12 - Appendix: the statistical basis of thermodynamics

Summary

Overview

To truly appreciate how thermodynamic principles apply to chemical systems, it is of great value to see how these principles arise from a statistical treatment of how microscopic behavior is reflected on the macroscopic scale. While this appendix by no means provides a complete introduction to the subject, it may provide a view of thermodynamics that is refreshing and exciting for readers not familiar with the deep roots of thermodynamics in statistical physics. The primary goal here is to provide rigorous derivations for the probability laws used in Chapter 1 to introduce thermodynamic quantities such as entropy and free energies.

The NVE ensemble

Thermodynamic principles arise from a statistical treatment of matter by studying different idealized ensembles of particles that represent different thermodynamic systems. The first ensemble that we study is that of an isolated system: a collection of N particles confined to a volume V, with total internal energy E. A system of this sort is referred to as an NVE system or ensemble, as N, V, and E are the three thermodynamic variables that are held constant. N, V, and E are extensive variables. That is, their values are proportional to the size of the system. If we combine NVE subsystems into a larger system, then the total N, V, and E are computed as the sums of N, V, and E of the subsystems. Temperature, pressure, and chemical potential are intensive variables, for which values do not depend on the size of the system.