1. The problem statement, all variables and given/known data I didn't have enough space to make the topic any more precise. Here is the full question: Express the Internal Energy with Internal Pressure. 2. Relevant equations This is what I know: the internal pressure is (dU/Dv)T the fundamental equation for internal energy is dU = T*dS - P*dV The third Maxwell relation: (dP/dT)v = (dS/dV)t Cv = (dU/dT)v 3. The attempt at a solution dividing by dV and imposing the constant T, then using the third Maxwell relation, we arive at (dU/dV)t = T*(dP/dT)v - P then I am supposed to consider the internal energy as a function of T and V. dU(T,V) = (dU/dT)v*dT + (dU/dV)t*dV this is where I come to my issue. Through google I found that (dU/dV)t *dV is -P I can't find anything that gives me the relationship between T*(dP/dT)v and (dU/dT)v*dT I know that (dU/dT)v is the Constant volume heat capacity. but I don't understand the transition... if that makes sense. I don't understand how those two terms are equivalent.