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(B) For a non-linear polyatomic gas,the degrees of freedom $(f)$ are calculated as follows:Translational degrees of freedom = $3$Rotational degrees of

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$1.2$

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(B) For a non-linear polyatomic gas,the degrees of freedom $(f)$ are calculated as follows:Translational degrees of freedom = $3$Rotational degrees of freedom = $3$Vibrational degrees of freedom = $2 	imes 2 = 4$ (since each vibrational mode contributes $2$ degrees of freedom).Total degrees of freedom $f = 3 + 3 + 4 = 10$.The ratio of molar specific heats $\beta$ (often denoted as $\gamma$) is given by the formula $\beta = 1 + \frac{2}{f}$.Substituting the value of $f$:$\beta = 1 + \frac{2}{10} = 1 + 0.2 = 1.2$.

If one mole of a polyatomic gas has two vibrational modes and $\beta$ is the ratio of molar specific heats for the polyatomic gas $\left(\beta=\frac{C_{P}}{C_{V}}\right)$,then the value of $\beta$ is:

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