Consider a classical system of n noninteracting diatomic molecules enclosed in a box of volume v at temperature t. the hamiltonian of the system is taken to be h= where m = 2m the total mass of the molecule, m/2 the reduced mass of the molecule, p is the momentum of the center of mass, pi p2, and p the reduced momentum p = (pi-p2)/2, and r = irl-r21 a calculate the helmholtz free energy, f, of the system. b calculate the internal energy u from the relation u = θ(3f)/a3. does this agree with the result you would get from the equipartition theorem? c what is the specific heat at constant volume? d calculate the mean square molecular diameter < 2 > . you can get this in two ways: from < r2 > = 20(f/n)/ak or from the equipartition theorem. do they agree? e calculate the pressure p =-x/ov.