Thermodynamic Quantities Within the Framework of the Canonical Ensemble

Abstract

The chapter describes the handling of the mathematical relations previously found within the framework of the canonical ensemble through the partition function in order to assimilate them to the expressions of classical thermodynamic functions. Concerning now the introduction of the nonmechanical functions such as the entropy and the temperature into the realm of statistical thermodynamics, the strategy consists in comparing the expressions concerning the mechanical quantities obtained (thanks to the theory of the canonical ensemble) and those stemming from classical thermodynamics. Therefore, the statistical expressions of internal energy, entropy, pressure, and chemical potential are obtained. Some of these functions are calculated with the aid of the characteristic function of the canonical function which spontaneously introduces itself into the calculations.