Callen, Herbert B

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THERMODYNAMICSAND AN INTRODUCTION TOTHERMOSTATISTICSSECOND EDITIONHERBERT B. CALLENUniversity of PennsylvaniaJOHN WILEY & SONSNew York Chichester Brisbane Toronto SingaporeCONTENTSPART IGENERAL PRINCIPLES OFCLASSICAL THERMODYNAMICSIntroduction The Nature of Thermodynamics and the Basis ofThermostatistics	21 THE PROBLEMAND THE POSTULATES 51 .1 The Temporal Nature of Macroscopic Measurements 51 .2 The Spatial Nature of Macroscopic Measurements 61.3 The Composition of Thermodynamic Systems 91 .4 The Internal Energy 111.5 Thermodynamic Equilibrium 131.6 Walls and Constraints 151.7 Measurability of the Energy 161.8 Quantitative Definition of Heat-Units 181.9 The Basic Problem of Thermodynamics 251 .10 The Entropy Maximum Postulates 272 THE CONDITIONS OF EQUILIBRIUM 352.1 Intensive Parameters 352.2 Equations of State 372.3 Entropic Intensive Parameters 402.4 Thermal Equilibrium-Temperature 432.5 Agreement with Intuitive Concept of Temperature 452.6 Temperature Units 462.7 Mechanical Equilibrium 492.8 Equilibrium with Respect to Matter Flow 542.9 Chemical Equilibrium 56Xii Contents3 SOME FORMAL RELATIONSHIPS,AND SAMPLE SYSTEMS	593.1 The Euler Equation 593.2 The Gibbs-Duhem Relation 603.3 Summary of Formal Structure 633.4 The Simple Ideal Gas and MulticomponentSimple Ideal Gases 663 .5 The "Ideal van der Waals Fluid" 743 .6 Electromagnetic Radiation 783.7 The "Rubber Band" 803.8 Unconstrainable Variables; Magnetic Systems 813.9 Molar Heat Capacity and Other Derivatives 844 REVERSIBLE PROCESSES ANDTHEMAXIMUM WORK THEOREM 914.1 Possible and Impossible Processes 914.2 Quasi-Static and Reversible Processes 954.3 Relaxation Times and Irreversibility 994.4 Heat Flow: Coupled Systems and Reversal of Processes 1014.5 The MaximumWork Theorem 1034.6 Coefficients of Engine, Refrigerator, andHeat Pump Performance 1134.7 The Carnot Cycle 1184.8 Measurability of the Temperature and of the Entropy 1234.9 Other Criteria of Engine Performance; Power Output and"Endoreversible Engines" 1254.10 Other Cyclic Processes 1285 ALTERNATIVE FORMULATIONSAND LEGENDRE TRANSFORMATIONS 1315 .1 The Energy Minimum Principle 1315 .2 Legendre Transformations 1375 .3 Thermodynamic Potentials 1465.4 Generalized Massieu Functions 1516 THE EXTREMUM PRINCIPLE IN THELEGENDRE TRANSFORMED REPRESENTATIONS 1536.1 The Minimum Principles for the Potentials" 1536.2 The Helmholtz Potential 1576.3 The Enthalpy; The Joule-Thomson or "Throttling" Process 1606.4 The Gibbs Potential ; Chemical Reactions 1676.5 Other Potentials 1726.6 Compilations of Empirical Data; The Enthalpy of Formation 1736.7 The Maximum Principles for the Massieu Functions 179Contents xin7 MAXWELLRELATIONS	1817.1 The Maxwell Relations 1817.2 A Thermodynamic Mnemonic Diagram 1837.3 A Procedure for the Reduction of Derivatives inSingle-Component Systems 1867.4 Some Simple Applications 1907.5 Generalizations: Magnetic Systems 1998 STABILITY OF THERMODYNAMIC SYSTEMS 2038.1 Intrinsic Stability of Thermodynamic Systems 2038.2 Stability Conditions for Thermodynamics Potentials 2078.3 Physical Consequences of Stability 2098.4 Le Chatelier's Principle ; The Qualitative Effectof Fluctuations 2108.5 The Le Chatelier-Braun Principle 2129 FIRST-ORDER PHASE TRANSITIONS 2159.1 First-Order Phase Transitions in Single-Component Systems 2159.2 The Discontinuity in the Entropy-Latent Heat 2229.3 The Slope of Coexistence Curves ; the Clapeyron Equation 2289.4 Unstable Isotherms and First-Order Phase Transitions 2339.5 General Attributes of First-Order Phase Transitions 2439.6 First-Order Phase Transitions in MulticomponentSystems-Gibbs Phase Rule 2459.7 Phase Diagrams for Binary Systems 24810 CRITICAL PHENOMENA 25510.1 Thermodynamics in the Neighborhood of the Critical Point 25510.2 Divergence and Stability 26110.3 Order Parameters and Critical Exponents 26310.4 Classical Theory in the Critical Region ; Landau Theory 26510.5 Roots of the Critical Point Problem 