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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 | |