3/9/11

The Drude model fails to describe the dependence of the temperature to the magnetic susceptibility, specific heat and the value of Lorenz number. However, the Drude model give the universal value of Lorenz number but there is a difference by a factor of 2. These issues can be solved by the Sommerfeld model.
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4 comments:

  1. Robert Lewis-SwanMarch 10, 2011 at 8:49 AM

    I found the differences between it and the Sommerfield model to be quite interesting, particularly due to the completely different fundamental derivation - stemming completely from statistical mechanics. Its interesting that coming from completely different directions there is a certain amount of qualitative overlap in the predictions, yet even being so different, they both fall down in similar areas.

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  2. ThurayaMarch 10, 2011 at 1:52 PM

    I want to know if sommerfeld model depends just on room temperature? and can it deal with more than room temperture or not?

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  3. AnonymousMarch 10, 2011 at 3:06 PM

    Drude model suggests higher the valency higher the conductivity but the best metals have one or two valence electrons. Also the Hall effect allows to determine the sign of the charge carriers. But in contrast to the assumptions of the Drude theory some metals (e. g. Be, Mg, In, Al) show a Hall current indicating positive charge. The specific heat (Cv) is achieved only asymptotically at high temperatures. At low temperatures it generically shows a T3-proportional part which is present in semi-conductors and insulators, too. The only part remaining for a possible electronic contribution is T-proportional, at room temperature about 100 times smaller than (Cv =3/2 Kb). Therefore some other factor in k/σ=3/2 (k/e)^2 T should be wrong by a factor of about 100.

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  4. strailMarch 10, 2011 at 6:57 PM

    The Sommerfeld model derivation of the Lorentz number used the same thermal conductivity as the Drude model: kappa = (1/3)v^2.tau.c_v, but used v_f^2 which was larger than the classical thermal value (v_f^2 = 2E_f/m) and the specific heat c_v that was smaller (by ~ k_b.T/E_f), which gave kappa/sigma.T = 2.44x10^(-8) W.Ohm/K^2, which is around twice the Drude prediction.

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