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Wien's Displacement Law

  1. Jan 17, 2008 #1
    1. The problem statement, all variables and given/known data

    u(f, T) = (8 pi h f^3)/(c^3 (e^(h f/ k T) - 1))
    find an equation for the frequency, fmax, at which the energy density, u, is a maximum.

    2. Relevant equations

    C,h,pi, and k are constants.

    3. The attempt at a solution

    I took the derivative and set the equation equal to 0. My problem is I end up with a non-analytical equation. Instead I end up with the transcendental equation:

    3(e^x - 1) - x e^x = 0 which I am not sure how to solve I know I must use Lambert's Product Law but I am unsure of how the W function works.

    as well x = (h f)/(k T)
    Last edited: Jan 17, 2008
  2. jcsd
  3. Jan 17, 2008 #2


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    Science Advisor
    Homework Helper

    Solve it nummerically instead, or iterate.
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