27010.6 Scaling and Universality 27211 THE NERNST POSTULATE 27711.1 Nernst's Postulate, and the Principle of Thomsenand Bertholot 27711.2 Heat Capacities and Other Derivatives at Low Temperatures 28011.3 The "Unattainability" of Zero Temperature 28112 SUMMARY OF PRINCIPLESFOR GENERAL SYSTEMS 28312.1 General Systems 28312.2 The Postulates 283Xiv Contents12.3	The Intensive Parameters 28412.4 Legendre Transforms 28512.5 Maxwell Relations 28512.6 Stability and Phase Transitions 28612.7 Critical Phenomena 28712.8 Properties at Zero Temperature 28713 PROPERTIES OF MATERIALS 28913.1 The General Ideal Gas 28913.2 Chemical Reactions in Ideal Gases 29213.3 Small Deviations from "Ideality"-The Virial Expansion 29713.4 The "Law of Corresponding States" for Gases 29913.5 Dilute Solutions : Osmotic Pressure and Vapor Pressure 30213.6 Solid Systems 30514 IRREVERSIBLE THERMODYNAMICS 30714.1 General Remarks 30714.2 Affinities and Fluxes 30814.3 Purely-Resistive and Linear Systems 31214.4 The Theoretical Basis of the Onsager Reciprocity 31414.5 Thermoelectric Effects 31614.6 The Conductivities 31914.7 The Seebeck Effect and the Thermoelectric Power 32014.8 The Peltier Effect 32314.9 The Thomsen Effect 324PART IISTATISTICAL MECHANICS15 STATISTICAL MECHANICS IN THEENTROPY REPRESENTATION:THE MICROCANONICAL FORMALISM15.1 Physical Significance of the Entropy for Closed Systems15.2 The Einstein Model of a Crystalline Solid15.3 The Two-State System15 .4 A Polymer Model-The Rubber Band Revisited15.5 Counting Techniques and their Circumvention;High Dimensionality32932933333733934316 THE CANONICAL FORMALISM; STATISTICALMECHANICS IN HELMHOLTZ REPRESENTATION 34916.1 The Probability Distribution 34916.2 Additive Energies and Factorizability of the Partition Sum 35316.3	Internal Modes in a Gas 35516.4 Probabilities'in Factorizable Systems 35816.5 Statistical Mechanics of Small Systems: Ensembles 36016.6 Density of States and Density-of-Orbital States 36216.7 The Debye Model of Non-metallic Crystals 36416.8 Electromagnetic Radiation 36816.9 The Classical Density of States 37016.10 The Classical Ideal Gas 37216.11 High Temperature Properties-TheL Equipartition Theorem 37517 ENTROPY AND DISORDER; GENERALIZEDCANONICAL FORMULATIONS 37917.1 Entropy as a Measure of Disorder 37917.2 Distributions of Maximal Disorder 38217.3 The Grand Canonical Formalism 38518 QUANTUM FLUIDS 39318.1 Quantum Particles ; A "Fermion Pre-Gas Model" 39318.2 The Ideal Fermi Fluid 39918.3 The Classical Limit and the Quantum Criteria 40218.4 The Strong Quantum Regime ; Electrons in a Metal 40518.5 The Ideal Bose Fluid 41018.6 Non-Conserved Ideal Bose Fluids ; ElectromagneticRadiation Revisited 41218.7 Bose Condensation 41319 FLUCTUATIONS 42319.1 The Probability Distribution of Fluctuations 42319.2 Moments and The Energy Fluctuations 42419.3 General Moments and Correlation Moments 42620 VARIATIONAL PROPERTIES, PERTURBATIONEXPANSIONS, AND MEAN FIELD THEORY 43320.1 The Bogoliubov Variational Theorem 43320.2 Mean Field Theory 44020.3 Mean Field Theory in Generalized Representation ;the Binary Alloy 449PART IIIFOUNDATIONSContents xa21 POSTLUDE: SYMMETRY AND THE CONCEPTUALFOUNDATIONS OF THERMOSTATISTICS 45521 .1 Statistics 455XUi Contents21 .2 Symmetry	45821.3 Noether's Theorem 46021 .4 Energy, Momentum and Angular Momentum ; the Generalized"First Law" of Thermodynamics 46121 .5 Broken Symmetry and Goldstone's Theorem 46221 .6 Other Broken Symmetry Coordinates-Electric andMagnetic Moments 46521.7 Mole Numbers and Gauge Symmetry 46621.8 Time Reversal, the Equal Probability of Microstates,and the Entropy Principle 46721.9 Symmetry and Completeness 469APPENDIX ASOME RELATIONS INVOLVINGPARTIAL DERIVATIVES 473A.1 Partial Derivatives 473A.2 Taylor's Expansion 474A.3 Differentials 475A.4 Composite Functions 475A.5 Implicit Functions 476APPENDIX BMAGNETIC SYSTEMS 479GENERAL REFERENCES 485INDEX 487

Thermodynamics and an introduction to thermostatistics

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