Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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) =


    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


    User Avatar
    Science Advisor
    Homework Helper

    Don't you have to use the Stefan-Boltzmann law ??
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?