We imagine that an electron at position has been scattered last at a distance given by the mean free path , and we make the simplifying assumption that in this event the electron has assumed a velocity of absolute magnitude given by the mean value which corresponds to the local temperature . It follows that an electron at with direction of flight has a velocity given by (Fig. 9). Averaging over the direction , one obtains for the mean electronic velocity

Expanding

and

one arrives at

According to this result the different speeds, corresponding to different kinetic energies, of electrons arrived from different directions lead to a mean velocity in a direction opposite to the temperature gradient. This is the phenomenon of thermodiffusion! With (22) one obtains the corresponding current density as

Introducing an off-diagonal transport coefficient this result can be written as

Comparison of (24) with (22) and (23) yields for