Wiedemann–Franz law

In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (κ) to the electrical conductivity (σ) of a metal is proportional to the temperature (T).

${\displaystyle {\frac {\kappa }{\sigma }}=LT}$

Theoretically, the proportionality constant L, known as the Lorenz number, is equal to

${\displaystyle L={\frac {\kappa }{\sigma T}}={\frac {\pi ^{2}}{3}}\left({\frac {k_{\rm {B}}}{e}}\right)^{2}=2.44\times 10^{-8}\;\mathrm {V^{2}{\cdot }K} ^{-2},}$

where k_B is the Boltzmann constant and e is the elementary charge.

This empirical law is named after Gustav Wiedemann and Rudolph Franz, who in 1853 reported that κ/σ has approximately the same value for different metals at the same temperature. The proportionality of κ/σ with temperature was discovered by Ludvig Lorenz in 1872.