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Homework Help: Number of Thermal photons

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that the number of photons [tex]\sum_n <s_n>[/tex] in equilibrium at temperature [tex] \tau [/tex] in a cavity of volume V is
    [tex] N = 2.404\pi^{-2}V(\tau / \hbar c)^3 [/tex]


    2. Relevant equations
    [tex] <s> = \sum_s s P(s) = Z^{-1} \sum s~ exp[-s \hbar \omega/ \tau] ~~~ (1)[/tex]

    [tex] <s> = 1/exp[\hbar \omega / \tau] - 1] ~~~ (2)[/tex]

    [tex] \omega_n = n \pi c/ L ~~~ (3)[/tex]

    3. The attempt at a solution
    I have tried to convert omega and take the sum using (3), but haven't had any luck with that. Also I have tried taking the double summation over <s> but have run into a stumbling block with Z being of a similar form of the exact form (2) of <s>.
     
  2. jcsd
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