This topic will differ in style from those we looked at previously. Though it may not seem as if we have covered much, we have laid nearly all of the necessary groundwork to solve any thermodynamics problem.
Here, we will talk about gases, and apply our current tools to the systems to discover all of their relevant properties. To begin with, We will point out the distinctions between classical gases and degenerate gasses by talking about fermions and bosons.
We will embark upon a broad analysis of a classical ideal gas, discussing its distribution function, chemical potential, free energy, pressure, energy and entropy. We will define a new property of a system known as the heat capacity and discuss alternate formulations of it. We will close the discussion of ideal gasses by looking at a classical shortcut known as equipartition.
Having done the work for the easier case, we will turn to the Fermi gas and see why study of such gasses is at the cutting edge of so many fields. We will finally look at the Boson gas, and talk about the intriguing Bose condensate.