Given that translational and rotational degrees of freedom typically behave classically, but vibrations behave quantum mechanically, the total (avg) energy of a diatomic is predicted to be U= (5/2)RT+, where is obtained from Eq.124.

A. Verify the first equality in R (beta(delta e)^2e^Beta(delta e)/[e^Beta(delta e)-1]^2 using the chain rule, and then verify the second equality in the same bolded equation by evaluating the derivative with respect to Beta(and then manipulating the result to show that it is equivalent to the final expression).?

B. Use Cv/R= 5/2+ (beta(delta e)^2e^beta(delta e)/[e^beta(delta e)-1]^2 to predict the molar heat capacity of Cl2 gas at 300 K, using the information provided in problem 9, above, and compare your result with the experimental molar heat capacity of cl2, cv~ 26 J/(kmol) at 300 K?