THERMODYNAMICS THERMOSTATISTICS AND AN INTRODUCTION TO SECOND EDITION. University of Pennsylvania

Transcription

1 THERMODYNAMICS AND AN INTRODUCTION TO THERMOSTATISTICS SECOND EDITION HERBERT B. University of Pennsylvania CALLEN JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore

2 CONTENTS PART I GENERAL PRINCIPLES OF CLASSICAL THERMODYNAMICS Introduction The Nature of Thermodynamics and the Basis of Thermostatistics 2 1 THE PROBLEM AND THE POSTULATES The Temporal Nature of Macroscopic Measurements The Spatial Nature of Macroscopic Measurements The Composition of Thermodynamic Systems The Internal Energy Thermodynamic Equilibrium Walls and Constraints Measurability of the Energy Quantitative Definition of Heat-Units The Basic Problem of Thermodynamics The Entropy Maximum Postulates 27 2 THE CONDITIONS OF EQUILIBRIUM Intensive Parameters Equations of State Entropic Intensive Parameters Thermal Equilibrium-Temperature Agreement with Intuitive Concept of Temperature Temperature Units Mechanical Equilibrium Equilibrium with Respect to Matter Flow Chemical Equilibrium 56

3 Xii Contents 3 SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS The Euler Equation The Gibbs-Duhem Relation Summary of Formal Structure The Simple Ideal Gas and Multicomponent Simple Ideal Gases The "Ideal van der Waals Fluid" Electromagnetic Radiation The "Rubber Band" Unconstrainable Variables; Magnetic Systems Molar Heat Capacity and Other Derivatives 84 4 REVERSIBLE PROCESSES AND THE MAXIMUM WORK THEOREM Possible and Impossible Processes Quasi-Static and Reversible Processes Relaxation Times and Irreversibility Heat Flow : Coupled Systems and Reversal of Processes The Maximum Work Theorem Coefficients of Engine, Refrigerator, and Heat Pump Performance The Carnot Cycle Measurability of the Temperature and of the Entropy Other Criteria of Engine Performance ; Power Output and "Endoreversible Engines" Other Cyclic Processes ALTERNATIVE FORMULATIONS AND LEGENDRE TRANSFORMATIONS The Energy Minimum Principle Legendre Transformations Thermodynamic Potentials Generalized Massieu Functions THE EXTREMUM PRINCIPLE IN THE LEGENDRE TRANSFORMED REPRESENTATIONS The Minimum Principles for the Potentials" The Helmholtz Potential The Enthalpy; The Joule-Thomson or "Throttling" Process The Gibbs Potential ; Chemical Reactions Other Potentials Compilations of Empirical Data ; The Enthalpy of Formation The Maximum Principles for the Massieu Functions 179

4 Contents xin 7 MAXWELL RELATIONS The Maxwell Relations A Thermodynamic Mnemonic Diagram A Procedure for the Reduction of Derivatives in Single-Component Systems Some Simple Applications Generalizations : Magnetic Systems STABILITY OF THERMODYNAMIC SYSTEMS Intrinsic Stability of Thermodynamic Systems Stability Conditions for Thermodynamics Potentials Physical Consequences of Stability Le Chatelier's Principle ; The Qualitative Effect of Fluctuations The Le Chatelier-Braun Principle FIRST-ORDER PHASE TRANSITIONS First-Order Phase Transitions in Single-Component Systems The Discontinuity in the Entropy-Latent Heat The Slope of Coexistence Curves ; the Clapeyron Equation Unstable Isotherms and First-Order Phase Transitions General Attributes of First-Order Phase Transitions First-Order Phase Transitions in Multicomponent Systems-Gibbs Phase Rule Phase Diagrams for Binary Systems CRITICAL PHENOMENA Thermodynamics in the Neighborhood of the Critical Point Divergence and Stability Order Parameters and Critical Exponents Classical Theory in the Critical Region ; Landau Theory Roots of the Critical Point Problem Scaling and Universality THE NERNST POSTULATE Nernst's Postulate, and the Principle of Thomsen and Bertholot Heat Capacities and Other Derivatives at Low Temperatures The "Unattainability" of Zero Temperature SUMMARY OF PRINCIPLES FOR GENERAL SYSTEMS General Systems The Postulates 283

5 Xiv Contents 12.3 The Intensive Parameters Legendre Transforms Maxwell Relations Stability and Phase Transitions Critical Phenomena Properties at Zero Temperature PROPERTIES OF MATERIALS The General Ideal Gas Chemical Reactions in Ideal Gases Small Deviations from "Ideality"-The Virial Expansion The "Law of Corresponding States" for Gases Dilute Solutions : Osmotic Pressure and Vapor Pressure Solid Systems IRREVERSIBLE THERMODYNAMICS General Remarks Affinities and Fluxes Purely-Resistive and Linear Systems The Theoretical Basis of the Onsager Reciprocity Thermoelectric Effects The Conductivities The Seebeck Effect and the Thermoelectric Power The Peltier Effect The Thomsen Effect 324 PART II STATISTICAL MECHANICS 15 STATISTICAL MECHANICS IN THE ENTROPY REPRESENTATION : THE MICROCANONICAL FORMALISM 15.1 Physical Significance of the Entropy for Closed Systems 15.2 The Einstein Model of a Crystalline Solid 15.3 The Two-State System 15.4 A Polymer Model-The Rubber Band Revisited 15.5 Counting Techniques and their Circumvention ; High Dimensionality THE CANONICAL FORMALISM ; STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION The Probability Distribution Additive Energies and Factorizability of the Partition Sum 353

6 Contents xa 16.3 Internal Modes in a Gas Probabilities'in Factorizable Systems Statistical Mechanics of Small Systems : Ensembles Density of States and Density-of-Orbital States The Debye Model of Non-metallic Crystals Electromagnetic Radiation The Classical Density of States The Classical Ideal Gas High Temperature Properties-TheL Equipartition Theorem ENTROPY AND DISORDER; GENERALIZED CANONICAL FORMULATIONS Entropy as a Measure of Disorder Distributions of Maximal Disorder The Grand Canonical Formalism QUANTUM FLUIDS Quantum Particles ; A "Fermion Pre-Gas Model" The Ideal Fermi Fluid The Classical Limit and the Quantum Criteria The Strong Quantum Regime ; Electrons in a Metal The Ideal Bose Fluid Non-Conserved Ideal Bose Fluids ; Electromagnetic Radiation Revisited Bose Condensation FLUCTUATIONS The Probability Distribution of Fluctuations Moments and The Energy Fluctuations General Moments and Correlation Moments VARIATIONAL PROPERTIES, PERTURBATION EXPANSIONS, AND MEAN FIELD THEORY The Bogoliubov Variational Theorem Mean Field Theory Mean Field Theory in Generalized Representation ; the Binary Alloy 449 PART III FOUNDATIONS 21 POSTLUDE: SYMMETRY AND THE CONCEPTUAL FOUNDATIONS OF THERMOSTATISTICS Statistics 455

7 XUi Contents 21.2 Symmetry Noether's Theorem Energy, Momentum and Angular Momentum ; the Generalized "First Law" of Thermodynamics Broken Symmetry and Goldstone's Theorem Other Broken Symmetry Coordinates-Electric and Magnetic Moments Mole Numbers and Gauge Symmetry Time Reversal, the Equal Probability of Microstates, and the Entropy Principle 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