Elements of Equilibrium Statistical Thermodynamics

Abstract

The goal of this chapter is to explain the principles of equilibrium statistical thermodynamics necessary to understand how chemical equilibrium constants can be calculated from molecular and spectroscopic data, and the exploration of a microscopic background of phenomenological thermodynamics. The treatment of statistical thermodynamics also begins with the discussion of simple, isolated systems adding a further simplification of restricting the treatment to a single component. The mechanical model of this system, the microcanonical ensemble is described in details, along with a couple of examples: the Einstein solid and the two-state system. Calculation of thermodynamic functions from the partition function is also explained. Similarly to the treatment of phenomenological thermodynamics, the model of constant temperature systems – the canonical ensemble – is derived from modeling a “microcanonical reservoir” containing the modeled system. Factorization of the canonical partition function and the calculation of translational, rotational, vibrational, and electronic contributions are described in detail, along with the calculation of thermodynamic functions and fundamental equations from the partition function. Properties of the canonical many-particle and single-particle energy functions are discussed. A discussion on the general properties of the statistical expression of entropy is provided, along with a critical analysis of its interpretation as “disorder.” After the demonstration of the principal of equipartition, the chapter ends with the discussion of the calculation of the chemical equilibrium constant from canonical partition functions.