Consider a classical system of N noninteracting diatomic molecules enclosed in a box of volume V at temperature T. The Hamiltonian for a single molecule is taken to be 1 H (P₁, P₂,11,12) = (p₁ + p) + {Kr - 1212 = > 2m. Where P₁, P₂, 81, F₂, are the momenta and coordinates of the two atoms in a molecule. Find:
(A) the Helmholtz free energy of the system;
(B) the specific heat at constant volume; and
(C) the mean square molecule diameter (r₁ - 1212). 7.3 Repeat the last problem, using the Hamiltonian 1 H(P₁, P₂, 11,r₂) 2m(p} + på) + el'12 – rol - where e and ſo are given positive constants and r₁₂ = 1rı - 12l.