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PHY 418: Statistical Mechanics I
Prof. S. Teitel: stte@pas.rochester.edu ---- Spring 2023

Unit 2

Unit 1 • Unit 2 • Unit 3 • Unit 4

Classical Ensembles

In this we unit begin our discussion of statistical mechanics, which provides the link between mechanics and thermodynamics. We start with a simple discussion of the kinetic theory of the ideal gas. We then move on to the more general statistical ensemble approach which is based on the ergodic hypothesis. In this unit we will confine our discussion to systems obeying classical mechanics. We will discuss the microcanonical ensemble for systems at fixed total energy, the canonical ensemble for systems at fixed temperature, and the grand canonical ensemble for systems at fixed chemical potential. We will discuss the partition functions for each of these ensembles and their relation to the corresponding thermodynamic potential. We will discuss several examples and discuss the relationship between entropy and information.

Below is a list of links to course notes for each topic in this unit, followed by links to recorded video lectures.

Notes and Video Lectures

• Notes 2-1 • Video 2-1 [31 min] - Kinetic Theory of the Ideal Gas and the Maxwell Velocity Distribution

• Notes 2-2 • Video 2-2 [37 min] - The Ergodic Hypothesis -- Time vs Ensemble Averages
                           A review of ergodic theory may be found here.

• Notes 2-3 • Video 2-3 [28 min] - Liouville's Theorem

• Notes 2-4 • Video 2-4 [50 min] - The Microcannonical Ensemble and Entropy

• Notes 2-5 • Video 2-5 [24 min] - Entropy of the Ideal Gas in the Microcanonical Ensemble

• Notes 2-6 • Video 2-6 [33 min] - Entropy of Mixing and the Gibbs Paradox

• Notes 2-7 • Video 2-7 [49 min] - Indistinguishable Particles

• Notes 2-8 • Video 2-8 [54 min] - The Canonical Ensemble

• Notes 2-9 • Video 2-9 [45 min] - Equivalence of the Microcanonical and Canonical Ensembles

• Notes 2-10 • Video 2-10 [47 min] - Average Energy Vs Most Probably Energy; Stirling's Formula

• Notes 2-11 • Video 2-11 [44 min] - Factorization of the Canonical Partition Function for Non-Interacting Particles

• Notes 2-12 • Video 2-12 [28 min] - The Virial Theorem and the Equipartition Theorem for Classical Systems

• Notes 2-13 • Video 2-13 [58 min] - Examples: The Specific Heat of Solids, Curie Paramagnetism

• Notes 2-14 • Video 2-14 [28 min] - A Note About the Proper Choice of Coordinates

• Notes 2-15 • Video 2-15 [61 min] - Entropy and Information

• Notes 2-16 • Video 2-16 [34 min] - The Grand Canonical Ensemble

• Notes 2-17 • Video 2-17 [62 min] - The Grand Canonical Ensemble and the Grand Potential

• Notes 2-18 • Video 2-18 [14 min] - Non-Interacting Particles in the Grand Canonical Ensemble

• Notes 2-19 • Video 2-19 [58 min] - Chemical Equilibrium and an Example: A Gas in Equillibrium with Adsorption Sites