The Heat Capacity of a Diatomic Gas at High Temperatures

Abstract

while the \(\frac{7}{2}\) plateau is a key theoretical prediction of the equipartition theorem, real-world experiments cannot provide an unambiguous observation on this plateau. This discrepancy underscores the necessity of classical statistical mechanics in explaining thermal behavior. In this paper, we model the diatomic molecule as a stretchable dumbbell, and calculate the partition function and thermodynamic quantities of this model. Our calculation shows that the rotational modes and the vibrational mode cannot be decoupled completely and the equipartition theorem becomes not applicable anymore. For a diatomic molecule with a harmonic interaction between the two atoms, our calculation shows that the heat capacity should reach a \(\frac{9}{2}\) plateau instead of the \(\frac{7}{2}\) plateau. The height of the plateau can be shifted by the anharmonicity in the potential. Moreover, simulations are performed on our diatomic model by using the Monte Carlo Metropolis algorithm. The Monte Carlo simulations reveal that replacing the interatomic potential with the more realistic Morse potential leads to a heat capacity plateau value higher than \(\frac{9}{2}\), with the plateau increasing as the dissociation energy of the diatomic molecule decreases.