Question

A vessel contains a mixture of $1$ mole of oxygen and two moles of nitrogen at $300 \,K$. The ratio of the rotational kinetic energy per $O_{2}$ molecule to that per $N_{2}$ molecule is

• A. 1:02
• B. 2:01
• C. 1:01
• D. depends on the moment of inertia of the two molecules

Answer 1

Answer: (C)

1:01

Answer 2

Both $O_{2}$ and $N_{2}$ are diatomic gases. Rotational degree of freedom in both cases is two. Therefore average rotational kinetic energy per molecule for each of them is $2\left( \frac{1}{2}KT \right)$ or the ratio is $1 : 1$.