The translational motion of an atom, i.e. its position in the Cartesian coordinate system, is described by three coordinates: x, y and z. The translational motion of a molecule 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 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
. According to the equipartition theorem, each velocity energy component of the molecule has an average energy of
.