Thermodynamic relations

Also known as coefficient relations.

$T=\left({\frac {\partial U}{\partial S}}\right)_{V}$

$P=-\left({\frac {\partial U}{\partial V}}\right)_{S}$

$T=\left({\frac {\partial H}{\partial S}}\right)_{p}$

$V=\left({\frac {\partial H}{\partial p}}\right)_{S}$

$S=-\left({\frac {\partial F}{\partial T}}\right)_{V}$

$p=-\left({\frac {\partial A}{\partial V}}\right)_{T}$

$S=-\left({\frac {\partial G}{\partial T}}\right)_{p}$

$V=\left({\frac {\partial G}{\partial p}}\right)_{T}$