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Introduction
Thermodynamics & Statistical Mechanics:
An intermediate level course
Richard Fitzpatrick
Associate Professor of Physics
The University of Texas at Austin
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
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
About this document ...
Richard Fitzpatrick 2006-02-02
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