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Black body radiation, Plancks' Law question?

  1. Feb 16, 2014 #1
    1. The problem statement, all variables and given/known data

    A cylinder of length 0.02m emits 100W and is at 2000K. It is a perfect black body. What is it's diameter?


    2. Relevant equations

    Planck's Law:

    B(λ,T) =

    http://en.wikipedia.org/wiki/Planck's_law

    solid radian = A/r^2 (not sure if needed or not)


    3. The attempt at a solution


    surface area = 0.02 x 2 pi r + 2 pi r^2

    solid radians of the cylinder = (pi r^2) / (r^2 + 0.01^2)

    r is radius of the cylinder

    frequency of peak radiation = 2.07 x 10^14

    (I used Wien's displacement law to get the peak frequency)

    B x surface area x solid radians x frequency = 100W

    (I'm using dimensional analysis here, not really sure what's going on)

    100 = 9.104 x 10^-10 x (0.04 pi r + 2 pi r^2) x (pi r^2)/(r^2 x 10^-6) x 2.07 x 10^14

    which rearranges to...

    5.303 x 10^-14 (r^2 + 1x10^-6) = 0.04 (pi)^2 r^3 + 2 (pi)^2 r^4

    I cant solve for r :(

    any help or explanation is much appreciated
     
  2. jcsd
  3. Feb 16, 2014 #2

    dextercioby

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    Homework Helper

    Don't you have to use the Stefan-Boltzmann law ??
     
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