For a diatomic gas,let gamma_1 = frac{C_p}{C_ | vedclass

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(D) The adiabatic index is given by the formula $\gamma = 1 + \frac{2}{f}$,where $f$ is the number of degrees of freedom.For a rigid diatomic molecule

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$\gamma_2 < \gamma_1$

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(D) The adiabatic index is given by the formula $\gamma = 1 + \frac{2}{f}$,where $f$ is the number of degrees of freedom.For a rigid diatomic molecule,the degrees of freedom $f_1 = 5$ ($3$ translational + $2$ rotational).Thus,$\gamma_1 = 1 + \frac{2}{5} = 1 + 0.4 = 1.4$.For a diatomic molecule with a vibrational mode,the degrees of freedom $f_2 = 7$ ($3$ translational + $2$ rotational + $2$ vibrational).Thus,$\gamma_2 = 1 + \frac{2}{7} \approx 1 + 0.286 = 1.286$.Comparing the two values,$\gamma_2 < \gamma_1$.

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