Question

A vessel contains a mixture of 1 mole of oxygen and 2 moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O2 molecule to that per N2 molecule is?

(a) 1:1

(b) 1: 2

(c) 2:1

(d) Depends on the moment of inertia of the two molecules

The question was asked by my college professor while I was bunking the class.

My doubt stems from Ideal Gases in section Kinetic Theory of Gases of Engineering Physics I

Answer 1

The correct answer is (d) Depends on the moment of inertia of the two molecules

The explanation is: Both gases are diatomic. Both have two rotational degrees of freedom at 300K. Average rotational kinetic energy per molecule of each gas will be same=2×1/2 kT=1kT

Hence the required ratio is 1:1.