# Electronic theremal conductivity

1. Sep 30, 2009

### pafcu

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 $$K=400 \mathrm{W/(m\cdot K)}$$ at room temperature.

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

The resistivity of copper at room temperature is $$\rho=16.78 \times 10^{-9} \mathrm{\Omega m}$$.
Using this resistivity and the temperature $$T=300K$$ gives $$K_e=437\mathrm{W/(m\cdot K)}$$ 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. Sep 30, 2009

### Mapes

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 ). 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
3. Oct 2, 2009

### Vanadium 50

Staff Emeritus
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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