The heat capacity of a diatomic gas is in the limit of low temperatures. As the temperature is increased, rotational modes eventually become active and add to the heat capacity, making the total heat capacity equal to . 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 to the heat capacity, making the total heat capacity equal to . So the ratio of the heat capacity at very high temperatures to the heat capacity at very low temperatures is:
Thus, answer (D) is correct.