Free electron model: Difference between revisions

Revision as of 19:47, 16 January 2024

Revision as of 22:07, 16 January 2024

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\end{matrix}\right.</math>

The free electron model is closer to the measured value of <math>L=2.44\times10^{-818} </math> V²/K² while the Drude prediction is off by about half the value, which is not a large difference. The close prediction to the Lorenz number in the Drude model was a result of the classical kinetic energy of electron being about 100 smaller than the quantum version, compensating the large value of the classical heat capacity.

However, Drude's mode predicts the wrong order of magnitude for the [[Seebeck coefficient]] (thermopower), which relates the generation of a potential difference by applying a temperature gradient across a sample <math>\nabla V =S \nabla T</math>. This coefficient can be showed to be <math>S=-{c_{\rm V}}/{|ne|}</math>, which is just proportional to the heat capacity, so the Drude model predicts a constant that is hundred times larger than the value of the free electron model. While the latter get as coefficient that is linear in temperature and provides much more accurate values in the order of a few tens of µV/K at room temperature.