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| Preface | |
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| Introduction | |
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| The Statistical Foundation of Classical Thermodynamics | |
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| A Classification Scheme for Statistical Thermodynamics | |
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| Why Statistical Thermodynamics? | |
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| Fundamentals of Statistical Thermodynamics | |
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| Probability and Statistics | |
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| Probability: Definitions and Basic Concepts | |
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| Permutations and Combinations | |
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| Probability Distributions: Discrete and Continuous | |
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| The Binomial Distribution | |
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| The Poisson Distribution | |
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| The Gaussian Distribution | |
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| Combinatorial Analysis for Statistical Thermodynamics | |
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| Distinguishable Objects | |
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| Indistinguishable Objects | |
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| Probability Theory and Statistical Mathematics (Chapter 2) | |
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| The Statistics of Independent Particles | |
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| Essential Concepts from Quantum Mechanics | |
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| The Ensemble Method of Statistical Thermodynamics | |
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| The Two Basic Postulates of Statistical Thermodynamics | |
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| The M-B Method: System Constraints and Particle Distribution | |
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| The M-B Method: Microstates and Macrostates | |
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| The Most Probable Macrostate | |
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| Bose-Einstein and Fermi-Dirac Statistics | |
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| Bose-Einstein Statistics | |
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| Fermi-Dirac Statistics | |
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| The Most Probable Particle Distribution | |
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| Entropy and the Equilibrium Particle Distribution | |
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| The Boltzmann Relation for Entropy | |
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| Identification of Lagrange Multipliers | |
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| The Equilibrium Particle Distribution | |
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| Thermodynamic Properties in the Dilute Limit | |
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| The Dilute Limit | |
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| Corrected Maxwell-Boltzmann Statistics | |
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| The Molecular Partition Function | |
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| The Influence of Temperature | |
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| Criterion for Dilute Limit | |
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| Internal Energy and Entropy in the Dilute Limit | |
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| Additional Thermodynamic Properties in the Dilute Limit | |
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| The Zero of Energy and Thermodynamic Properties | |
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| Intensive Thermodynamic Properties for the Ideal Gas | |
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| Statistical Modeling for Thermodynamics (Chapters 3-4) | |
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| Quantum Mechanics and Spectroscopy | |
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| Basics of Quantum Mechanics | |
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| Historical Survey of Quantum Mechanics | |
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| The Bohr Model for the Spectrum of Atomic Hydrogen | |
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| The de Broglie Hypothesis | |
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| A Heuristic Introduction to the Schrodinger Equation | |
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| The Postulates of Quantum Mechanics | |
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| The Steady-State Schrodinger Equation | |
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| Single-Particle Analysis | |
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| Multiparticle Analysis | |
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| The Particle in a Box | |
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| The Uncertainty Principle | |
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| Indistinguishability and Symmetry | |
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| The Pauli Exclusion Principle | |
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| The Correspondence Principle | |
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| Quantum Analysis of Internal Energy Modes | |
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| Schrodinger Wave Equation for Two-Particle System | |
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| Conversion to Center-of-Mass Coordinates | |
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| Separation of External from Internal Modes | |
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| The Internal Motion for a Two-Particle System | |
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| The Rotational Energy Mode for a Diatomic Molecule | |
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| The Vibrational Energy Mode for a Diatomic Molecule | |
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| The Electronic Energy Mode for Atomic Hydrogen | |
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| The Electronic Energy Mode for Multielectron Species | |
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| Electron Configuration for Multielectron Atoms | |
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| Spectroscopic Term Symbols for Multielectron Atoms | |
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| Electronic Energy Levels and Degeneracies for Atoms | |
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| Electronic Energy Levels and Degeneracies for Diatomic Molecules | |
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| Combined Energy Modes for Atoms and Diatomic Molecules | |
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| Selection Rules for Atoms and Molecules | |
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| The Spectroscopy of Diatomic Molecules | |
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| Rotational Spectroscopy Using the Rigid-Rotor Model | |
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| Vibrational Spectroscopy Using the Harmonic-Oscillator Model | |
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| Rovibrational Spectroscopy: The Simplex Model | |
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| The Complex Model for Combined Rotation and Vibration | |
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| Rovibrational Spectroscopy: The Complex Model | |
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| Electronic Spectroscopy | |
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| Energy-Mode Parameters for Diatomic Molecules | |
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| Quantum Mechanics and Spectroscopy (Chapters 5-7) | |
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| Statistical Thermodynamics in the Dilute Limit | |
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| Interlude: From Particle to Assembly | |
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| Energy and Degeneracy | |
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| Separation of Energy Modes | |
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| The Molecular Internal Energy | |
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| The Partition Function and Thermodynamic Properties | |
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| Energy-Mode Contributions in Classical Mechanics | |
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| The Phase Integral | |
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| The Equipartition Principle | |
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| Mode Contributions | |
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| Thermodynamic Properties of the Ideal Gas | |
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| The Monatomic Gas | |
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| Translational Mode | |
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| Electronic Mode | |
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| The Diatomic Gas | |
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| Translational and Electronic Modes | |
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| The Zero of Energy | |
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| Rotational Mode | |
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| Quantum Origin of Rotational Symmetry Factor | |
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| Vibrational Mode | |
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| Rigorous and Semirigorous Models for the Diatomic Gas | |
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| The Polyatomic Gas | |
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| Rotational Contribution | |
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| Vibrational Contribution | |
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| Property Calculations for Polyatomic Molecules | |
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| Thermodynamic Properties of the Ideal Gas (Chapters 8-9) | |
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| Statistical Thermodynamics for Ideal Gas Mixtures | |
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| Equilibrium Particle Distribution for the Ideal Gas Mixture | |
