Mathematical Thermodynamics

There are some mathematical consequences of our friends, $U$, $S$, $H$, $F$, and $G$, being state functions. They are the Maxwell relations. It is useful to know they exist because it allows you to form relations between different quantities that are not intuitive at all. They are good fodder from questions on exams in other thermodynamics courses. I'd like you to understand where they come from and be able to manipulate them in the calm quiet atmosphere of your home, but I won't put questions about them on exams. What's the point? I would feel perfectly comfortable asking you questions about why they are important or where the Maxwell relations come from. There are also some implications that follow from the maths that imply how you should draw free energy curves--for some reason, materials scientists are amused by this fact.

We will have to go through some exercises about how to do mathematical manipulations in thermodynamics. I happen to like this kind of thing. You are expected to have seen them so I will teach them to you and give you some homework exercises.