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→Additional predictions: thermal conductivity |
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The thermal conductivity is given by <math>\kappa=c_V \ell \langle v\rangle/3 </math> for free particles, which is proportional to the heat capacity and the mean free path which depend on the model (<math>\langle v\rangle </math> is the mean speed or the Fermi speed in the case of the free electron model). This implies that the ratio between thermal and electric conductivity is given by the [[Wiedemann–Franz law]],
:<math>\frac \kappa \sigma = \frac{m_{\rm e}c_V \ell \langle v \rangle }{3n e^2\tau} = L T</math>
where <math>L </math> is the Lorenz number, given by
:<math>L=\left\{\begin{matrix}\displaystyle \frac{8}{\pi}\left(\frac{k_{\rm B}}{e}\right)^2\;, & \text{Drude}\\
\displaystyle\frac{\pi^2}{3}\left(\frac{k_{\rm B}}{e}\right)^2\;,&\text{free electron model.}
\end{matrix}\right.</math>
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