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PART Ⅰ GENERAL PRINCIPLES OF CLASSICAL THERMODYNAMICS 1

Introduction The Nature of Thermodynamics and the Basis of Thermostatistics 2

1 THE PROBLEM AND THE POSTULATES 5

1.1 The Temporal Nature of Macroscopic Measurements 5

1.2 The Spatial Nature of Macroscopic Measurements 6

1.3 The Composition of Thermodynamic Systems 9

1.4 The Internal Energy 11

1.5 Thermodynamic Equilibrium 13

1.6 Walls and Constraints 15

1.7 Measurability of the Energy 16

1.8 Quantitative Definition of Heat—Units 18

1.9 The Basic Problem of Thermodynamics 25

1.10 The Entropy Maximum Postulates 27

2 THE CONDITIONS OF EQUILIBRIUM 35

2.1 Intensive Parameters 35

2.2 Equations of State 37

2.3 Entropic Intensive Parameters 40

2.4 Thermal Equilibrium—Temperature 43

2.5 Agreement with Intuitive Concept of Temperature 45

2.6 Temperature Units 46

2.7 Mechanical Equilibrium 49

2.8 Equilibrium with Respect to Matter Flow 54

2.9 Chemical Equilibrium 56

3 SOME FORMAL RELATIONSHIPS，AND SAMPLE SYSTEMS 59

3.1 The Euler Equation 59

3.2 The Gibbs-Duhem Relation 60

3.3 Summary of Formal Structure 63

3.4 The Simple Ideal Gas and Multicomponent Simple Ideal Gases 66

3.5 The “Ideal van der Waals Fluid” 74

3.6 Electromagnetic Radiation 78

3.7 The “Rubber Band” 80

3.8 Unconstrainable Variables； Magnetic Systems 81

3.9 Molar Heat Capacity and Other Derivatives 84

4 REVERSIBLE PROCESSES AND THE MAXIMUM WORK THEOREM 91

4.1 Possible and Impossible Processes 91

4.2 Quasi-Static and Reversible Processes 95

4.3 Relaxation Times and Irreversibility 99

4.4 Heat Flow：Coupled Systems and Reversal of Processes 101

4.5 The Maximum Work Theorem 103

4.6 Coefficients of Engine，Refrigerator，and Heat Pump Performance 113

4.7 The Carnot Cycle 118

4.8 Measurability of the Temperature and of the Entropy 123

4.9 Other Criteria of Engine Performance； Power Output and“Endoreversible Engines” 125

4.10 Other Cyclic Processes 128

5 ALTERNATIVE FORMULATIONS AND LEGENDRE TRANSFORMATIONS 131

5.1 The Energy Minimum Principle 131

5.2 Legendre Transformations 137

5.3 Thermodynamic Potentials 146

5.4 Generalized Massieu Functions 151

6 THE EXTREMUM PRINCIPLE IN THE LEGENDRE TRANSFORMED REPRESENTATIONS 153

6.1 The Minimum Principles for the Potentials 153

6.2 The Helmholtz Potential 157

6.3 The Enthalpy； The Joule-Thomson or “Throttling” Process 160

6.4 The Gibbs Potential； Chemical Reactions 167

6.5 Other Potentials 172

6.6 Compilations of Empirical Data； The Enthalpy of Formation 173

6.7 The Maximum Principles for the Massieu Functions 179

7 MAXWELL RELATIONS 181

7.1 The Maxwell Relations 181

7.2 A Thermodynamic Mnemonic Diagram 183

7.3 A Procedure for the Reduction of Derivatives in Single-Component Systems 186

7.4 Some Simple Applications 190

7.5 Generalizations：Magnetic Systems 199

8 STABILITY OF THERMODYNAMIC SYSTEMS 203

8.1 Intrinsic Stability of Thermodynamic Systems 203

8.2 Stability Conditions for Thermodynamics Potentials 207

8.3 Physical Consequences of Stability 209

8.4 Le Chatelier’s Principle； The Qualitative Effect of Fluctuations 210

8.5 The Le Chatelier-Braun Principle 212

9 FIRST-ORDER PHASE TRANSITIONS 215

9.1 First-Order Phase Transitions in Single-Component Systems 215

9.2 The Discontinuity in the Entropy-Latent Heat 222

9.3 The Slope of Coexistence Curves； the Clapeyron Equation 228

9.4 Unstable Isotherms and First-Order Phase Transitions 233

9.5 General Attributes of First-Order Phase Transitions 243

9.6 First-Order Phase Transitions in Multicomponent Systems—Gibbs Phase Rule 245

9.7 Phase Diagrams for Binary Systems 248

10 CRITICAL PHENOMENA 255

10.1 Thermodynamics in the Neighborhood of the Critical Point 255

10.2 Divergence and Stability 261

10.3 Order Parameters and Critical Exponents 263

10.4 Classical Theory in the Critical Region； Landau Theory 265

10.5 Roots of the Critical Point Problem 270

10.6 Scaling and Universality 272

11 THE NERNST POSTULATE 277

