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

Question

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?.

Answer 1

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?

Yes, any material that emits well at a specific wavelength also absorbs well at that same wavelength. Heat transfers from hot to cold because at every wavelength a hotter object emits more (per unit surface area) than a cold object does. Radiative thermal energy goes both ways, but the net is from hot to cold.

A black body is a perfect absorber, and hence emits better than any other body. Deep space is very close to a 3 K black body. The atmosphere is (in this context) around 300 K, but is not a black body. In the atmospheric window it is transparent and neither absorbs nor emits radiation at those wavelengths.

The Sky Cool material is designed to be a good absorber/emitter at this wavelength precisely so that it will not send heat to or receive heat from the atmosphere. Since it is in thermal contact with space it will transfer energy to space in this window. At most other wavelengths the Sky Cool reflects radiation, it neither receives nor emits well in the ranges where the atmosphere is not transparent.