Consider N non-interacting diatomic molecules stuck on a metal surface. 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 e > 0 associated with a molecule standing up, and zero energy for molecules lying flat along x or y directions.

What are the possible energy levels for this system of N particles, and what is the number of microstates associated to each energy level?
Find the entropy and energy of the system as a function of the temperature, T.
What is the probability of a specific molecule standing up?
What is the largest possible value of the energy of the system at any temperature?