γA is the specific heat ratio of monoatomic gas A having 3… | JEE Main 2025 (2 Apr, Shift 1)

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Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

$\gamma_A$ 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 $\frac{\gamma_A}{\gamma_B} = \left(1 + \frac{1}{n}\right)$ , then the value of $n$ is ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Gas A (monoatomic): $\gamma_A = \dfrac{5}{3}$ .
Gas B: $C_V = 3R + R = 4R$ , $C_P = 5R$ , $\gamma_B = \dfrac{5}{4}$ .
$\dfrac{\gamma_A}{\gamma_B} = \dfrac{5}{3}\times\dfrac{4}{5} = \dfrac{4}{3} = 1 + \dfrac{1}{3}$
So $n = 3$ .

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