Week 1:
1. Introduction
1.1 The Statistical Foundation of Classical Thermodynamics
1.2 A Classification Scheme for Statistical Thermodynamics
1.3 Why Statistical Thermodynamics?
2. Probability and Statistics
2.1 Probability: Definitions and Basic Concepts
2.2 Permutations and Combinations
2.3 Probability Distributions: Discrete and Continuous
2.4 The Binomial Distribution
2.5 The Poisson Distribution
2.6 The Gaussian Distribution
2.7 Combinatorial Analysis for Statistical Thermodynamics
2.7.1 Distinguishable Objects
2.7.2 Indistinguishable Objects
Week 2, 3:
3. The Statistics of Independent Particles
3.1 Essential Concepts from Quantum Mechanics
3.2 The Ensemble Method of Statistical Thermodynamics
3.3 The Two Basic Postulates of Statistical Thermodynamics
3.3.1 The M–B Method: System Constraints and Particle Distribution
3.3.2 The M–B Method: Microstates and Macrostates
3.4 The Most Probable Macrostate
3.5 Bose–Einstein and Fermi–Dirac Statistics
3.5.1 Bose–Einstein Statistics
3.5.2 Fermi-Dirac Statistics
3.5.3 The Most Probable Particle Distribution
3.6 Entropy and the Equilibrium Particle Distribution
3.6.1 The Boltzmann Relation for Entropy
3.6.2 Identification of Lagrange Multipliers
3.6.3 The Equilibrium Particle Distribution
Week 4:
4. Thermodynamic Properties in the Dilute Limit
4.1 The Dilute Limit
4.2 Corrected Maxwell–Boltzmann Statistics
4.3 The Molecular Partition Function
4.3.1 The Influence of Temperature
4.3.2 Criterion for Dilute Limit
4.4 Internal Energy and Entropy in the Dilute Limit
4.5 Additional Thermodynamic Properties in the Dilute Limit
4.6 The Zero of Energy and Thermodynamic Properties
4.7 Intensive Thermodynamic Properties for the Ideal Gas
Week 5, 6:
5. Basics of Quantum Mechanics
5.1 Historical Survey of Quantum Mechanics
5.2 The Bohr Model for the Spectrum of Atomic Hydrogen
5.3 The de Broglie Hypothesis
5.4 A Heuristic Introduction to the Schrödinger Equation
5.5 The Postulates of Quantum Mechanics
5.6 The Steady-State Schrödinger Equation
5.6.1 Single-Particle Analysis
5.6.2 Multiparticle Analysis
5.7 The Particle in a Box
5.8 The Uncertainty Principle
5.9 Indistinguishability and Symmetry
5.10 The Pauli Exclusion Principle
5.11 The Correspondence Principle
6. Quantum Analysis of Internal Energy Modes
6.1 Schrödinger Wave Equation for Two-Particle System
6.1.1 Conversion to Center-of-Mass Coordinates
6.1.2 Separation of External from Internal Modes
6.2 The Internal Motion for a Two-Particle System
6.3 The Rotational Energy Mode for a Diatomic Molecule
6.4 The Vibrational Energy Mode for a Diatomic Molecule
6.5 The Electronic Energy Mode for Atomic Hydrogen
6.6 The Electronic Energy Mode for Multielectron Species
6.6.1 Electron Configuration for Multielectron Atoms
6.6.2 Spectroscopic Term Symbols for Multielectron Atoms
6.6.3 Electronic Energy Levels and Degeneracies for Atoms
6.6.4 Electronic Energy Levels and Degeneracies for Diatomic Molecules
6.7 Combined Energy Modes for Atoms and Diatomic Molecules
6.8 Selection Rules for Atoms and Molecules
Week 7:
7. The Spectroscopy of Diatomic Molecules
7.1 Rotational Spectroscopy Using the Rigid-Rotor Model
7.2 Vibrational Spectroscopy Using the Harmonic-Oscillator Model
7.3 Rovibrational Spectroscopy: The Simplex Model
7.4 The Complex Model for Combined Rotation and Vibration
7.5 Rovibrational Spectroscopy: The Complex Model
7.6 Electronic Spectroscopy
7.7 Energy-Mode Parameters for Diatomic Molecules
Week 8:
8. Interlude: From Particle to Assembly
8.1 Energy and Degeneracy
8.2 Separation of Energy Modes
8.3 The Molecular Internal Energy
8.4 The Partition Function and Thermodynamic Properties
8.5 Energy-Mode Contributions in Classical Mechanics
8.5.1 The Phase Integral
8.5.2 The Equipartition Principle
8.5.3 Mode Contributions
Week 9, 10:
9 Thermodynamic Properties of the Ideal Gas
9.1 The monoatomic gas
9.1.1 Translation Mode
9.1.2 Electronic Mode
9.2 The Diatomic Gas
9.2.1 Translational and Electronic Modes
9.2.2 The Zero of Energy
9.2.3 Rotational Mode
9.2.4 Quantum Origin of Rotational Symmetry Factor
9.2.5 Vibrational Mode
9.3 Rigorous and Semirigorous Models for the Diatomic Gas
9.4 The Polyatomic Gas
9.4.1 Rotational Contribution
9.4.2 Vibrational Contribution
9.4.3 Property Calculations for Polyatomic Molecules
10. Statistical Thermodynamics for Ideal Gas Mixtures
10.1 Equilibrium Particle Distribution for the Ideal Gas Mixture
10.2 Thermodynamic Properties of the Ideal Gas Mixture
10.3 The Reacting Ideal Gas Mixture
10.3.1 Equilibrium Particle Distribution for Reactive Ideal Gas Mixture
10.3.2 Equilibrium Constant: Introduction and Development
10.4 Equilibrium Constant: General Expression and Specific
Examples
10.4.1 Dissociation of a Homonuclear Diatomic
10.4.2 The Homonuclear–Heteronuclear Conversion Reaction
10.4.3 The Ionization Reaction
Week 11, 12:
11. Concentration and Temperature Measurements
11.1 Mode Temperatures
11.2 Radiative Transitions
11.2.1 Spectral Transfer of Radiation
11.2.2 The Einstein Coefficients
11.2.3 Line Broadening
11.3 Absorption Spectroscopy
11.4 Emission Spectroscopy
11.4.1 Emissive Diagnostics
11.4.2 The problem of Self-Absorption
11.5 Fluorescence Spectroscopy
11.6 Sodium D-Line Reversal
11.7 Advanced Diagnostic Techniques
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