is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If , then the value of n is ________

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Solution

Q.
$γ_{A}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $γ_{B}$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{γ_{A}}{γ_{B}} = (1 + \frac{1}{n})$ , then the value of n is ________. [2025]

Ans.
(3)

$γ = 1 + \frac{2}{f}$

$f_{A} = 3 \Rightarrow γ_{A} = \frac{5}{3}$

$f_{B} = 3 + 3 + 2 = 8, γ_{B} = 1 + \frac{2}{8} = \frac{5}{4}$

$\frac{γ_{A}}{γ_{B}} = \frac{4}{3} = 1 + \frac{1}{3} \Rightarrow n = 3$

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