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Maximum temperature under radiation

  1. Nov 7, 2012 #1
    Hello everyone,
    As you all know, the temperature of a metal increases under electromagnetic radiation. The metal also has a black body radiation which decreases its temperature. There is an equilibrium temperature which is the maximum temperature of the metal under the radiation. I am looking for formulas or publication that gives me this final temperature.

  2. jcsd
  3. Nov 7, 2012 #2


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    Hm, it seems you want to calculate the net energy flow with

    [tex]dE_- = -p(T)\,dt = -\sigma\,A\,T^4\,dt[/tex]

    where p(T) is the integrated density from Stefan-Boltzmann, and from an external radiation source with

    [tex]dE_+ = p_0\,dt[/tex]

    Then you are looking for

    [tex]dE_- + dE_+ = 0[/tex]

    Last edited: Nov 7, 2012
  4. Nov 7, 2012 #3
    Yes, actually the equilibrium T of the material because of this net energy.
  5. Nov 7, 2012 #4


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    OK, you have

    [tex]dE_+ + dE_- = 0[/tex]
    [tex]p_0\,dt - \sigma\,A\,T^4\,dt = 0[/tex]
    [tex]p_0 = \sigma\,A\,T^4 [/tex]

    So the temperature is constant iff the black body radiation is balanced by radiation received from the external source.
  6. Nov 7, 2012 #5
    Thank you Tom.
    That makes sense. I checked it couple of times and my results were not match with the publications. I will check again to find the reason of the difference.

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