The Wiedemann–Franz law is a principle in solid-state physics and materials science that relates the electrical conductivity of a metal to its thermal conductivity. It states that the ratio of the thermal conductivity (\(K\)) to the electrical conductivity (\(\sigma\)) of a metal is proportional to the temperature (\(T\)).
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The Wiedemann-Franz law relates the electronic thermal conductivity of a normal degenerate metal to its electrical conductivity:An isotropic kinetic theory estimate gives . With electronic heat capacity density , and , the ratio is . Approximately elastic scattering with a smooth energy dependence gives equal heat and charge relaxation times. Inelastic electron-phonon scattering can make them different; the law also concerns the electronic contribution, not additional lattice heat conduction.[ref]
https://arxiv.org/abs/1810.05646. Abstract: acoustic-phonon violations at finite temperature and restoration when impurity scattering dominates