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

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

qr,ortho = 3e−2Θr/T + 7e−12Θr/T               (1)

qr,para = 1 + 5e−6Θr/T                             (2)

and for equilibrium hydrogen

qr = 1 + 9e−2Θr/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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