11.1 Nernst’s Postulate，and the Principle of Thomsen and Bertholot 277

11.2 Heat Capacities and Other Derivatives at Low Temperatures 280

11.3 The “Unattainability” of Zero Temperature 281

12 SUMMARY OF PRINCIPLES FOR GENERAL SYSTEMS 283

12.1 General Systems 283

12.2 The Postulates 283

12.3 The Intensive Parameters 284

12.4 Legendre Transforms 285

12.5 Maxwell Relations 285

12.6 Stability and Phase Transitions 286

12.7 Critical Phenomena 287

12.8 Properties at Zero Temperature 287

13 PROPERTIES OF MATERIALS 289

13.1 The General Ideal Gas 289

13.2 Chemical Reactions in Ideal Gases 292

13.3 Small Deviations from “Ideality”—The Virial Expansion 297

13.4 The “Law of Corresponding States” for Gases 299

13.5 Dilute Solutions：Osmotic Pressure and Vapor Pressure 302

13.6 Solid Systems 305

14 IRREVERSIBLE THERMODYNAMICS 307

14.1 General Remarks 307

14.2 Affinities and Fluxes 308

14.3 Purely-Resistive and Linear Systems 312

14.4 The Theoretical Basis of the Onsager Reciprocity 314

14.5 Thermoelectric Effects 316

14.6 The Conductivities 319

14.7 The Seebeck Effect and the Thermoelectric Power 320

14.8 The Peltier Effect 323

14.9 The Thomsen Effect 324

ART Ⅱ TATISTICAL MECHANICS 329

15 STATISTICAL MECHANICS IN THE ENTROPY REPRESENTATION：THE MICROCANONICAL FORMALISM 329

15.1 Physical Significance of the Entropy for Closed Systems 329

15.2 The Einstein Model of a Crystalline Solid 333

15.3 The Two-State System 337

15.4 A Polymer Model—The Rubber Band Revisited 339

15.5 Counting Techniques and their Circumvention；High Dimensionality 343

16 THE CANONICAL FORMALISM； STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION 349

16.1 The Probability Distribution 349

16.2 Additive Energies and Factorizability of the Partition Sum 353

16.3 Internal Modes in a Gas 355

16.4 Probabilities in Factorizable Systems 358

16.5 Statistical Mechanics of Small Systems：Ensembles 360

16.6 Density of States and Density-of-Orbital States 362

16.7 The Debye Model of Non-metallic Crystals 364

16.8 Electromagnetic Radiation 368

16.9 The Classical Density of States 370

16.10 The Classical Ideal Gas 372

16.11 High Temperature Properties—The Equipartition Theorem 375

17 ENTROPY AND DISORDER； GENERALIZED CANONICAL FORMULATIONS 379

17.1 Entropy as a Measure of Disorder 379

17.2 Distributions of Maximal Disorder 382

17.3 The Grand Canonical Formalism 385

18 QUANTUM FLUIDS 393

18.1 Quantum Particles； A “Fermion Pre-Gas Model” 393

18.2 The Ideal Fermi Fluid 399

18.3 The Classical Limit and the Quantum Criteria 402

18.4 The Strong Quantum Regime； Electrons in a Metal 405

18.5 The Ideal Bose Fluid 410

18.6 Non-Conserved Ideal Bose Fluids； Electromagnetic Radiation Revisited 412

18.7 Bose Condensation 413

19 FLUCTUATIONS 423

19.1 The Probability Distribution of Fluctuations 423

19.2 Moments and The Energy Fluctuations 424

19.3 General Moments and Correlation Moments 426

20 VARIATIONAL PROPERTIES，PERTURBATION EXPANSIONS，AND MEAN FIELD THEORY 433

20.1 The Bogoliubov Variational Theorem 433

20.2 Mean Field Theory 440

20.3 Mean Field Theory in Generalized Representation；the Binary Alloy 449

PART Ⅲ FOUNDATIONS 455

21 POSTLUDE：SYMMETRY AND THE CONCEPTUAL FOUNDATIONS OF THERMOSTATISTICS 455

21.1 Statistics 455

21.2 Symmetry 458

21.3 Noether’s Theorem 460

21.4 Energy，Momentum and Angular Momentum； the Generalized “First Law” of Thermodynamics 461

21.5 Broken Symmetry and Goldstone’s Theorem 462

21.6 Other Broken Symmetry Coordinates—Electric and Magnetic Moments 465

21.7 Mole Numbers and Gauge Symmetry 466

21.8 Time Reversal，the Equal Probability of Microstates，and the Entropy Principle 467

21.9 Symmetry and Completeness 469

APPENDIX A SOME RELATIONS INVOLVING PARTIAL DERIVATIVES 473

A.1 Partial Derivatives 473

A.2 Taylor’s Expansion 474

A.3 Differentials 475

A.4 Composite Functions 475

A.5 Implicit Functions 476

APPENDIX B MAGNETIC SYSTEMS 479

GENERAL REFERENCES 485

INDEX 487