Q 11-12-160JEE MainJEE Main 2025 (2 Apr, Shift 1)Easy
$\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\dfrac{\gamma_A}{\gamma_B} = \left(1 + \dfrac{1}{n}\right)$, then the value of $n$ is ______.
Numerical value type. Enter your answer.
Answer: 3
$\gamma = 1 + \dfrac{2}{f}$.
Gas A: $f = 3$, $\gamma_A = \dfrac53$.
Gas B: a vibrational mode contributes 2 (kinetic and potential energy), so $f = 3 + 3 + 2 = 8$ and $\gamma_B = 1 + \dfrac28 = \dfrac54$.
$$\frac{\gamma_A}{\gamma_B} = \frac{5/3}{5/4} = \frac43 = 1 + \frac13 \Rightarrow n = 3$$
Solution by Sreeraj P, M.Sc Physics