# Partial differential equations?

## Main Question or Discussion Point

Hello, PF! As I was reading my P-Chem textbook, I noticed most thermodynamic equations involve partial derivatives, like these ones: $$C_V = {\left( \frac {\partial E}{\partial T} \right )}_V$$ $${\left( \frac {\partial H}{\partial T} \right )}_P = {\left( \frac {\partial E}{\partial T} \right )}_P + P{\left( \frac {\partial V}{\partial T} \right )}_P$$ However, none of these equations is ever actually called a PDE by the author. Is it implied they are PDEs given they involve partial derivatives, or are they not classified as PDEs such as the wave or heat equations? Thanks in advance!

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dextercioby
Homework Helper
They are not equations, but equalities, because there's no unknown function and no boundary conditions. In the first equality you wrote, you should determine what E(T,V) looks like, then partially differentiate wrt T, to get the function C_V(T,V). For the second, there's an equality involving 3 different functions, H(T,P), E(T,P) and V(T,P).

I get it now, they are not equations in the sense that they need not be solved, right? They are just showing the relation between thermodynamic functions.

Mark44
Mentor
I get it now, they are not equations in the sense that they need not be solved, right? They are just showing the relation between thermodynamic functions.
Right.