# Molecules of an ideal gas are known to have 3 translatinal D.O.F and two rotational D.O.F. The gas is maintained at temperature T. The total internal energy, U of a mole of this gas and the value of  $\gamma \left ( =\frac{cp}{cv} \right )$ are given respectively, by: Option: 1 and  Option: 2 and  Option: 3   and Option: 4 and

For 1 mole  $U=\frac{fRT}{2}$  and  $\gamma =\frac{C_p}{C_v}=\frac{f+2}{f}$

So if $U=5RT$ then we get $f= 10$ (which is not possible)

and  $U=\frac{5}{2}RT$ then we get $f= 5$ and  $\gamma =\frac{C_p}{C_v}=\frac{f+2}{f}=\frac{7}{5}$

So option C is correct

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