Planar Rotation of Two-Dimensional Ideal Gas of Heterodiatomic Molecules

Question:
Consider a system of N heterodiatomic molecules weakly absorbed on a surface. Assume they do not interact with each other (two-dimensional ideal gas). The energy levels for planar rotation are

where J = 0, 1, 2, …. and I is the moment of inertia for rotation of the molecule. The degeneracy of all levels is 2, except for the J = 0 level which is non-degenerate. Find expressions valid at high temperature for the contribution of planar rotation to q, F, U, S and CV .

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