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Homework Help: Estimating the average time between collisions (electrons in Cu solid)

  1. Jul 13, 2012 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    The thermal conductivity of Cu at room temperature is 400 W/(mK). Use this value to determine the average time between collisions, [itex]\tau[/itex]. Compare this value with the electrical conductivity.


    2. Relevant equations
    Not sure. I take T=300K for room temperature.
    From a book and with little algebra, [itex]\tau = \frac{3 \kappa }{C_e \overline v ^2}[/itex]. Where [itex]C_e=nc[/itex], the specific heat of the electrons per volume unit. [itex]\overline v =<v^2> [/itex].
    Also, [itex]<v^2>=\frac{3K_BT}{m_e}[/itex] and apparently [itex]C=\frac{3}{2}n k_B [/itex](they do not state what n is, but I think it's the electronic density because they said that c is the specific heat per electron)


    3. The attempt at a solution
    Using only the given data, I do not see a clear way to solve the problem, it seems like a data is missing (for example the electron density). Am I missing a way to solve the problem?

    If I had "n", I'd be done, because [itex]\tau = \frac{2\kappa m_e }{3nk_B^2T}[/itex] and everything is known but n.
    I guess I'm missing something obvious, yet I don't see it. Thanks for any help.
     
  2. jcsd
  3. Jul 15, 2012 #2

    fluidistic

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    Well I used an extra datum, namely that the distance between atoms is worth 0.2 nm. I could calculate the electron density n to be worth [itex]1.25 \times 10 ^{29} m^{-3}[/itex], which gave me [itex]\tau \approx 3.40 \times 10 ^{-14}s[/itex].
    With the electrical conductivity the result is about [itex]\tau \approx 2 \times 10 ^{-14}s[/itex].
    So they are about the same order of magnitude but not exactly the same.
     
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