A different approach to introducing statistical mechanics

TL;DR

This paper presents an accessible numerical approach using spreadsheets to teach statistical mechanics concepts like entropy, temperature, and heat capacity through simple models, making the subject more understandable without complex mathematics.

Contribution

It introduces a spreadsheet-based method for exploring statistical mechanics concepts with simple models, bridging classical and statistical approaches.

Findings

Numerical computation of multiplicities illustrates the second law.

Graphs of entropy vs. energy demonstrate temperature definition.

Spreadsheet exercises elucidate heat capacity and Boltzmann distribution.

Abstract

The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid -- a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can exchange energy, one immediately sees that some configurations are overwhelmingly more probable than others. Graphs of entropy vs. energy for the two systems can be used to motivate the theoretical definition of temperature, $T= (\partial S/\partial U)^{-1}$, thus bridging the gap between the classical and statistical approaches to entropy. Further spreadsheet exercises can be used to compute the heat capacity of an Einstein solid, study the Boltzmann distribution, and explore the properties of a two-state paramagnetic system.