Kinetic Theory of Gases
8.0 Degrees of Freedom
8.0 Degrees of Freedom
The number of possible independent ways in which a system can have energy is called degree of freedom for the system. The independent ways are independent motions which can be translational, rotational or vibrational or any combination of these. Given below are the degrees of freedom of different gases.
- For monoatomic gas molecules, the degrees of freedom are three in number and all are translational, their moment of inertia is negligible, hence they do not possess rotational degree of freedom.
- For diatomic gas molecules, the total number of degree of freedom is five($5$), out of which $3$ is translational and $2$ is rotational. The moment of inertia about the axis joining the two atoms is negligible compared to that about the other two axes, same is for linear polyatomic molecules.
- For non-linear polyatomic molecule, the degree of freedom are six in number: $3$ translational and $3$ rotational.
- In case of diatomic or polyatomic gas molecules, the atoms within the molecule may also vibrate with respect to each other. Thus molecules have two additional degree of freedom for vibration. One for $PE$ and one for $KE$ of vibration.
| Atomicity of Gas | Translational | Rotational | Vibrational | Total | ||
Monoatomic $He$, $Ar$, $Ne$, etc. | $3$ | $0$ | $0$ | $3$ |   | |
Diatomic $H_2$, $Cl_2$, $O_2$, $N_2$ etc. | $3$ | $2$ | $0$ | $5$ |   | |
Triatomic or Polyatomic | Triatomic (linear) $CO_2$, ${C_2}{H_2}$ | $3$ | $2$ | $0$ | $5$ | |
Triangular (non-linear) ${H_2}O$, $N{H_3}$, $C$$H_4$ | $3$ | $3$ | $0$ | $5$ |   | |
