1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Tricky Derivation of Blackbody Equations.

  1. Apr 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Starting with the Planck distribution:

    [tex] R(\lambda,T) = \frac{c}{4} \frac{8 \pi}{\lambda^4} (\frac{hc}{\lambda})(\frac{1}{e^{hc/(\lambda kT)}-1})[/tex]

    Derive the blackbody Stefan-Boltzmann law (ie total flux is proportional to T4) by integrating the above expression over all wavelengths. Thus show that

    R(T) = [tex] \frac{2 \pi^5 k^4}{15h^3 c^2} T^4 [/tex]

    and [tex]\int[/tex] [tex] \frac{x^3}{e^x -1} dx = \frac{\pi^4}{15}[/tex]

    3. The attempt at a solution

    I know I need to substitute [tex]x = \frac{hc}{kT} \frac{1}{\lambda}[/tex]. And somehow I think I can use the form KR([tex]\lambda[/tex],T) = A([tex]\lambda[/tex])B([tex]\lambda[/tex])
  2. jcsd
  3. Apr 28, 2010 #2
    Just use that substitution and try to get it into the form of the integral provided.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook