Problem 6.176

Derive Eq. $(6.4 \mathrm{c}),$ making use of the Boltzmann distribution. From Eq. (6.4c) obtain the expression for molar vibration heat capacity $C_{V}$ vib of diatomic gas. Calculate $C_{V}$ vib for $\mathrm{Gl}_{2}$ gas at the temperature $300 \mathrm{~K}$. The natural vibration frequency of these molecules is equal to $1.064 \cdot 10^{14} \mathrm{~s}^{-1}$,