# A Course In Statistical Thermodynamics

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A Course in Statistical Thermodynamics explores the physical aspects of the methodology of statistical thermodynamics without the use of advanced mathematical methods. This book is divided into 14 chapters that focus on a correct statement of the Gibbsian ensemble theory couched in quantum-mechanical terms throughout. The introductory chapters emphasize the concept of equilibrium, phase space, the principle of their quantization, and the fundamentals of quantum mechanics and spectroscopy. These topics are followed by an exposition of the statistical method, revealing that the structure of the physical theory is closely modeled on mathematical statistics. A chapter focuses on stationary ensembles and the restatement of the First, Second, and Third Law of Thermodynamics. The remaining chapters highlight the various specialized applications of statistical thermodynamics, including real and degenerate gases, simple solids, radiation, magnetic systems, nonequilibrium states, and fluctuations. These chapters also provide a rigorous derivation of Boltzmann's equation, the H-theorem, and the vexing paradox that arises when microscopic reversibility must be reconciled with irreversible behavior in the large. This book can be used for two semesters in the junior or senior years, or as a first-year graduate course in statistical thermodynamics.

## Table of Contents

Preface

Acknowledgments

Introduction

Chapter 1. Summary of Classical Thermodynamics

1.1. The Two Views of Matter

1.2. Definitions and Concepts

1.3. Equilibrium and Nonequilibrium Thermodynamics

1.4. The Laws of Thermodynamics

1.5. Continuum Thermodynamics

Problems for Chapter 1

List of Symbols for Chapter 1

Part 1. Fundamental Theory

Chapter 2. Introduction to Statistical Thermodynamics and Mechanical Models

2.1. Prefatory Remarks

2.2. Microscopic Description of Thermodynamic Systems. Statistical Thermodynamics, Classical and Quantum Mechanics

2.3. Mechanical Models

Problems for Chapter 2

List of Symbols for Chapter 2

Chapter 3. Quantum Mechanics

3.1. Description of the Motion

3.2. The Physical Basis of Quantum Mechanics

3.3. The Wave Function

3.4. The Mathematical Basis of Quantum Mechanics. Schrödinger's Equation

3.5. Stationary States. Schrödinger's Time-Independent Equation

3.6. Complementarity and Heisenberg's Uncertainty Principle

3.7. Translational Motion of a Single, Independent Molecule

3.8. Particle in a Container

3.9. Two Identical Particles in a Container

3.10. Quantization of Rotation

3.11. Quantization of Vibration

3.12. Collection of Independent Particles

3.13. Spin

3.14. Density of Quantum Cells in Phase Space

3.15. Spectroscopy

3.16. Summary of Results from Quantum Mechanics

Problems for Chapter 3

List of Symbols for Chapter 3

Chapter 4. Topics in Mathematics

4.1. Combinatorial Formulas

4.2. Most Probable Distribution Subject to a Constraint

4.3. On Approximating a Series by an Integral

4.4. The Statistical Method

Problems for Chapter 4

List of Symbols for Chapter 4

Chapter 5. Foundations of Statistical Thermodynamics

5.1. Introductory Remarks

5.2. The Statistical Method

5.3. Gibbsian Ensembles

5.4. Liouville's Equation

5.5. Geometrical Structure of the Statistical Sample Space

5.6. Relation between Theories Based on Different Ensembles

5.7 Microcanonical Ensemble

5.8 Canonical Ensemble

5.9 Grand Canonical Ensemble

5.10 Statistical Interpretation of Entropy

5.11 Method of the Most Probable Distribution

5.12 Partition Function

5.13 Change in the Partition Function during a Reversible Process

5.14 Comparison with Classical Thermodynamics

5.15 Explicit Formulas; Chemical Potential

5.16 Boltzmann's Principle

5.17 The Laws of Thermodynamics

5.18 The Method of the Most Probable Distribution and the Grand Canonical Ensemble

