Statistical Mechanics - Physics at Oregon State University
Statistical Mechanics - Physics at Oregon State University
Statistical Mechanics - Physics at Oregon State University
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Contents<br />
1 Found<strong>at</strong>ion of st<strong>at</strong>istical mechanics. 1<br />
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br />
1.2 Program of st<strong>at</strong>istical mechanics. . . . . . . . . . . . . . . . . . . 4<br />
1.3 St<strong>at</strong>es of a system. . . . . . . . . . . . . . . . . . . . . . . . . . . 5<br />
1.4 Averages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<br />
1.5 Thermal equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . 14<br />
1.6 Entropy and temper<strong>at</strong>ure. . . . . . . . . . . . . . . . . . . . . . . 16<br />
1.7 Laws of thermodynamics. . . . . . . . . . . . . . . . . . . . . . . 19<br />
1.8 Problems for chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . 20<br />
2 The canonical ensemble 23<br />
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23<br />
2.2 Energy and entropy and temper<strong>at</strong>ure. . . . . . . . . . . . . . . . 26<br />
2.3 Work and pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . 28<br />
2.4 Helmholtz free energy. . . . . . . . . . . . . . . . . . . . . . . . . 31<br />
2.5 Changes in variables. . . . . . . . . . . . . . . . . . . . . . . . . . 32<br />
2.6 Properties of the Helmholtz free energy. . . . . . . . . . . . . . . 33<br />
2.7 Energy fluctu<strong>at</strong>ions. . . . . . . . . . . . . . . . . . . . . . . . . . 35<br />
2.8 A simple example. . . . . . . . . . . . . . . . . . . . . . . . . . . 37<br />
2.9 Problems for chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . 39<br />
3 Variable number of particles 43<br />
3.1 Chemical potential. . . . . . . . . . . . . . . . . . . . . . . . . . 43<br />
3.2 Examples of the use of the chemical potential. . . . . . . . . . . . 46<br />
3.3 Differential rel<strong>at</strong>ions and grand potential. . . . . . . . . . . . . . 48<br />
3.4 Grand partition function. . . . . . . . . . . . . . . . . . . . . . . 50<br />
3.5 Overview of calcul<strong>at</strong>ion methods. . . . . . . . . . . . . . . . . . . 55<br />
3.6 A simple example. . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
3.7 Ideal gas in first approxim<strong>at</strong>ion. . . . . . . . . . . . . . . . . . . . 58<br />
3.8 Problems for chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . 64<br />
4 St<strong>at</strong>istics of independent particles. 67<br />
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67<br />
4.2 Boltzmann gas again. . . . . . . . . . . . . . . . . . . . . . . . . 74<br />
III
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