Problem 7.8. What is the partition function for a van der Waals gas with N particles? Note that the result is phenomenological and might involve some guessing. It is useful to compare it to the partition function for an ideal gas. Remember that the particles are indistinquishable, so when using the partition function one must insert a counting factor. Use this partition function to compute the internal energy, U(N, T, V), the pressure, P(N,T, V), and the entropy, S(U, V, N).