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Thermal properties of materials

Using the Wiedemann–Franz law κ = LσT (Lorenz number L = 2.44×10⁻⁸ W·Ω/K²), which value is closest to the estimated thermal conductivity of copper with an electrical conductivity σ = 5.9×10⁷ S/m at 300 K?

  1. AAbout 430 W/(m·K)
  2. BAbout 39 W/(m·K)
  3. CAbout 1.4 W/(m·K)
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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.

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More Thermal properties of materials questions

  1. The thermal conductivity of pure copper at room temperature is about 400 W/(m·K), but in brass with about 30% zinc in solid solution it drops to about 120 W/(m·K). What is the main reason?
  2. The lattice thermal conductivity of an insulating single crystal decreases roughly in proportion to 1/T as temperature rises, at temperatures comparable to or above the Debye temperature. What is the main reason?
  3. For silicon (density 2330 kg/m³, specific heat 700 J/(kg·K)), take the room-temperature thermal conductivity as 150 W/(m·K) and the average phonon speed as 6000 m/s. Estimating the phonon mean free path l from κ = (1/3)Cvl, which has the same form as in the kinetic theory of gases (C is the heat capacity per unit volume), which value is closest?
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  5. A metal plate and a wooden board are left long enough at the same room temperature (about 20℃). When touched by hand, the metal feels colder. What is the main reason?