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The exact expressions for the transport coefficients of a metal are used to show that the Wiedemann-Franz law is valid provided that (a) the electrons do not interact with each other and form a degenerate Fermi-Dirac assembly, (b) the scattering of the electrons is due to impurities or lattice vibrations and is elastic. The derivation is valid no matter how strong the scattering and it is therefore more general than the usual weak-coupling derivation of the Wiedemann-Franz law.
Chester et al. (1961) studied this question.
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