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Introduction
Thermodynamics and Statistical Mechanics
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Introduction
Intended Audience
Major Sources
Why Study Thermodynamics?
Atomic Theory of Matter
What is Thermodynamics?
Need for Statistical Approach
Microscopic and Macroscopic Systems
Classical and Statistical Thermodynamics
Classical and Quantum Approaches
Probability Theory
Introduction
What is Probability?
Combining Probabilities
Two-State System
Combinatorial Analysis
Binomial Probability Distribution
Mean, Variance, and Standard Deviation
Application to Binomial Probability Distribution
Gaussian Probability Distribution
Central Limit Theorem
Exercises
Statistical Mechanics
Introduction
Specification of State of Many-Particle System
Principle of Equal A Priori Probabilities
-Theorem
Relaxation Time
Reversibility and Irreversibility
Probability Calculations
Behavior of Density of States
Exercises
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
Exercises
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
Classical Thermodynamics
Introduction
Ideal Gas Equation of State
Specific Heat
Calculation of Specific Heats
Isothermal and Adiabatic Expansion
Hydrostatic 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
Applications of Statistical Thermodynamics
Introduction
Canonical Probability Distribution
Spin-1/2 Paramagnetism
System with Specified Mean Energy
Calculation of Mean Values
Partition Function
Ideal Monatomic Gas
Gibb's Paradox
General Paramagnetism
Equipartition Theorem
Harmonic Oscillators
Specific Heats
Specific Heats of Gases
Specific Heats of Solids
Maxwell Velocity Distribution
Effusion
Ferromagnetism
Exercises
Quantum Statistics
Introduction
Symmetry Requirements in Quantum Mechanics
Illustrative Example
Formulation of Statistical Problem
Fermi-Dirac Statistics
Photon Statistics
Bose-Einstein Statistics
Maxwell-Boltzmann Statistics
Quantum Statistics in Classical Limit
Quantum-Mechanical Treatment of Ideal Gas
Derivation of van der Waals Equation of State
Planck Radiation Law
Black-Body Radiation
Stefan-Boltzmann Law
Conduction Electrons in Metal
Sommerfeld Expansion
White-Dwarf Stars
Chandrasekhar Limit
Neutron Stars
Bose-Einstein Condensation
Exercises
Multi-Phase Systems
Introduction
Equilibrium of Isolated System
Equilibrium of Constant-Temperature System
Equilibrium of Constant-Temperature Constant-Pressure System
Stability of Single-Phase Substance
Equilibrium Between Phases
Clausius-Clapeyron Equation
Phase Diagrams
Vapor Pressure
Phase Transformations in Van der Waals Fluid
Exercises
Physical Constants
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
Wave Mechanics
Introduction
Photoelectric Effect
Electron Diffraction
Representation of Waves via Complex Numbers
Schrödinger's Equation
Probability Interpretation of Wavefunction
Wave Packets
Heisenberg's Uncertainty Principle
Stationary States
Three-Dimensional Wave Mechanics
Simple Harmonic Oscillator
Angular Momentum
About this document ...
Richard Fitzpatrick 2016-01-25
-Theorem