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Blackbody radiation equations

  1. Oct 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that the total energy of the radiation in a volume V at temperature T is
    9t24g4.png
    Hint:
    30rl8k6.png

    2. Relevant equations
    2mgt5e8.png
    21jbxb7.png

    3. The attempt at a solution
    The hint doesn't make sense to me, and those are the equation that I found to be perhaps relevant. Do I integrate the second equation? I'm not sure how to start this problem.
    I think the hint is to help in integrating the second "relevant" equation, so integrating f^3 / exp(hf/K_BT)-1 from zero to infinity should equal pi^4/15?
     
    Last edited: Oct 4, 2015
  2. jcsd
  3. Oct 4, 2015 #2

    SteamKing

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    Staff Emeritus
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    Homework Helper

    Yes, you need to integrate the equation for dU/df.

    Make the substitution x = hf / KbT and use the Hint.
     
  4. Oct 4, 2015 #3
    Then
    x = hf / K_b T
    dx = h / K_b T * df
    df = K_b T / h * du
    performing the integral then gives pi^4/15 * (K_b T / h)
    then together with the rest of the constants it gives [8pi^5V K_b T] / [15c^3] , which doesn't look look like the final answer, did I do something wrong or are there additional steps?

    Edit: Oops sorry there is a mistake in the first equation given in the problem. The pi has an exponent of 5 not 2, and the k_B has an exponent of 4 not 2.

    But still I can't seem to obtain that equation, all I get is [8pi^5V K_b T] / [15c^3], the h is missing
     
    Last edited: Oct 4, 2015
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