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.

Thanks
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 Recognitions: Science Advisor Hm, it seems you want to calculate the net energy flow with $$dE_- = -p(T)\,dt = -\sigma\,A\,T^4\,dt$$ where p(T) is the integrated density from Stefan-Boltzmann, and from an external radiation source with $$dE_+ = p_0\,dt$$ Then you are looking for $$dE_- + dE_+ = 0$$ Correct?
 Yes, actually the equilibrium T of the material because of this net energy.

Recognitions:

OK, you have

$$dE_+ + dE_- = 0$$
$$p_0\,dt - \sigma\,A\,T^4\,dt = 0$$
$$p_0 = \sigma\,A\,T^4$$

So the temperature is constant iff the black body radiation is balanced by radiation received from the external source.
 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. Cheers

 Tags black body, equilibrium, heat transfer, temperature, thermodynamics