Q 11-12-002NEETNEET 2026Top questionMedium
An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_P/C_V$ of the gas is $8/7$, then the value of $f$ is :
Answer: (A) $4$
Each vibrational mode contributes 2 degrees of freedom (kinetic and potential energy). The total number of degrees of freedom is
$$F = 3 + 3 + 2f$$
$$\gamma = 1 + \frac{2}{F} = \frac{8}{7} \;\Rightarrow\; \frac{2}{F} = \frac{1}{7} \;\Rightarrow\; F = 14$$
$$6 + 2f = 14 \;\Rightarrow\; f = 4$$
Solution by Sreeraj P, M.Sc Physics