Thermodynamic relations

These thermodynamic relations are also known as coefficient relations.

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

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

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

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

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

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

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

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

where

• $H$ is the enthalpy
• $T$ is the temperature
• $G$ is the Gibbs energy function
• $U$ is the internal energy,
• $V$ is the volume
• $A$ is the Helmholtz energy function
• $p$ is the pressure
• $S$ is the entropy

See also

• Maxwell's relations