# Is my method of calculating thermal conductivity of a metal wrong?

I am trying to determine the thermal conductivity of pure copper at various temperatures using the Weidemann-Franz Law but for some reason it is not matching up to textbook data. I used the Bloch formula to determine electrical resistivity and this formula is $$r_{e}=4r_{0}(\frac{T}{\Theta})^{5}\int_0^\frac{\Theta}{T} \! \frac{e^{x}x^{5}}{(e^{x}-1)^{2}} \, \mathrm{d}x$$ I have a table that gives the electrical resistivity at 295 K and I used the value to determine $r_{0}$ for when I go to calculate the electrical resistivities at other temperatures. I then find the electrical conductivity using $$\sigma=\frac{1}{r_{e}}$$ and I use Weidemann-Franz law to find thermal conductivity. This equation is $$k=\sigma T (Lz)$$ where $Lz$ is $2.44x10^{-8} \frac{W \Omega}{K^{2}}$

Now when I calculate the thermal conductivity at 200 K, 400 K, 600 K, and 800 K, to be 465, 414, 405 and 402. The textbook values at these temperatures are 413, 393, 379, 366.

It seems that if I keep increasing the temperature, the difference between my values at each temperature decreases but the difference between the textbook value at each temperature is a constant value of approximately 14. I can't seem to figure out whats wrong. Any help would be appreciated.

• Since this is homework, let me give you some food for thought. I would ask myself how good should the Bloch formula be? What assumptions were made to derive it, and how well does copper meet those assumptions? Can I determine if the Bloch formula should overestimate the real value or underestimate it? – garyp Apr 8 '14 at 3:54
• You're using the wrong value of $L$, it should be $2.23×10^{−8}$ W$Ω$$K^{−2}$ according to en.wikipedia.org/wiki/Wiedemann%E2%80%93Franz_law – DumpsterDoofus Apr 8 '14 at 12:36