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 \(1.064 \cdot 10^{14} \mathrm{~s}^{-1}\),