HamiltoniansandPhaseSpace 311
19.2 ModelHamiltonians 312
19.3 ClassicalCanonicalEnsemble 316
19.4 ThermodynamicPropertiesandAverages 318
19.5 IdealGases 322
19.6 HarmonicSolids 326
Problems 328
20. QuantumSystems 331
20.1 EnergyEigenstates 331
20.2 QuantumCanonicalEnsemble 333
20.3 IdealGases 334
20.4 EinsteinModel 337
20.5 ClassicalApproximation 341
Problems 344
Appendix20.A.IdealGasEigenstates 344
21. IndependentParticlesandParamagnetism 349
21.1 Averages 349
