Law of equipartition of energy

Question

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

Moderate

Solution

Kinetic energy per degree of freedom is $\frac{1}{2}\mathrm{KT}$

As diatomic gas posses two degree of freedom for rotational motion therefore rotational kinetic energy = $2.\frac{1}{2}\mathrm{KT}=\mathrm{KT}$

In the problem both gases are diatomic and have same temperature. Therefore the average rotational kinetic energy will be equal to one.

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