Now, from the fundamental thermodynamic relation d U = T d S − − p d V , we obtain the following expression, after dividing by d V and fixing T : ( ∂ ∂ U ∂ ∂ V ) T = T ( ∂ ∂ S ∂ ∂ V ) T − − p = T ( ∂ ∂ p ∂ ∂ T ) V − − p .