A container holds 1 , text{mole} of oxygen an | vedclass

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$(A)$ According to the equipartition theorem, the average kinetic energy associated with each degree of freedom per molecule is $\frac{1}{2} kT$.Both

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$1 : 1$

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$(A)$ According to the equipartition theorem, the average kinetic energy associated with each degree of freedom per molecule is $\frac{1}{2} kT$.Both oxygen $(O_2)$ and nitrogen $(N_2)$ are diatomic molecules.For a diatomic molecule, there are $2$ rotational degrees of freedom.Therefore, the average rotational kinetic energy per molecule for both gases is $2 	imes \frac{1}{2} kT = kT$.Since the temperature $T$ is the same for both gases, the average rotational kinetic energy per molecule is identical for both $O_2$ and $N_2$.The ratio of the average rotational kinetic energy of $O_2$ to $N_2$ is $1 : 1$.

$A$ container holds $1 \, \text{mole}$ of oxygen and $2 \, \text{moles}$ of nitrogen at a temperature of $300 \, K$. What is the ratio of the average rotational kinetic energy of $O_2$ to that of $N_2$?

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