Question

A vessel contains a mixture of 1 mole of oxygen and two moles of nitrogen at $300K$. The ratio of the rotational kinetic energy per $O_2$ molecule to that per $N_2$ molecule is

• A. 1: 1
• B. 1: 2
• C. 2: 1
• D. Depends on the moment of inertia of the two molecules.

Answer 1

The correct option is A

1: 1

Since both the gases are diatomic, each has two degree of freedom associated with rotational motion. According to the law of equipartition of energy, the rotational kinetic energy per degree of freedom is $\left(\frac{1}{2}\right)KT$. Since the temperatures of the two gases are equal, their rotational kinetic energies will be equal. Hence the correct choice is (a)