The entropy S(U, V) is a function of U and V in equilibrium. Using the chain rule, dV. This is always true; it's a mathematical identity. The "Fundamental Relation of Thermodynamics" says that in equilibrium: where T is temperature, S is entropy, U is internal energy, p is pressure, and V is volume. This describes how, in equilibrium, S depends on changes in U and V. Here are other derivatives to evaluate, always assuming equilibrium so you can use the Fundamental Relation. A) What's d. vi ds? B) What's UV dV? C) What's duts. n dV?