Rotational Contributions to the Heat Capacities of Normal and Equilibrium Hydrogen at Low Temperatures

Question:
At low temperatures (T<< Θ_r ) the rotational partition functions for ortho- and para-H₂ molecules are

q_r,ortho = 3e^−2Θ_r/T + 7e^−12Θ_r/T               (1)

q_r,para = 1 + 5e^−6Θ_r/T                             (2)

and for equilibrium hydrogen

q_r = 1 + 9e^−2Θ_r/T                                (3)

Calculate the rotational contributions to the heat capacities of normal hydrogen (3:1 mixture of ortho and para) and of equilibrium hydrogen in the limit of low temperatures. What is larger?

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