Consider a heteronuclear diatomic molecule with moment of inertia I. In this problem, only the rotational motion of the molecule should be considered. a) Using classical statistical mechanics, calculate the specific heat C_v (T) of this system at temperature T. b) In quantum mechanics, this system has energy levels E_j = h^2/2I j(j + 1), j = 0, 2, 3, ... Each level j is (2j + 1)-fold degenerate. Derive expressions for the partition function z and the average energy U of this system. c) By simplifying your expressions in (b), derive an expression for the specific heat C_v(T) that is valid at very low temperatures. In what range of temperatures is your expression valid? d) By simplifying your answer to (b), derive a high temperature approximation to the specific heat C_V (T). What is the range of validity of your approximation?