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 per N$_2$ molecule is

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

Answer 1

Answer: (A)

1:01

Answer 2

Average kinetic energy per molecule per degree of freedom $=\frac{1}{2}kT$ Since, both the gases are diatomic and at same temperature (300 K), both will have the same number of rotational degree of freedom i.e. two. Therefore, both the gases will have the same average rotational kinetic energy per molecule
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, =2 \times \frac{1}{2}kT \, or \, kT$
$\Rightarrow \, \, \, \, \,$Thus, ratio will be 1: 1