The Canonical Ensemble: Notion of Distribution

Abstract

The goal of statistical thermodynamics is to permit to appreciate the significance of the thermodynamic functions in terms of molecular parameters. Firstly, this chapter illustrates this point with the aid of the study of the canonical ensemble. It deals with the obtaining of the probabilities of the systems constituting the canonical ensemble to be in some energy states. It provides a description of the canonical ensemble and describes the followed strategy to calculate the average of the mechanical properties such as the pressure and energy with the help of the reasoning based on the fact that the mechanical variables have well-definite values in a given quantum state. It leads to the notion of distribution of the systems in the ensemble. It is the set of the numbers of systems found in well-defined energy states exhibiting the same composition (in one or several compounds) and the same volume. There can exist several distributions. Calculations, exemplified in the chapter, permit to obtain the elementary and global probabilities that a system of the ensemble would be in a definite energetic state. Once the probabilities are obtained, it becomes possible to calculate the canonical partition function.