N diatomic molecules are stuck on a metal surface of square symmetry. Each molecule can either lie flat 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 > 0 associated with a molecule standing up, and zero energy for molecules lying flat along x or y directions.
1. How many microstates have the smallest value of energy? What is the largest microstate energy?
2. For microcanonical macrostates of energy U = E, calculate the number of states Ω(E, N), and the entropy S(E, N).
3. Calculate the heat capacity CN (T) and sketch it. 4. What is the probability that a specific molecule is standing up?