Spécialisation Statistical Thermodynamics

Course 1 first explores the basics of both macroscopic and microscopic thermodynamics from a postulatory point of view. In this view, the meaning of temperature, thermodynamic pressure and chemical potential are especially clear and easy to understand. In addition , the development of the Fundamental Relation and its various transformations leads to a clear path to property relations and to the concept of ensembles needed to understand the relationship between atomic and molecular structural properties and macroscopic properties. We then explore the relationship between atomic and molecular structure and macroscopic properties by taking a statistical point of view. Using a postulatory approach, the method for doing this is made clear. This leads to the development of the partition function which describes the distribution of molecular quantum states as a function of the independent, macroscopic thermodynamic properties.

Course 2 of Statistical Thermodynamics presents an introduction to quantum mechanics at a level appropriate for those with mechanical or aerospace engineering backgrounds. Using a postulatory approach that describes the steps to follow, the Schrodinger wave equation is derived and simple solutions obtained that illustrate atomic and molecular structural behavior. More realistic behavior is also explored along with modern quantum chemistry numerical solution methods for solving the wave equation.

Course 3 of Statistical Thermodynamics, Ideal Gases, explores the behavior of systems when intermolecular forces are not important. This done by evaluating the appropriate partition functions for translational, rotational, vibrational and/or electronic motion. We start with pure ideal gases including monatomic, diatomic and polyatomic species. We then discuss both non-reacting and reacting ideal gas mixtures as both have many industrial applications. Computational methods for calculating equilibrium properties are introduced. We also discuss practical sources of ideal gas properties. Interestingly, in addition to normal low density gases, photons and electrons in metals can be described as though they are ideal gases and so we discuss them.

Course 4 of Statistical Thermodynamics addresses dense gases, liquids, and solids. As the density of a gas is increased, intermolecular forces begin to affect behavior. For small departures from ideal gas behavior, known as the dense gas limit, one can estimate the change in properties using the concept of a configuration integral, a modification to the partition function. This leads to the development of equations of state that are expansions in density from the ideal gas limit. Inter molecular potential energy functions are introduced and it is explored how they impact P-V-T behavior. As the density is increased, there is a transition to the liquid state. We explore whether this transition is smooth or abrupt by examining the stability of a thermodynamic system to small perturbations. We then present a brief discussion regarding the determination of the thermodynamic properties of liquids using concept of the radial distribution function (RDF), and how the function relates to thermodynamic properties. Finally, we explore two simple models of crystalline solids.