Thermodynamics and Statistical Mechanics

Author:            Richard Fitzpatrick

Publisher:         World Scientific

Publication Date:  2020

ISBN:              978-981-122-335-8

This book provides a comprehensive exposition of the theory of equilibrium thermodynamics and statistical dynamics at a level suitable for well-prepared undergraduate students. The fundamental message of the book is that all results in equilibrium thermodynamics and statistical mechanics follow from a single unprovable axiom---namely, the principle of equal a priori probabilities---combined with elementary probability theory, elementary classical mechanics, and elementary quantum mechanics.

1. Introduction. Atomic Theory of Matter; What is Thermodynamics? Need for a Statistical Approach; Microscopic and Macroscopic Systems; Classical and Statistical Therodynamics; Classical and Quantum Approaches.

2. Probability Theory. Introduction; What is Probability?; Combining Probabilities; Two-State System; Combinatorial Analysis; Binomial Probability Distrubution; Mean, Variance, and Standard Deviation; Application to Binomial Probability Distribution; Gaussian Probability Distribution; Central Limit Theorem; Exercises.

3. Statistical Mechanics. Introduction; Specification of State of Many-Particle System; Principle of Equal A Priori Probabilities; H-Theorem; Relaxation Time; Reversibility and Irreversibility; Probability Calculation; Behavior of Density of States; Exercises.

4. Heat and Work. Brief History of Heat and Work; Macrostates and Microstates; Microscopic Interpretation of Heat and Work; Quasi-Static Processes; Exact and Inexact Differentials; Heat and Work; Exercises.

5. Statistical Thermodynamics. Introduction; Thermal Interaction Between Macrosystems; Temperature; Mechanical Interaction Between Macrosystems; General Interaction Between Macrosystems; Entropy; Properties of Entropy; Uses of Entropy; Entropy and Quantum Mechanics; Laws of Thermodynamics; Exercises.

6. Classical Thermodynamics. Introduction; Ideal Gas Equation of State; Specific Heat; Calculation of Specific Heats; Isothermal and Adiabatic Expansion; Hydeostatic Equilibrium of Atmosphere; Isothermal Atmosphere; Adiabatic Atmosphere; Internal Energy; Enthalpy; Helmholtz Free Energy; Gibbs Free Energy; General Relation Between Specific Heats; Free Expansion of Gas; Van der Waals Gas; Joule-Thompson Throttling; Heat Engines; Refrigerators; Exercises.

7. Multi-Phase Systems. Introduction; Equilibrium of Isolated System; Equilibrium of Constant-Temperature System; Equilibrium of Constant-Temperature Constant-Pressure System; Stability of Single-Phase System; Equilibrium Between Phases; Clausius-Clapeyron Equation; Phase Diagrams; Vapor Pressure; Phase Transformation in van der Waals Fluid; Exercises.

8. Applications of Statistical Thermodynamics. Introduction; Canonical Probability Distribution; Spin-1/2 Paramagnetism; System with Specified Mean Eenrgy; Calculation of Mean Values; Partiton Function; Ideal Monatomic Gas; Gibbs Paradox; General Paramagnetism; Equipartition Theorem; Harmonic Oscillators; Specific Heats; Specific Heats of Gases; Specific Heats of Solids; Maxwell Velocity Distribution; Effusion; Ferromagnetism; Exercises.

9. Chemical Equilibria. Introduction; Grand Canonical Probability Distribution; Systems of Several Components; Equilibrium Between Phases; Gibbs Phase Rule; Dilute Solutions; Molality; Osmosis; Boiling and Freezing Points; General Conditions for Chemical Equilibrium; Dissociation of Water; Ideal Gas Mixture; Chemical Potentials of Ideal Gas Mixture; Law of Mass Action; Temperature Dependence of Equilibrium Constant; Saha Equation; Exercises.

10. Quantum Statistics. Introduction; Symmetry Requirements in Quantum Mechanics; Illustrative Example; Formulation of Statistical Problem; Fermi-Dirac Statistics; Photon Statistics; Bose-Einstein Statistics; Maxwell-Boltzman Statistics; Quantum Statistics in Classical Limit; Quantum-Mechanical Treatment of Ideal Gas; Derivation of van der Waals Equation; Plank Radiation Law; Black-Body Radiation; Stefam-Boltzmann Law; Conduction Electrons in Metal; Sommerfeld Expansion; White-Dwarf Stars; Chandresekhar Limit; Neutron Stars; Bose-Einstein Condensation; Exercises.

A. Physical Constants.

B. Classical Mechanics. Generalized Coordinates; Generalized Forces; Lagrange's Equation; Generalized Momenta; Calculus of Variations; Conditional Variation; Multi-Function Variation; Hamilton's Principle; Hamilton's Equations.

C. Wave Mechanics. Introduction; Photoelectric Effect; Electron Diffraction; Representation of Waves via Complex Numbers; Schrodinger's Equation; Probability Interpretation of Wavefunction; Wave Packets; Heisenberg's Uncertainty Principle; Stationary States; Three-Dimensional Wave Mechanics; Simple Harmonic Oscillator; Angular Momentum.

Bibliography.