First slide

Law of equipartition of energy

Question

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

Moderate

A

1 : 1
B

1 : 2
C

2 : 1
D

Depends on the moments of inertia of the two molecules

Solution

Kinetic energy per degree of freedom = $\frac{1}{2} kT$ . As diatomic gas possess two degree of freedom for rotational motion therefore rotational K.E.= 2 $(\frac{1}{2} kT)$ = kT . ln 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.

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