Heat Capacity of Argon and Diatomic Molecules

The figure shows the experimental heat capacities of argon and two diatomic molecules (H2 and F2) as a function of temperature. The horizontal dashed lines indicate the predicted heat capacity of a classical molecule with only translation (bottom), or only translation and rotation (middle), or translation, rotation and vibration (top) degrees of freedom.

Argon behaves perfectly classically over the entire temperature range, while the heat capacities of H2 and F2 deviate from the classical prediction at low temperatures. This is because the rotational quantum states of H2 and F2 are sufficiently large that they only become active at temperatures well above 100 K.

Questions

• Why does argon behave perfectly classically over the entire temperature range?
• Why do the heat capacities of H2 and F2 deviate from the classical prediction at low temperatures?
• What is the reason for the unusually high rotational frequency of H2?

Answers

• Argon behaves perfectly classically over the entire temperature range because the quantum spacing between translational states of argon is small compared to kBT, even at temperatures below 100 K.
• The heat capacities of H2 and F2 deviate from the classical prediction at low temperatures because the rotational quantum states of H2 and F2 are sufficiently large that they only become active at temperatures well above 100 K.
• The reason for the unusually high rotational frequency of H2 is that it has a very light nucleus. This makes it easier for the molecule to rotate, and hence leads to a higher rotational frequency.