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) $4$
Concept. $\gamma = 1 + \dfrac{2}{F}$; each vibrational mode adds 2 degrees of freedom (kinetic and potential).
Step 1. Total degrees of freedom. $\dfrac{2}{F} = \dfrac87 - 1 = \dfrac17 \Rightarrow F = 14$.
Step 2. Vibrational modes. $6 + 2f = 14 \Rightarrow f = 4$.
Answer. $4$ (Option A).
Solution by Sreeraj P, M.Sc Physics