The heat capacity of a diatomic gas is $3/2 N k$ in the limit of low temperatures. As the temperature is increased, rotational modes eventually become active and add $N k T$ to the heat capacity, making the total heat capacity equal to $5/2 N k$ . This occurs at a temperature well below room temperature. As the temperature increases well above room temperature, vibrational modes also become active and also add $N k T$ to the heat capacity, making the total heat capacity equal to $7/2 N k$ . So the ratio of the heat capacity at very high temperatures to the heat capacity at very low temperatures is:

$\begin{align*}\frac{7/2 N k}{3/2 N k} = \boxed{\frac{7}{3}}\end{align*}$
Thus, answer (D) is correct.

Solution to 1996 Problem 79