Energy Partition In Diatomic Gas

A rigid diatomic molecule has five active degrees of freedom: three translational and two rotational. By the law of equipartition, each degree of freedom stores the same average energy $\frac{1}{2}{k}_{B}T$, so the total internal energy divides equally among the five modes. The translational share comes from three of these five, giving a fraction $\frac{3}{5}=0.6$. Equivalently, translational energy is $\frac{3}{2}{k}_{B}T$ out of a total $\frac{5}{2}{k}_{B}T$ per molecule. This partition is independent of temperature, because raising the temperature scales the energy in every mode by the same amount and leaves the ratios unchanged. The value 0.4 mistakenly assigns the larger share to rotation, reversing the count. The value 1.0 ignores rotational energy entirely, as if the gas were monatomic. The value 0.33 wrongly divides three translational modes by an assumed nine total degrees of freedom. This is a direct consequence of the NCERT equipartition theorem applied to molecular structure, and notably only the translational part contributes to pressure and temperature. As a plausibility check, the rotational fraction must be the complement $2/5=0.4$, and the two fractions sum to unity, confirming that translational motion accounts for exactly 60 % of the internal energy of a rigid diatomic gas.