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  4. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K . The ratio of the average rotational kinetic energy per O 2 molecule to that per N 2 molecule is

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Q. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300\, K .$ The ratio of the average rotational kinetic energy per $O _{2}$ molecule to that per $N _{2}$ molecule is

Solution:

Kinetic energy per degree of freedom $=\frac{1}{2} k T$ . As diatomic gas possess two degree of freedom for rotational motion therefore rotational K.E. $=2\left(\frac{1}{2} k T\right)=k T .$ In the problem both gases (oxygen and nitrogen) are diatomic and have same temperature (300 K) therefore ratio of average rotational kinetic energy will be equal to one.