Thermodynamic functions

Most important functions

• Thermodynamic potentials: $(U, H, F, G)$
• First derivatives: $(P, V, T, S)$
• Second derivatives: $(C_P, C_V, \alpha, \beta)$

Important relationships

Legendre transformation

Legendre transformation helps us to change the natural variable for a function.

For $Y(X)$, given $P = \mathrm{d}Y / \mathrm{d}X$, we have $\Psi(P) = Y - PX$.

Maxwell relations

For a good function exchange in the order of derivative does not matter. Its general form, according to Wikipedia, is called Schwarz’s theorem:

In thermodynamics, …

Other methods

Everything as a function of $(T,P)$

References

• Maxwell relations - Wikipedia