According to the law of equipartition of energy, the total number of degrees of freedom of a polyato

Question

According to the law of equipartition of energy, the total number of degrees of freedom of a polyatomic gas of constant $\gamma=\frac{C_P}{C_V}$ (where $C_P$ and $C_V$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively) is

Professor PC Thomas Classes · Answer

(a) : Let $f$ be the total degrees of freedom of the polyatomic gas. We know that molar specific heat at constant volume is $C_V = \frac{f}{2}R$. Also, $C_P = C_V + R = (\frac{f}{2} + 1)R$. Therefore, $\gamma = \frac{C_P}{C_V} = \frac{\frac{f}{2} + 1}{\frac{f}{2}} = 1 + \frac{2}{f}$. Rearranging this gives $\gamma - 1 = \frac{2}{f}$, which implies $f = \frac{2}{\gamma - 1}$.