1. The problem statement, all variables and given/known data Use partial differential calculus to show that if 3 quantities p, V, T are related to each other by some unknown but smooth (which means all derivatives are well defined) equation of state f (P, V, T ) = 0. Then the partial derivatives must satisfy the relation ∂p/∂T = - (∂V /∂T ) / ( (∂V /∂p) ) 2. Relevant equations Not sure any would help in this case. 3. The attempt at a solution I'm not even sure where to start since I haven't a proper understanding of the problem. If p, V, and T are related then how does f (P, V, T ) = 0 help?