Question

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300\text{K}$. The ratio of the average rotational kinetic energy of $O_2$ molecules to that of $N_2$ molecules per degree of freedom is

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. Depends on moment of inertia.

Answer 1

The correct option is A $1:1$

According to law of equipartition of energy,
Energy associated with each molecule for each degree of freedom $E=\frac{1}{2}KT$

Both $N_2$ and $O_2$ are diatomic gas
$\therefore$Rotational degree of freedom $\left(f_r\right)$$=2$ for both $N_2$ and $O_2$
$\therefore$ Average rotational kinetic energy per molecule, $f_r=\frac{1}{2}KT$
(Average rotational kinetic energy per molecule depends upon degree of freedom and temperature. It does not depends on mole.)

$\therefore$ Average rotational kinetic energy associated of $O_2$ molecule per degree of freedom = Average rotational kinetic energy associated of $N_2$ molecule per degree of freedom