Equipartition theorem: Translational motion

The translational motion of an atom, i.e. its location in the Cartesian system, is described by three coordinates: x, y and z. The translational motion of a molecule that is composed of multiple atoms is similarly described by only three coordinates, which indicate the centre of mass of the molecule. The energy associated with this motion is kinetic energy:

where is the velocity vector of the molecule with .

So, the translational motion of a molecule has three degrees of freedom with the associated energies components of:

For a system of particles, the average translational energy of a particle is:

where  is the square of the root mean square speed of the gas in the -direction.

We have shown in the article on kinetic theory of gases that . Hence, the average translational energy of a molecule is and according to the equipartition theorem, each velocity energy component of the molecule has an average energy of .


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