the Wiedemann-Franz law
/ VEE-deh-mahn FRANTS /
There is a beautiful shortcut hidden in metals: divide a metal's thermal conductivity by its electrical conductivity and — at a given temperature — you get almost the same number for copper, silver, gold, iron, and lead. The Wiedemann-Franz law says a good electrical conductor is a good heat conductor in a fixed, predictable ratio, because the same electrons do both jobs.
The law is k / (sigma x T) = L, where k is thermal conductivity, sigma is electrical conductivity, T is absolute temperature, and L is the Lorenz number — a near-universal constant, L about 2.44 x 10^-8 W-ohm/K^2. Rearranged, k = L x sigma x T. So if you measure a metal's electrical conductivity you can estimate its thermal conductivity without a separate heat experiment. It works because both transport channels ride on the free-electron sea, and the constant L emerges from fundamental constants (the electron charge and Boltzmann's constant).
Be honest about the limits: the law holds well for pure metals near and above room temperature, where electron scattering is elastic. It breaks down at intermediate low temperatures (where scattering changes character) and it ignores the phonon contribution to k — which is why it fails badly for semiconductors and insulators, where phonons, not electrons, carry most of the heat. Use it as an excellent rule of thumb for metals, not as a universal law of nature.
Estimate copper's thermal conductivity from its electrical conductivity (about 5.9 x 10^7 per ohm-meter) at 300 K: k = L x sigma x T = 2.44e-8 x 5.9e7 x 300, which is about 432 W/m-K — close to the measured 400.
One measured constant links two properties for metals — but only because electrons carry both.
The law fails for semiconductors and insulators because there phonons, not electrons, carry most of the heat — so a low electrical conductivity does not imply a proportionally low thermal conductivity (again, diamond).