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# Chapter 15: Statistical Mechanics

Statistical mechanics is the study of systems with large numbers of particles and serves to connect microscopic properties of individual particles to macroscopically observable quantities. This chapter limits its focus of statistical mechanics to a comparison between the classical and quantum statistics and some of the associated applications. Quantum statistics operates when particles are indistinguishable and the type of statistics depends on the spin of the particles: Bose-Einstein statistics for bosons (integer or zero spin particles) and Fermi-Dirac statistics for fermions (half-integer spin particles).

# Table of Contents

## Sections

- Section 15.1: Exploring Functions:
*g*(ε),*f*(ε), and*n*(ε). - Section 15.2: Entropy and Probability.
- Section 15.3: Understanding Probability Distributions.
- Section 15.4: Exploring Classical, Bose-Einstein, and Fermi-Dirac Statistics.
- Section 15.5: Statistics of an Ideal Gas, a Blackbody, and a Free Electron Gas.
- Section 15.6: Exploring the Equipartition of Energy.
- Section 15.7: Specific Heat of Solids

## Problems

- Problem 15.1: Find the average energy per particle for a given distribution.
- Problem 15.2: Compare the temperature of distributions.
- Problem 15.3: Determine number of particles near Fermi level.
- Problem 15.4: Rank Fermi energy and temperature.
- Problem 15.5: Temperature required for particles to be above the Fermi level.
- Problem 15.6: Speed of particles in ideal gas.
- Problem 15.7: Blackbody radiation.
- Problem 15.8: Equipartition.
- Problem 15.9: Rank solids by Debye temperature.
- Problem 15.10: Determine properties of rotating molecules from rotational spectrum.