First slide

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 $O_{2}$ molecule to that per $N_{2}$ molecule is

Moderate

A

1 : 1
B

1 : 2
C

2 : 1
D

depends on the moment of inertia of the two molecules

Solution

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