Mathfest 2007

If you like math, the abstract bone-crushing kind that makes your eyes all puppy-doggy, then Wednesday was the best thermodynamic day of your life.

Not only did we introduce the last two members of the big four: A [helmholtz energy] and G [gibbs energy], but, more importantly, we derived the four fundamental differentials:

dU = TdS - PdV [the fundamental differential]
dH = TdS +VdP
dA = -SdT - PdV
dG = -SdT + VdP

From each of these differentials, two fundamental equations and one Maxwell relation can be found. These 12 expressions, coupled to the 1st and 2nd Laws, is what Thermodynamics rests on. Except for chemical potential, nearly nothing new in terms of concepts will be presented for the rest of the quarter. The Four Laws, Maxwell relations, the four fundamental differentials and eight fundamental relations have now been developed -- the task from here is to extend them to real-world applications. We will especially do just that when addressing phase changes.

We also showed how ∆A and ∆G could be related to total work and nonexpansion work, respectively, under certain conditions. The gibbs energy change is especially important in chemistry, when T and P are constant, which leads to criteria for spontaneity and equilibrium.