Statistical Thermodynamics in Brief

Abstract

The object of statistical thermodynamics is to set up a theory at the molecular scale permitting an interpretation of the classical thermodynamics which, itself, applies to the macroscopic level. Statistical thermodynamics is founded on several postulates and, also, on the principles of quantum mechanics. It permits to calculate the mechanical properties of a thermodynamic system. The obtaining of the expressions relating the mechanical properties to molecular quantities is founded on the ensemble theory of Gibbs. Several kinds of ensembles are considered and used according to the thermodynamic environment of the studied system. The most important are the following:

• The canonical ensemble: The canonical ensemble is a closed, isothermal and volume-constant system

• The grand ensemble or the great ensemble, or the grand canonical ensemble: It corresponds to an open, isothermal, and volume-constant system

• The microcanonical ensemble: It corresponds to an isolated system

• The isothermal, isobaric ensemble.

There happens to exist a well-definite mathematical function, characteristic of each kind of ensembles. When it is known, it permits to calculate the other thermodynamic quantities at the macroscopic scale. These mathematical functions are called partition functions.