JEE Main 2023 — Kinetic Theory of Gases Question with Solution

The formula for degree of freedom is given by 

$f=3N-k$

where $N$ is the number of particles, $k$ is the individual relationship in the system.

For a monoatomic gas particle, $N=1, k=0$. So, $f=3$

Hence, monoatomic gas has $3$ translational degree of freedom.

For a rigid diatomic gas molecule, there are $5$ degrees of freedom, $3$ translational and $2$ rotational. A diatomic gas can have two extra degrees of freedom due to rotation along two independent axes.

A non rigid diatomic molecule has one extra degree of freedom than a rigid one. This is the vibrational degree of freedom. Hence, it has $6$ degrees of freedom.

So, a non rigid diatomic gas has $3$ translational, $2$ rotational and $1$ vibrational degrees of freedom.

A polyatomic gas has more than two atoms per molecule. Hence, the total number of degrees of freedom is $3$ translational, $3$ rotational and more than one vibrational degree of freedom.