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(D) The total number of degrees of freedom $(f)$ is the sum of translational and rotational degrees of freedom: $f = 3 + 2 = 5$.The total internal ene

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$U = \frac{5}{2} RT$ and $\gamma = \frac{7}{5}$

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(D) The total number of degrees of freedom $(f)$ is the sum of translational and rotational degrees of freedom: $f = 3 + 2 = 5$.The total internal energy $(U)$ for one mole of an ideal gas is given by the formula $U = \frac{f}{2} RT$. Substituting $f = 5$,we get $U = \frac{5}{2} RT$.The adiabatic index $\gamma$ is defined as the ratio of molar heat capacities,$\gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}$.Substituting $f = 5$ into the formula for $\gamma$,we get $\gamma = 1 + \frac{2}{5} = \frac{7}{5}$.

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