# Statistical Thermodynamics

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## Overview

This specialization is designed for those working in advanced fields such as combustion, high temperature gas dynamics, environmental sciences, or materials processing, or someone who wishes to build a background for understanding advanced experimental diagnostic techniques in these or similar fields.

## Syllabus

Course 1: Fundamentals of Macroscopic and Microscopic 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: Quantum Mechanics
- 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: Ideal Gases
- 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: Dense Gases, Liquids and Solids
- 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.

Course 5: Non-Equilibrium Applications of Statistical Thermodynamics
- Course 5 of Statistical Thermodynamics explores three different applications of non-equilibrium statistical thermodynamics. The first is the transport behavior of ideal gases, with some discussion of transport in dense gases and liquids. It starts with simple estimates of the transport properties of an ideas gas. It then introduces the Boltzmann Equation and describes the Chapman-Enskog solution of that equation in order to obtain the transport properties. It closes with a discussion of practical sources of transport properties. Spectroscopic methods have become increasingly common as a way of determining the thermodynamic state of a system. Here we present the underlying concepts of the subject and explores how spectroscopy can be used to determine thermodynamic and flow properties. Chemical kinetics are important in a variety of fluid/thermal applications including combustion, air quality, fuel cells and material processing. Here we cover the basics of chemical kinetics, with a particular focus on combustion. It starts with some definitions, including reaction rate and reaction rate constant. It then explores methods for determining reaction rate constants. Next, systems of reactions, or reaction mechanisms, are explored, including the oxidation of hydrogen and hydrocarbon fuels. Finally, computational tools for carrying out kinetic calculations are explored.