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I was reading this article: Passive radiative cooling below ambient air temperature under direct sunlight

The authors are improving upon the age-old idea of reflecting incoming sunlight while radiating heat away. The point that I don't get is why do they need to meet this criteria:

...radiate heat to outer space through a transparency window in the atmosphere between 8 and 13 micrometres.

They also state that

Further, the cold darkness of the Universe can be used as a renewable thermodynamic resource, even during the hottest hours of the day.

Further in the article they do not elaborate on why specifically they need to use the outer space as a heat sink. The equations don't imply anything about that.

The only way I can figure out this being useful is not heating the atmosphere and preventing the heat from being trapped at all, radiating it away from Earth, thus combating global warming. The fact that the apparatus is using outer space as a heat sink or just using the atmosphere should not have any significant impact on radiative cooling properties. Is this reasoning correct?

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  • $\begingroup$ The rate of energy loss through radiation or conduction (the only two methods possible between Earth's atmosphere and space) depend upon the temperature difference or temperature gradient. Though the plasma surrounding the Earth has a high "temperature," space itself can be approximated to be less than 3-4 degrees Kelvin, I think. Does that help? $\endgroup$
    – honeste_vivere
    Jan 11, 2015 at 20:12
  • $\begingroup$ Well, not really, I think, since my question about something different: does radiating heat at a specific frequency so that the atmoshpere would be transparent for it matter for the radiative cooling properties of the radiator itself? $\endgroup$
    – Alexander Chernyshev
    Jan 11, 2015 at 20:30
  • $\begingroup$ Ah, then the answer is yes. If the radiation encounters an opaque (or even translucent) obstacle before entering space, it will either reflect or be absorbed the the obstacle. In either case, all the energy will not be allowed to leave the system through radiation alone. $\endgroup$
    – honeste_vivere
    Jan 11, 2015 at 20:33
  • $\begingroup$ Right, but you're assuming that the system is the whole Earth. I'm asking to just consider what the practical effects would be on cooling properties of the apparatus. I assume that the heating would occur somewhere far away and dissipate. So the system I'm considering is just the radiator itself (and mabe the casing). $\endgroup$
    – Alexander Chernyshev
    Jan 12, 2015 at 13:21

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Short answer: For their heat sink they choose outer space (-270 °C) instead of the atmosphere (avg. near surface = 17 °C) for the simple reason that space is much colder as Anna V points out. If the cooler didn't emit through the atmosphere's transparency window, the cooler would also absorb extra radiation from the atmosphere and warm up due to Kirchhoff's law of thermal radiation: "a body emits radiation at a given temperature and frequency exactly as well as it absorbs the same radiation."

That's why the graph of cooler emissivity/absorptivity from the paper is labeled as such-- they are equivalent:

enter image description here

Say instead of aiming for the transparency window they designed the cooler 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 more radiation from the warm atmosphere overall which would heat it up.

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  • $\begingroup$ Not to mention you'd have second order effects - by emitting where the atmosphere absorbs, you'd heat the atmosphere and increase how much it radiates back at you, etc. $\endgroup$
    – Sean E. Lake
    Aug 23, 2022 at 4:43
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The fact that the apparatus is using outer space as a heat sink or just using the atmosphere should not have any significant impact on radiative cooling properties. Is this reasoning correct?

No, it is not. The cooling properties of the apparatus depend on the heat sink to which the heat is aimed, as the final result will be an equilibrium of apparatus/environment . If the heat sink is the atmosphere the apparatus can only cool down to the atmosphere's temperature. As the temperature differential with outer space is enormous equilibrium will not be reached and the apparatus will keep cooling. The aim of the apparatus is to reduce the heat content of the earth system by transferring it radiatively to space.

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