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(D) The total internal energy $U$ of $\mu$ moles of an ideal gas is given by $U = \frac{f}{2} \mu RT$,where $f$ is the degree of freedom,$\mu$ is the

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$5 : 6$

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(D) The total internal energy $U$ of $\mu$ moles of an ideal gas is given by $U = \frac{f}{2} \mu RT$,where $f$ is the degree of freedom,$\mu$ is the number of moles,$R$ is the universal gas constant,and $T$ is the absolute temperature.For $O_2$ (a diatomic gas),the degree of freedom $f_1 = 5$ and $\mu_1 = 1$.So,$U_{O_2} = \frac{5}{2} (1) RT = 2.5 RT$.For $He$ (a monoatomic gas),the degree of freedom $f_2 = 3$ and $\mu_2 = 2$.So,$U_{He} = \frac{3}{2} (2) RT = 3 RT$.The ratio is $\frac{U_{O_2}}{U_{He}} = \frac{2.5 RT}{3 RT} = \frac{2.5}{3} = \frac{5}{6}$.

The ratio of total energy of all molecules of one mole of $O_2$ to the total energy of all molecules of two moles of $He$ at the same temperature is

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