An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and f number of vibrational modes. If…

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $\displaystyle f$ number of vibrational modes. If the ratio of heat capacities $\displaystyle \mathrm{C}_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}$ of the gas is $\displaystyle 8 / 7$, then the value of $\displaystyle f$ is :