# The Wiedemann FranzLorenz

In the nineteenth century, physicists had difficulties measuring the thermal conductivity of materials. Gustave Heinrich Wiedemann (1826-1899) observed in 1853 that, at least for metals, the ratio, A/a, appeared to be constant. If so, the thermal conductivity could be inferred from the easily measure electric conductivity. Eventually, a "law" was formulated in collaboration with Rudolf Franz (1827-1902) and Ludwig Valentine Lorenz (1829-1891) expressing the relationship between thermal conductivity, electric conductivity and absolute temperature. This is the Wiedemann-Franz-Lorenz law, which can be justified based on a simple classical model of electric conduction.

Consider the heat conduction in a unidimensional gas along which there is a temperature gradient (Figure 5.11). A surface, A, at the origin of coordinates is normal to the molecular motion. We assume that there is no net mass flow. Then, nivi + n2V2 = 0. (5.33)

We now use the symbol, Í, as the mean free path (not as the length of the arms, as before). The molecules that cross A coming from the left originate, on the average, from a point of coordinate -Í/2. Their kinetic energy is U(-Í/2). Those that come from the right have an energy U(Í/2). Half the molecules move to the left and half to the right. The net energy flux, that 