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Thermodynamics and Statistical Mechanics

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Lecture Notes by Richard Fitzpatrick,
The University of Texas at Austin

TOC

# Introduction

* Intended audience
* Major sources
* Why study thermodynamics?
* The atomic theory of matter
* Thermodynamics
* The need for a statistical approach
* Microscopic and macroscopic systems
* Thermodynamics and statistical thermodynamics
* Classical and quantum approaches

# Probability theory

* Introduction
* What is probability?
* Combining probabilities
* The two-state system
* Combinatorial analysis
* The binomial distribution
* The mean, variance, and standard deviation
* Application to the binomial distribution
* The Gaussian distribution
* The central limit theorem

# Statistical mechanics

* Introduction
* Specification of the state of a many particle system
* The principle of equal a priori probabilities
* The $H$ theorem
* The relaxation time
* Reversibility and irreversibility
* Probability calculations
* Behaviour of the density of states

# Heat and work

* A brief history of heat and work
* Macrostates and microstates
* The microscopic interpretation of heat and work
* Quasi-static processes
* Exact and inexact differentials

# 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
* The laws of thermodynamics

# Classical thermodynamics

* Introduction
* The equation of state of an ideal gas
* Heat capacity or specific heat
* Calculation of specific heats
* Isothermal and adiabatic expansion
* Hydrostatic equilibrium of the atmosphere
* The isothermal atmosphere
* The adiabatic atmosphere
* Heat engines
* Refrigerators

# Applications of statistical thermodynamics

* Introduction
* Boltzmann distributions
* Paramagnetism
* Mean values
* Partition functions
* Ideal monatomic gases
* Gibb’s paradox
* The equipartition theorem
* Harmonic oscillators
* Specific heats
* Specific heats of gases
* Specific heats of solids
* The Maxwell distribution

# Quantum statistics

* Introduction
* Symmetry requirements in quantum mechanics
* An illustrative example
* Formulation of the statistical problem
* Fermi-Dirac statistics
* Photon statistics
* Bose-Einstein statistics
* Maxwell-Boltzmann statistics
* Quantum statistics in the classical limit
* The Planck radiation law
* Black-body radiation
* The Stefan-Boltzmann law
* Conduction electrons in a metal
* White-dwarf stars
* The Chandrasekhar limit
* Neutron stars

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