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When the temperature increases the energy per photon increases, which in part decreases the overall wavelengths of the black-body and the intensity increases because of the emission rate. which means that light intensity at each frequency is determined by the black-body temperature, but this is a full circle. When you introduce energy to a black-body what exactly is happening?

If the energy of photons is determined by the wavelength than what exactly determines the emission rate?

See Equipartition theorem video or Equipartition theorem

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Something's happen that makes you get the equilibrium (in thermodynamics the intermediate prosses doesn't matter if you tell that it was reversible). If you want to measure the intensity of the black body radiation, you can use a diffraction gratting, and then use some device that measures light intensity (for example, a second black body that you make go to thermal equilibrium with the radiation falling inside it, and then ussing a thermometer in thermal equilibrium with this second black body).

English isn't my native language, and I learned it mostly reading papers on arxiv plus google translate a few years ago. Zorry if it wasn't clear what I answered.

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