# How does Kirchoff's law of Thermal radiation explain that to cool below ambient temperature have to radiate through atmospheric transparency window?

Kirchhoff's law of thermal radiation is "a body emits radiation at a given temperature and frequency exactly as well as it absorbs the same radiation." Is this law valid only at thermal equilibrium? The atmospheric transparency window lies at wave lengths 8-13 micrometers or Mid infrared. At these wavelengths thermal radiation is not absorbed (trapped by greenhouse gases) by the lower atmosphere but escapes into the troposphere and space.

Please note the answer to a question about the need to use the atmospheric transparency window to achieve passive radiative cooling below ambient air temperature https://physics.stackexchange.com/a/160301/343877

The answerer states " Lets say one creates a material/optical film that instead of aiming at the transparency window they designed the material to emit at frequency X that the atmosphere does absorb. By Kirchhoff's law of thermal radiation, since the atmosphere absorbs at X it also emits at X. And likewise since the cooler emits at X it also absorbs at X. That would result in the cooler absorbing extra radiation from the atmosphere at frequency X, which would heat it up."

Could you please clarify this answer in quotation marks? Wouldn't the same thing happen to a material/film like the Sky Cool material designed to emit at frequencies Y (8-13 micrometer or the atmospheric transmission window) wouldn't this cooler also absorb at Y because it emits at Y, thus also heating up by absorbing heat from the atmosphere at those wavelengths? Thus also being unable to cool below ambient temperature by radiating. Or am I misunderstanding Kirchoff's law of thermal radiation?

The way I am looking at it is if you radiating into space, then the heat exchange is really going on with space, not the atmosphere..and space is returning some radiation back. But you radiate more into space than you get back (because you are at a thermal disequlibrium, due to the tremendous temperature differential between the material and space which is at 5 K). Thus the material emitting at wavelengths of mid infrared (8-13 micrometers) that are not absorbed by the atmosphere( that radiate to space) cool down continuously.Is this reasoning correct?.

• The way I am looking at it is if you radiating into space, then the heat exchange is really going on with space, not the atmosphere..and space is returning some radiation back. But you radiate more into space than you get back (because you are at a thermal disequlibrium, due to the tremendous temperature differential between the material and space which is at 5 K). Thus the material emitting at wavelengths of mid infrared (8-13 micrometers) that are not absorbed by the atmosphere( that radiate to space) cool down continuously.Is this reasoning correct?. Commented Aug 23, 2022 at 19:51
• I like Dale's answer. If it's still not making sense, the whole point is: is the SkyCooler trying to reach thermal equilibrium with the atmosphere (warm) OR with space (very cold)?If we design so it's exchanging heat with space it will be much more effective. You can think of it like two people switching to speaking Spanish so that the third English-speaking person cannot listen to their conversation. The atmosphere does not "speak" in the wavelengths of the atmospheric transmission window. Commented Aug 24, 2022 at 13:13