Molecular adsorption: N diatomic molecules are stuck on a metal surface of square symmetry. Each molecule can either lie at on the surface, in which case it must be aligned to one of two directions, x and y, or it can stand up along the z, direction. There is an energy cost of 8 > 0 associated with a molecule standing up, and zero energy for molecules lying at along x or y directions. (a) How many microstates have the smallest value of energy? What is the largest microstate energy? (b) For microcanonical macrostates of energy E , calculate the number of states (ME, N), and the entropy S (E N ) (c) Calculate the heat capacity C (T) and sketch it. ((1) What is the probability that a specific molecule is standing up? (e) What is the largest possible value of the internal energy at any positive temperature