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Law of equipartition of energy

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 O2  molecule to that per N2  molecule is


Kinetic energy per degree of freedom is  12KT
As diatomic gas posses two degree of freedom for rotational motion therefore rotational kinetic energy =  2.12KT=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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