Wiedemann-Franz law
/ VEE-deh-mahn FRANTS /
Metals are good at carrying both electricity and heat — and it's no coincidence. The Wiedemann-Franz law says these two talents are tied together: divide a metal's heat conductivity by its electrical conductivity, then by temperature, and you get nearly the same number for almost every metal, from gold to lead.
The reason is that in a metal the same free electrons do both jobs. They ferry electric charge when you apply a voltage, and they ferry heat when one end is hotter. Since one set of carriers handles both, the two conductivities march in lockstep, and the ratio between them turns out to be a near-universal constant fixed only by fundamental constants of nature.
It matters as a clean test of the free-electron picture, and the model nails it — predicting the universal ratio almost exactly. The honest caveat: the agreement holds best at high and very low temperatures. In between, electrons can lose heat and charge by different mechanisms, the law sags below its ideal value, and the simple picture starts to fray.
Measure heat and electrical conductivity for copper, silver, gold and aluminium at room temperature and divide them as the law prescribes: all four spit out almost the same number, within a few percent — a striking sign that one kind of carrier is doing both jobs.
Different metals give nearly the same heat-to-charge conductivity ratio — one carrier, two jobs.
Drude's classical version stumbled onto the right answer by luck — two errors cancelled. Sommerfeld's quantum version arrives at the same value honestly, which is why the law is counted as a quantum success, not a classical one.