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Maximum temperature under radiation

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Nov7-12, 04:36 PM
P: 4
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.

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Nov7-12, 06:06 PM
Sci Advisor
P: 5,451
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]

Nov7-12, 06:28 PM
P: 4
Yes, actually the equilibrium T of the material because of this net energy.

Nov7-12, 07:44 PM
Sci Advisor
P: 5,451
Maximum temperature under radiation

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.
Nov7-12, 08:02 PM
P: 4
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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