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