Hi all, I have a small question about a proof. Question: Under control variables T, V, and N, derive an expression to relate internal energy as a function of volume. Assume that N is constant throughout. Thoughts: Starting with dU = TdS - PdV + udN. Cancel out dN --> dU = TdS - PdV Divide by dV --> (dU/dV) = (TdS/dV) - P In my answer key, It jumps from the above equation to (dU/dV) = (TdP/dT) - P I don't understand why dS/dV was replaced by dP/dT, how was that relationship derived? Thanks.