# Qha

is, the power density, is nv

The energy of each molecule is 1 kT, therefore nvdT dT ,

Here, the quantity, A, is the thermal conductivity as before.

If we assume that the electrons are the only conveyers of heat in a metal (a reasonable assumption) and that they act as a gas with each electron carrying |kT units of energy, then the heat conductivity should be

3nv'k

The factor 3 was included to account for the three degrees of freedom of electrons in a three-dimensional gas. Actually, this overestimates the thermal conductivity because we did not correctly consider the statistical number of electrons of a three-dimensional gas that cross a given surface per unit time. Although the numerical results are incorrect, the influence of the different physical parameters on the conductivity is correctly represented. Let us now examine the electric conductivity, a, a = qn(j,, (5.37)

where (, the mobility, is the velocity a carrier (a mobile charge) attains under the influence of a unit electric field; it is the ratio of the drift velocity, vd, to the electric field, E:

Under the usual assumption that collisions are isotropic, after each collision, the velocity of the electron is statistically zero (because it has equal probability of going in any direction). This being the case, the average drift velocity of an electron is 1 at, where a is the acceleration, qE/m, and t is the mean free time, '/v. Remember that v is the thermal velocity of the electron and is generally much larger than its drift velocity, vd.

The A/a ratio becomes because 