PART Ⅰ INDUCTIVE FOUNDATIONS OF CLASSICAL THERMODYNAMICS 1
1.Mathematical Preliminaries：Functions and Differentials 3
1.1 Physical Conception of Mathematical Functions and Differentials 3
1.2 Four Useful Identities 7
1.3 Exact and Inexact Differentials 10
1.4 Taylor Series 15
2.Thermodynamic Description of Simple Fluids 17
2.1 The Logic of Thermodynamics 17
2.2 Mechanical and Thermal Properties of Gases：Equations of State 18
2.3 Thermometry and the Temperature Concept 24
2.4 Real and Ideal Gases 30
2.4.1 Compressibility Factor and Ideal Gas Deviations 31
2.4.2 Van der Waals and Other Model Equations of State 36
2.4.3 The Virial Equation of State 44
2.5 Condensation and the Gas-Liquid Critical Point 47
2.6 Van der Waals Model of Condensation and Critical Behavior 50
2.7 The Principle of Corresponding States 54
2.8 Newtonian Dynamics in the Absence of Frictional Forces 56
2.9 Mechanical Energy and the Conservation Principle 58
2.10 Fundamental Definitions：System，Property，Macroscopic，State 60
2.10.1 System 60
2.10.2 Property 61
2.10.3 Macroscopic 63
2.10.4 State 64
2.11 The Nature of the Equilibrium Limit 65
3.General Energy Concept and the First Law 67
3.1 Historical Background of the First Law 67
3.2 Reversible and Irreversible Work 71
3.3 General Forms of Work 76
3.3.1 Pressure-Volume Work 76
3.3.2 Surface Tension Work 78
3.3.3 Elastic Work 79
3.3.4 Electrical（emf）Work 80
3.3.5 Electric Polarization Work 81
3.3.6 Magnetic Polarization Work 83
3.3.7 Overview of General Work Forms 84
3.4 Characterization and Measurement of Heat 85
3.5 General Statements of the First Law 87
3.6 Thermochemical Consequences of the First Law 89
3.6.1 Heat Capacity and the Enthalpy Function 89
3.6.2 Joule’s Experiment 91
3.6.3 Joule-Thomson Porous Plug Experiment 93
3.6.4 Ideal Gas Thermodynamics 95
3.6.5 Thermochemistry：Enthalpies of Chemical Reactions 101
3.6.6 Temperature Dependence of Reaction Enthalpies 107
3.6.7 Heats of Solution 108
3.6.8 Other Aspects of Enthalpy Decompositions 112
4.Engine Efficiency，Entropy，and the Second Law 117
4.1 Introduction：Heat Flow，Spontaneity，and Irreversibility 117
4.2 Heat Engines：Conversion of Heat to Work 122
4.3 Carnot’s Analysis of Optimal Heat-Engine Efficiency 123
4.4 Theoretical Limits on Perpetual Motion：Kelvin’s and Clausius’Principles 128
4.5 Kelvin’s Temperature Scale 130
4.6 Carnot’s Theorem and the Entropy of Clausius 134
4.7 Clausius’Formulation of the Second Law 139
4.8 Summary of the Inductive Basis of Thermodynamics 145
PART Ⅱ GIBBSIAN THERMODYNAMICS OF CHEMICAL AND PHASE EQUILIBRIA 147
5.Analytical Criteria for Thermodynamic Equilibrium 149
5.1 The Gibbs Perspective 149
5.2 Analytical Formulation of the Gibbs Criterion for a System in Equilibrium 152
5.3 Alternative Expressions of the Gibbs Criterion 157
5.4 Duality of Fundamental Equations：Entropy Maximization versus Energy Minimization 160
5.5 Other Thermodynamic Potentials：Gibbs and Helmholtz Free Energy 162
5.6 Maxwell Relations 164
5.7 Gibbs Free Energy Changes in Laboratory Conditions 170
5.8 Post-Gibbsian Developments 180
5.8.1 The Fugacity Concept 181
5.8.2 The “Third Law” of Thermodynamics：A Critical Assessment 183
6.Thermodynamics of Homogeneous Chemical Mixtures 195
6.1 Chemical Potential in Multicomponent Systems 195
6.2 Partial Molar Quantities 197
6.3 The Gibbs-Duhem Equation 201
6.4 Physical Nature of Chemical Potential in Ideal and Real Gas Mixtures 204
7.Thermodynamics of Phase Equilibria 209
7.1 The Gibbs Phase Rule 211
7.2 Single-Component Systems 216
7.2.1 The Phase Diagram of Water 217
