The law that the ratio of a metal's thermal conductivity κ to its electrical conductivity σ is proportional to absolute temperature, κ = LσT, where L is the Lorenz number, about 2.44×10⁻⁸ W·Ω/K².
Japanese name: ヴィーデマン・フランツの法則
Wiedemann–Franz law appears in 3 practice questions across 2 topics, including Thermal properties of materials, Battery and energy materials.
Answer: A. About 430 W/(m·K)
κ = 2.44×10⁻⁸×5.9×10⁷×300 ≈ 432 W/(m·K), about 430 W/(m·K). This is close to the measured value of about 400 W/(m·K), showing that conduction electrons carry most of the heat in metals. Electrons carry both charge and heat, and both are hindered by the same scattering, so κ/σ is proportional to the absolute temperature, with a proportionality constant, the Lorenz number, that is nearly the same for all metals. About 39 W/(m·K) uses the Celsius temperature of 27 instead of the absolute temperature. About 1.4 W/(m·K) forgets to multiply by the temperature. When alloying lowers the electrical conductivity, the thermal conductivity falls in nearly the same proportion.
However, raising the carrier concentration increases σ but decreases S, and also increases the heat carried by electrons (the Wiedemann–Franz law), so the optimum is a nearly degenerate semiconductor with a carrier concentration of about 10¹⁹–10²⁰ cm⁻³.
Which is a correct strategy for increasing the thermoelectr…Heat in metals is carried mainly by conduction electrons, so the thermal conductivity is nearly proportional to the electrical conductivity, the two being linked by the Wiedemann–Franz law.
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