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| Thermodynamic Properties of the Ideal Gas Mixture | |
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| The Reacting Ideal Gas Mixture | |
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| Equilibrium Particle Distribution for Reactive Ideal Gas Mixture | |
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| Equilibrium Constant: Introduction and Development | |
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| Equilibrium Constant: General Expression and Specific Examples | |
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| Dissociation of a Homonuclear Diatomic | |
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| The Homonuclear-Heteronuclear Conversion Reaction | |
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| The Ionization Reaction | |
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| Concentration and Temperature Measurements | |
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| Mode Temperatures | |
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| Radiative Transitions | |
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| Spectral Transfer of Radiation | |
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| The Einstein Coefficients | |
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| Line Broadening | |
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| Absorption Spectroscopy | |
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| Emission Spectroscopy | |
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| Emissive Diagnostics | |
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| The Problem of Self-Absorption | |
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| Fluorescence Spectroscopy | |
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| Sodium D-Line Reversal | |
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| Advanced Diagnostic Techniques | |
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| Chemical Equilibrium and Diagnostics (Chapters 10-11) | |
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| Statistical Thermodynamics Beyond the Dilute Limit | |
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| Thermodynamics and Information | |
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| Reversible Work and Heat | |
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| The Second Law of Thermodynamics | |
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| The Boltzmann Definition of Entropy | |
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| Information Theory | |
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| Spray Size Distribution from Information Theory | |
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| Elements of the Solid State | |
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| Statistical Thermodynamics of the Crystalline Solid | |
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| Einstein Theory for the Crystalline Solid | |
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| Debye Theory for the Crystalline Solid | |
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| Critical Evaluation of the Debye Formulation | |
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| The Band Theory of Metallic Solids | |
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| Thermodynamic Properties of the Electron Gas | |
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| The Metallic Crystal near Absolute Zero | |
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| Equilibrium Radiation | |
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| Bose-Einstein Statistics for the Photon Gas | |
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| Photon Quantum States | |
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| The Planck Distribution Law | |
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| Thermodynamics of Blackbody Radiation | |
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| The Influence of Wavelength for the Planck Distribution | |
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| The Solid State and Radiation (Chapters 13-14) | |
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| Nonequilibrium Statistical Thermodynamics | |
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| Elementary Kinetic Theory | |
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| The Maxwell-Boltzmann Velocity Distribution | |
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| The Maxwell-Boltzmann Speed Distribution | |
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| The Maxwell-Boltzmann Energy Distribution | |
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| Molecular Effusion | |
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| The Ideal Gas Pressure | |
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| Kinetics of Molecular Transport | |
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| Binary Collision Theory | |
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| Fundamentals of Molecular Transport | |
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| The Mean Free Path | |
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| The Molecular Flux | |
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| Transport Properties | |
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| Rigorous Transport Theory | |
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| Dimensionless Transport Parameters | |
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| Collision Integrals | |
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| The Lennard-Jones Potential | |
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| Rigorous Expressions for Transport Properties | |
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| Chemical Kinetics | |
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| The Bimolecular Reaction | |
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| The Rate of Bimolecular Reactions | |
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| Chemical Kinetics from Collision Theory | |
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| The Significance of Internal Energy Modes | |
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| Chemical Kinetics from Transition State Theory | |
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| Kinetic Theory and Molecular Transport (Chapters 15-17) | |
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| The Ensemble Method of Statistical Thermodynamics | |
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| The Canonical and Grand Canonical Ensembles | |
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| The Ensemble Method | |
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| The Canonical Ensemble | |
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| The Equilibrium Distribution for the Canonical Ensemble | |
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| Equilibrium Properties for the Canonical Ensemble | |
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| Independent Particles in the Dilute Limit | |
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| Fluctuations in Internal Energy | |
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| Grand Canonical Ensemble | |
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| The Equilibrium Distribution for the Grand Canonical Ensemble | |
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| Equilibrium Properties for the Grand Canonical Ensemble | |
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| Independent Particles in the Dilute Limit Revisited | |
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| Applications of Ensemble Theory to Real Gases | |
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| The Behavior of Real Gases | |
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| Equation of State for Real Gases | |
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| Canonical Partition Function for Real Gases | |
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| The Virial Equation of State | |
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| The Second Virial Coefficient | |
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| Rigid-Sphere and Square-Well Potentials | |
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| Implementation of Lennard-Jones Potential | |
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| The Third Virial Coefficient | |
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| Properties for Real Gases | |
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| Whence and Whither | |
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| Reprising the Journey | |
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| Preparing for New Journeys | |
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| The Continuing Challenge of Thermodynamics | |
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| Appendices | |
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| Physical Constants and Conversion Factors | |
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| Series and Integrals | |
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| Periodic Table | |
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| Mathematical Procedures | |
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| Thermochemical Data for Ideal Gases | |
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| Summary of Classical Thermodynamics | |
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| Review of Classical Mechanics | |
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| Review of Operator Theory | |
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| The Spherical Coordinate System | |
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| Electronic Energy Levels | |
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| Energy-Mode Parameters for Molecules | |
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| Normal Mode Analysis | |
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| Tabulation of Debye Function | |
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| Maxwell-Boltzmann Energy Distribution | |
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| Force Constants for the Lennard-Jones Potential | |
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| Collision Integrals for Calculating Transport Properties from the Lennard-Jones Potential | |
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| Reduced Second Virial Coefficient from the Lennard-Jones Potential | |
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| References and Acknowledgments | |
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| Index | |