In this link the document uses $F = ma = qE$ to get drift velocity(Eq.9.6,page10), and then to resistivity(Eq.9.8,page10). But the document also said velocity due to temperature is magnitudes larger than drift velocity (Eq.9.9,page11), and then assumes it also works on thermal velocity(Eq.9.11,page12). Using mean free time derived from $F = qE$ and saying it works for thermal motion did not make sense to me but I can't find a better explanation online.
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$\begingroup$ That's a 33-page chapter. Please quote what they say and give the page number for each "said" and "assumes". $\endgroup$– Dr. NateCommented Apr 4 at 18:57
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$\begingroup$ I've made edits. Mostly on chapter 2 Drude-Lorentz theory and its thermal properties. $\endgroup$– CroCommented Apr 5 at 3:11
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The author is illustrating Drude's thinking. The author is trying to distance himself from those claims because it turns out that equation 9.12 does not match the experimental data. Note that, nowadays, we do use the Drude model, but $\tau$ is a fitted parameter. This part of the chapter is giving historical context.
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$\begingroup$ But how do you justify substituting tau in 9.8 with thermal motion? In this context thermal motion should have nothing to do with F=qE therefore substituting tau with the one from thermal motion doesnt seem to make sense. $\endgroup$– CroCommented Apr 6 at 13:03
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$\begingroup$ Moreover, consider the source of this tau is from 9.6, it expresses the particle being accelerated by the electric field with a certain amount of time ooohhh and since thermal mean travel time dominates substitute in tau ok i get it now $\endgroup$– CroCommented Apr 6 at 13:07