If gamma is the ratio of specific heats of an | vedclass

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(A) The ratio of specific heats $\gamma$ is defined as the ratio of the molar specific heat at constant pressure $(C_p)$ to the molar specific heat at

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$\frac{2}{\gamma - 1}$

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(A) The ratio of specific heats $\gamma$ is defined as the ratio of the molar specific heat at constant pressure $(C_p)$ to the molar specific heat at constant volume $(C_v)$.For an ideal gas,$C_v = \frac{f}{2}R$ and $C_p = (\frac{f}{2} + 1)R$,where $f$ is the number of degrees of freedom.Thus,$\gamma = \frac{C_p}{C_v} = \frac{(\frac{f}{2} + 1)R}{(\frac{f}{2})R} = \frac{f + 2}{f}$.Rearranging the equation to solve for $f$:$\gamma f = f + 2$$\gamma f - f = 2$$f(\gamma - 1) = 2$$f = \frac{2}{\gamma - 1}$.

List-$I$	List-$II$
$(A)$ $3$ Translational degrees of freedom	$(I)$ Monoatomic gases
$(B)$ $3$ Translational,$2$ rotational degrees of freedom	$(III)$ Rigid diatomic gases
$(C)$ $3$ Translational,$2$ rotational and $1$ vibrational degrees of freedom	$(IV)$ Non-rigid diatomic gases
$(D)$ $3$ Translational,$3$ rotational and more than one vibrational degrees of freedom	$(II)$ Polyatomic gases

If $\gamma$ is the ratio of specific heats of an ideal gas,the number of degrees of freedom of the gas molecules is .......

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