5.19 Summary

Problems for Chapter 5

List of Symbols for Chapter 5

Chapter 6. Properties of Perfect Gases

6.1 Method

6.2 The Partition Function of a Perfect Gas

6.3 Pressure and Thermal Equation of State of a Perfect Gas

6.4 The Classical Partition Function

6.5 Equipartition of Energy in Classical Statistical Mechanics

6.6 The Maxwellian Velocity Distribution

6.7 Monatomic Gases

6.8 Entropy and the Sackur-Tetrode Equation

6.9 Internal Degrees of Freedom

6.10 Summarizing Remarks

6.11 Mixtures of Chemically Inert Perfect Gases

6.12 Reacting Perfect Gases. Law of Mass Action

6.13 Spectroscopic and Calorimetric Entropy of a Gas

6.14 Absolute Vapor-Pressure Curve

Problems for Chapter 6

List of Symbols for Chapter 6

Part 2. Applications

Chapter 7. Properties of Real Gases

7.1. Introductory Remarks

7.2. Quantum or Classical Partition Function

7.3. The Configurational Partition Function

7.4. First Approximation to Configurational Partition Function

7.5. The Second Virial Coefficient

7.6. Third Virial Coefficient

7.7. Higher Approximations and Other Thermodynamic Properties

7.8. The van der Waals Equation of State

7.9. The Law of Corresponding States

7.10. Properties of a Pure Substance near the Critical Point

Problems for Chapter 7

List of Symbols for Chapter 7

Chapter 8. Degenerate Perfect Gases

8.1. Prefatory Remarks

8.2. The Quantum-Mechanical Partition Function

8.3. The Kronecker Delta Function

8.4. The Average Occupation Numbers

8.5. The Perfect Quantum Gas

8.6. The Weakly Degenerate Gas

8.7. The Strongly Degenerate Fermi Gas

8.8. The Degenerate Boson Gas. The Bose-Einstein Condensation

Problems for Chapter 8

List of Symbols for Chapter 8

Chapter 9. Properties of Solids

9.1. Prefatory Remarks

9.2. The Properties of Crystalline Solids

9.3. Debye's Theory

9.4. Phonons

9.5. The Band Theory of Solids

9.6. Thermionic Emission

Problems for Chapter 9

List of Symbols for Chapter 9

Chapter 10. Radiation

10.1. A Descriptive Introduction

10.2. Properties of Electromagnetic Radiation

10.3. The Photon Gas in Equilibrium

10.4. Emission and Absorption of Black-Body Radiation

10.5. Relation between Black-Body Emissive Power and Spectral Density of Specific Energy

10.6. The Stefan-Boltzmann Law

10.7. The International Practical Temperature Scale of 1968

10.8. Kirchhoff's Law

10.9. Radiative Atomic Transitions. The Einstein Coefficients

10.10. The Laser

Problems for Chapter 10

List of Symbols for Chapter 10

Chapter 11. Magnetic Properties

11.1. Introduction

11.2. Fundamental Equation of Paramagnetic System

11.3. The Mechanical Model

11.4. The Partition Function

11.5. Magnetization

11.6. Classical Limit

11.7. Ferromagnetism

Problems for Chapter 11

List of Symbols for Chapter 11

Chapter 12. Kinetic Theory of Gases

12.1. Prefatory Remarks

12.2. Some Elementary Ideas

12.3. A Dynamical Derivation of the Perfect-Gas Law

12.4. The Mean Free Path

12.5. The Mean Free Path and Transport Properties

Problems for Chapter 12

List of Symbols for Chapter 12

Chapter 13. The Boltzmann Equation

13.1. Introduction

13.2. The Rate Equation

13.3. The Dynamics of a Binary Collision

13.4. The Boltzmann Equation

13.5. Concluding Remarks

13.6. Approach to Equilibrium. The H-Theorem

Problems for Chapter

List of Symbols for Chapter

Chapter 14. Fluctuations

14.1. Introduction

14.2. The Probability of a Thermodynamic Fluctuation

14.3. Fluctuations in a Subsystem

14.4. Brownian Motion

Problems for Chapter 14

List of Symbols for Chapter 14

Tables

Index

## Product details

- No. of pages: 596
- Language: English
- Copyright: © Academic Press 1971
- Published: January 28, 1971
- Imprint: Academic Press
- eBook ISBN: 9780323144933

## About the Author

### Joseph Kestin

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