\frac{1}{T}\frac{\partial^2 U}{\partial V\partial T}=-\frac{1}{T^2}(\frac{\partial U}{\partial V})_T+\frac{1}{T}\frac{\partial^2 U}{\partial T\partial V}-\frac{p}{T^2}+\frac{1}{T}(\frac{\partial p}{\partial T})_V