Free electron model: Difference between revisions

Revision as of 13:08, 11 May 2023

Revision as of 07:07, 16 May 2023

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While Drude's model predicts a similar value for the electric conductivity as the free electron model, the models predict slightly different thermal conductivities.

The thermal conductivity is given by <math>\kappa=c_V \tau\langle v\rangle^2\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^2\rangle^{1/2} </math> is the mean (square) speed of the electrons 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 \langle v^2 \rangle^2 }{3n e^2} = L T</math>

where <math>L </math> is the Lorenz number, given by