Specific heats of model gas molecules: An oral exam teaching strategy

Abstract

A teaching strategy is presented that investigates the specific heats of a simple harmonic oscillator, of a two-state system, and of an n-state system that interpolates between the two. One stage of the investigation provides a relation between the specific heats of two systems that differ by the addition of a single energy eigenstate. The strategy begins with a traditional analytic problem set whose results are investigated qualitatively in an oral exam. The oral exam raises questions that are then resolved in a second analytic problem set. As such, the strategy shows how conceptual understanding and rigorous analytic methods work together to solve problems. Although developed for a senior-level statistical mechanics course, the strategy is generally applicable to a wide range of course levels.