Wiedemann–Franz law

For the electronic part of a metal's thermal conductivity, the Wiedemann–Franz relation is commonly written κₑ/σ = LT, where κₑ is electronic thermal conductivity, σ is electrical conductivity, T is absolute temperature, and L is the Lorenz number. Equivalently, κₑ/(σT) is approximately constant under the relevant conditions. The law concerns electronic heat transport, not necessarily the total thermal conductivity: in many solids, lattice vibrations also carry heat.

In a metal, mobile electrons respond to an electric field and contribute to electrical conduction; they also carry energy as they move through a temperature gradient. Because both transport processes depend on electron motion and scattering, a connection between electrical and thermal conductivity can arise. A classical kinetic picture gives qualitative intuition, while a quantum treatment of the electron gas yields the Lorenz number used in the low-temperature metallic limit.

The relation is not exact for every material or experimental regime. A derivation based on degenerate Fermi–Dirac electrons and elastic scattering by impurities or lattice vibrations supports the law under those assumptions. Inelastic processes, electron interactions, additional heat carriers, and unusual material states can change the ratio. Measurements and applications therefore distinguish the electronic thermal conductivity from phonon or other contributions and specify the temperature and scattering regime.

The law provides a useful way to compare heat and charge transport in metals and to test whether conduction is consistent with the expected role of electrons. It helps researchers estimate an electronic contribution to thermal transport from electrical measurements when the assumptions are suitable. Deviations are not simply measurement errors: they can signal that the underlying assumptions, scattering processes, or additional carriers matter.