A Course In Statistical Thermodynamics
Published on 2. December 2012
596 pages
978-0-323-14493-3 (ISBN)
Description
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.
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Joseph Kestin
A Course In Statistical Thermodynamics
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07/1971
Academic Press
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Content
PrefaceAcknowledgmentsIntroduction 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 1Part 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 6Part 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.