7.2.2 Clapeyron and Clausius-Clapeyron Equations for Phase Boundaries 219
7.2.3 Illustrative Phase Diagrams for Pure Substances 224
7.3 Binary Fluid Systems 233
7.3.1 Vapor-Pressure（P-x）Diagrams：Raoult and Henry Limits 237
7.3.2 The Lever Rule 241
7.3.3 Positive and Negative Deviations 243
7.3.4 Boiling-Point Diagrams：Theory of Distillation 247
7.3.5 Immiscibility and Consolute Behavior 250
7.3.6 Colligative Properties and Van’t Hoff Osmotic Equation 253
7.3.7 Activity and Activity Coefficients 260
7.4 Binary Solid-Liquid Equilibria 263
7.4.1 Eutectic Behavior 264
7.4.2 Congruent Melting 265
7.4.3 Incongruent Melting and Peritectics 266
7.4.4 Alloys and Partial Miscibility 266
7.4.5 Phase Boundaries and Gibbs Free Energy of Mixing 267
7.5 Ternary and Higher Systems 273
8.Thermodynamics of Chemical Reaction Equilibria 281
8.1 Analytical Formulation of Chemical Reactions in Terms of the Advancement Coordinate 281
8.2 Criterion of Chemical Equilibrium：The Equilibrium Constant 282
8.3 General Free Energy Changes：de Donder’s Affinity 285
8.4 Standard Free Energy of Formation 286
8.5 Temperature and Pressure Dependence of the Equilibrium Constant 288
8.5.1 Temperature Dependence：Van’t Hoff Equation 288
8.5.2 Pressure Dependence 289
8.6 Le Chatelier’s Principle 290
8.7 Thermodynamics of Electrochemical Cells 292
8.8 Ion Activities in Electrolyte Solutions 296
8.9 Concluding Synopsis of Gibbs’Theory 305
PART Ⅲ METRIC GEOMETRY OF EQUILIBRIUM THERMODYNAMICS 311
9.Introduction to Vector Geometry and Metric Spaces 313
9.1 Vector and Matrix Algebra 315
9.2 Dirac Notation 323
9.3 Metric Spaces 328
10.Metric Geometry of Thermodynamic Responses 331
10.1 The Space of Thermodynamic Response Vectors 331
10.2 The Metric of Thermodynamic Response Space 333
10.3 Linear Dependence，Dimensionality，and Gibbs-Duhem Equations 337
11.Geometrical Representation of Equilibrium Thermodynamics 345
11.1 Thermodynamic Vectors and Geometry 345
11.2 Conjugate Variables and Conjugate Vectors 348
11.3 Metric of a Homogeneous Fluid 353
11.4 General Transformation Theory in Thermodynamic Metric Space 357
11.5 Saturation Properties Along the Vapor-Pressure Curve 360
11.6 Self-Conjugate and Normal Response Modes 363
11.7 Geometrical Characterization of Common Fluids 366
11.8 Stability Conditions and the “Third Law” for Homogeneous Phases 376
11.9 The Critical Instability Limit 379
11.10 Critical Divergence and Exponents 384
11.11 Phase Heterogeneity and Criticality 386
12.Geometrical Evaluation of Thermodynamic Derivatives 393
12.1 Thermodynamic Vectors and Derivatives 394
12.2 General Solution for Two Degrees of Freedom and Relationship to Jacobian Methods 401
12.3 General Partial Derivatives in Higher-Dimensional Systems 405
12.4 Phase-Boundary Derivatives in Multicomponent Systems 408
12.5 Stationary Points of Phase Diagrams：Gibbs-Konowalow Laws 414
12.6 Higher-Order Derivatives and State Changes 417
13.Further Aspects of Thermodynamic Geometry 421
13.1 Reversible Changes of State：Riemannian Geometry 424
13.2 Near-Equilibrium Irreversible Thermodynamics：Diffusional Geometry 429
13.3 Quantum Statistical Thermodynamic Origins of Chemical and Phase Thermodynamics 439
13.3.1 Nonequilibrium Displacement Variables of Mayer and Co-workers 442
13.3.2 Quantum Statistical Thermodynamics and the Statistical Origins of Metric Geometry 445
13.3.3 Evaluation of Molecular Partition Functions for Reactive Mixtures 452
13.3.4 Quantum Cluster Equilibrium Theory of Phase Thermodynamics 455
Appendix：Units and Conversion Factors 465
AUTHOR INDEX 469
SUBJECT INDEX 473