Q.For nitrogen gas (treated as a rigid diatomic molecule), find $C_v$, $C_p$, and $\gamma = C_p/C_v$ using the law of equipartition of energy.

Applying the law of equipartition of energy to a gas's degrees of freedom $f$ gives $C_v = \tfrac{f}{2}R$ (all heat at constant volume goes into internal energy) and, via Mayer's relation $C_p = C_v + R$ (extra heat needed at constant pressure to also do expansion work), $C_p = \tfrac{f+2}{2}R$. The ratio $\gamma = C_p/C_v = (f+2)/f$ therefore depends only on a molecule's structure: $\gamma = 5/3 \approx 1.67$ for monatomic gases ($f=3$), $7/5=1.4$ f …