Thermodynamic relations

These thermodynamic relations are also known as coefficient relations or Maxwell's relations.

$T={(\frac{\partial U}{\partial S})}_V$

$P=-{(\frac{\partial U}{\partial V})}_S$

$T={(\frac{\partial H}{\partial S})}_p$

$V={(\frac{\partial H}{\partial p})}_S$

$S=-{(\frac{\partial F}{\partial T})}_V$

$p=-{(\frac{\partial A}{\partial V})}_T$

$S=-{(\frac{\partial G}{\partial T})}_p$

$V={(\frac{\partial G}{\partial p})}_T$