General forms for the entropy We have derived the entropy of a classical ideal gas, which satisfies all the postulates of thermodynamics (except the Nernst postulate, which applies to quantum systems). However, when interactions are included, the entropy could be a very different function of U, V , and N. Here are some functions that are candidates for being the entropy of some system. [In each case, A is a positive constant.]
1. Which of the following equations for the entropy satisfy the postulates of thermodynamics (except the Nernst postulate)?
2. For each of the valid forms of the entropy in the previous part of the problem, find the three equations of state.