According to the law of equipartition of ener | vedclass

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(D) diatomic gas molecule typically has $3$ translational degrees of freedom and $2$ rotational degrees of freedom.It is given that the molecule has o

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$\frac{7}{2} R$

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(D) diatomic gas molecule typically has $3$ translational degrees of freedom and $2$ rotational degrees of freedom.It is given that the molecule has one additional vibrational mode.Each vibrational mode contributes $2$ degrees of freedom (one for kinetic energy and one for potential energy).Therefore, the total number of degrees of freedom $f = 3$ (translational) $+ 2$ (rotational) $+ 2$ (vibrational) $= 7$.The molar specific heat at constant volume is given by the formula $C_V = \frac{fR}{2}$.Substituting $f = 7$, we get $C_V = \frac{7R}{2}$.

According to the law of equipartition of energy, the molar specific heat of a diatomic gas at constant volume, where the molecule has one additional vibrational mode, is:

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