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Electronic theremal conductivity

  1. Sep 30, 2009 #1
    I'm trying to get some sort of value for the electronic contribution to the thermal conductivity of copper.

    Most sources seem to give the total thermal conductivity [tex]K=400 \mathrm{W/(m\cdot K)}[/tex] at room temperature.

    The electronic contribution should be given by the Wiedemann–Franz law
    [tex]K_e=\frac{L T}{\rho}[/tex]
    where [tex]L=(\pi^2/3)(k_B^2)\approx 2.443\times10^{-8}\mathrm{W\Omega/K^2}[/tex] ([tex]k_B[/tex] in eV).

    The resistivity of copper at room temperature is [tex]\rho=16.78 \times 10^{-9} \mathrm{\Omega m}[/tex].
    Using this resistivity and the temperature [tex]T=300K[/tex] gives [tex]K_e=437\mathrm{W/(m\cdot K)}[/tex] which is larger then the total value.

    I guess this shows that a) Either I have made some stupid mistake, or b) Wiedemann–Franz is not very accurate at this temperature.

    Is there some other way to get a idea of how large the electronic conductivity is? I'm interested in temperatures ranging from 300K up to about 1400 K.
     
  2. jcsd
  3. Sep 30, 2009 #2

    Mapes

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    Weidemann-Franz is an approximate relationship, and 10% error is typical; also, there's some inevitable error in the reported thermal and electronic conductivity values (I'll bet the thermal conductivity isn't exactly 400 W m-1 K-1 :smile:). I'd buy that copper's thermal conductivity is of almost entirely electronic origin.

    See http://books.google.com/books?id=nU...ge&q=conductivity copper temperature&f=false" for a lead on copper's electrical conductivity vs. temperature.
     
    Last edited by a moderator: Apr 24, 2017
  4. Oct 2, 2009 #3

    Vanadium 50

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    Mapes is right - this isn't exact, and I would expect that your "copper" isn't pure elemental copper either.

    I'm not sure why Bob S is bringing up beryllia when the question is about copper, but the reason it has good thermal conductivity and poor electrical conductivity is because the electrons aren't transporting the heat: phonons are.
     
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