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In winters, frost is formed on the grass and wood and not on concrete roads.Temperature of frost is lower than the temperature of the surrounding air.So a question arises ""Can a body become colder than the environment"" or there is something which I have misunderstood?

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    $\begingroup$ When the air temperature is above body temperature, you certainly hope you can stay cooler than it. $\endgroup$
    – Jon Custer
    Jan 8, 2023 at 16:01
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    $\begingroup$ Perhaps related: physics.stackexchange.com/a/679265/247642, physics.stackexchange.com/a/681432/247642 $\endgroup$
    – Roger V.
    Jan 9, 2023 at 9:13
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    $\begingroup$ "In winters frost is formed on the grass whose temperature is lower than the surrounding air." Proof? $\endgroup$
    – DanielSank
    Jan 9, 2023 at 9:42
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    $\begingroup$ There is a type of white paint which can keep a given surface $4^\circ C$ cooler than the ambient air in (noon) sunlight and up to $10^\circ C$ cooler at night. It works by reflecting most wavelengths of sunlight while still being able to radiate in infrared. It was developed by researchers at Purdue University. $\endgroup$ Jan 9, 2023 at 10:53
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    $\begingroup$ When you use the word "body", do you use it in the more general physical sense (essentially any given object, as e.g. "black body"), or do you refer to a body of a living being (in particular a human body)? $\endgroup$
    – printf
    Jan 9, 2023 at 21:02

3 Answers 3

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If conductive/convective heat transfer is low, then radiative heat loss can cool an object below the temperature of the surrounding air. As discussed in the answers to What is the temperature of the clear night sky from the surface of Earth?, the temperature of the night sky can easily be lower than the surface air. This has long been used to create ice in the desert at night.

If the air is dry and the object wet, then evaporation can cool an object below the surrounding air temperature. This is how earthen pots can keep their contents cool and how perspiration keeps humans from overheating.

See also the answers to How does frost form above freezing temperature?, Why does ice form on bridges even if the temperature is above freezing?, and Why does the windshield of my car freeze even if the outside temperature is above freezing?.

Some references to research, etc.

For those who who would like to read further on this, there is a large related research literature. For just one example in the natural world, both energy balance modelling and observation show that leaves of subalpine herbs can have frost episodes even when the air temperature is above freezing. (Thanks @Vladimir-F-Героям-слава).

To understand the potential of radiative cooling, an important number to keep in mind is that the power radiated by a $300\ K$ blackbody is $$W=\sigma T^4\approx 450\,\ \textrm{W/m}^2$$ which is almost half the maximum solar irradiance at the Earth's surface of $\sim 1 \,\ \textrm{KW/m}^2$.

If the sky is transparent to a significant fraction of the spectrum of blackbody radiation, significant cooling is possible. The peak of 300 K blackbody radiation is $\sim10$ microns, and happens that the atmosphere has a large transparency window for 8-13 micron infrared wavelengths.

It was originally thought that such radiative cooling was only significant in deserts or at high altitudes, but with carefully engineered thermal photonic materials that reflect almost all visible light, but radiate strongly in the infrared atmospheric transparency window, it is possible to passively cool objects below ambient air temperature even in direct sunlight at sea level. This is of great environmental and commercial interest, and although I am not sure what the current record is, one study made a theoretical estimate that temperatures as much as 60 °C below ambient is achievable, and an average reduction of 37 °C was been observed over a 24-hour cycle in populous area at sea level.

Even just using special ultra-white paint can keep surfaces 11 °C cooler than ambient at night and 4 °C cooler under noon sunlight. (Thanks @AccidentalTaylorExpansion.)

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    $\begingroup$ +1 However: If conductive/convective heat transfer is low, then radiative heat loss - isn't the radiative heat loss determined by the temperature? Can this really drive the temperature below that of the environment? Could you describes it in more details (equations.) $\endgroup$
    – Roger V.
    Jan 9, 2023 at 9:10
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    $\begingroup$ @RogerVadim: Yes. Because 50% of the environment is the sky, whose temperature is below 0°C more often than not. $\endgroup$ Jan 9, 2023 at 9:29
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    $\begingroup$ @EricDuminil 50% is a strong claim - the thread quoted in the answer suggests that the sky temperature is not as low as it may seem. Also, the light emitted is backscattered by air - so the radiation near Earth might be in quasi-equilibrium state (which is why we can treat planets and stars as black bodies.) $\endgroup$
    – Roger V.
    Jan 9, 2023 at 9:43
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    $\begingroup$ @RogerVadim Check the role of the sky view factor (SVF) in determining radiative balance in goemetrically complicated areas. Also remember that air temperatures near the ground are largely determined how the Earth surface heats during the day and cools during the night. The air then heats or cools by turbulent heat transfer. Objects under the clear sky are almost always hotter than the air during the day and colder than the air during the night. It is the rule, not the exception. It is how the daily changes of air temperature work, above the boundary layer the air temp. does not change. $\endgroup$ Jan 9, 2023 at 13:40
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    $\begingroup$ @RogerVadim For the basics you can check textbooks of general climatology or micrometeorology about radiation and heat balance of the Earth's surface. For this specific problem you can check articles like sciencedirect.com/science/article/pii/0168192394900205 $\endgroup$ Jan 9, 2023 at 14:00
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Frost is formed overnight, while the temperature of the air is below the freezing point. However, it does not immediately disappear as the temperature of the air rises, as some time is required for the sufficient amount of heat to be transferred to melt the ice/snow (see latent heat).

In this sense, an even more striking phenomenon is the winter snow that persists for days or weeks in Spring, after the temperature goes above the freezing in daytime; see Snowmelt.

Remarks

  • The premise of the question is that the second law of thermodynamics prohibits transfer of energy from a colder object to a hotter one/environment without external work done. In this sense, the human body on a hot day or refrigerator are poor examples, since there the cooling is achieved via such external work.
  • A comment below pointed out that we can have condensation on cold objects, even with the temperature of air above the freezing point. To some extent this has been already mentioned in the context of snowmelt (for those who followed the link), but it is still worth acknowledging explicitly.
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    $\begingroup$ Frost can form while the air temperature is above freezing as well. The water in the air sublimes onto the substrate. $\endgroup$ Jan 9, 2023 at 5:15
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    $\begingroup$ @RossMillikan I edited the answer to mention it. $\endgroup$
    – Roger V.
    Jan 9, 2023 at 9:25
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    $\begingroup$ Sorry, but this answer is misleading: Due to the radiative contact of the ground with space, it is the ground that cools down first in cloudless nights. And it reaches the freezing point before the air does. This is also the reason why clouds mean warm nights in winter as they block the radiative contact with space. Please take a look at David Bailey's answer. $\endgroup$ Jan 10, 2023 at 19:35
  • $\begingroup$ @cmaster-reinstatemonica I did take a look at David Bailey's answer, and there is a discussion following it. Please do some research before making categorical statements. $\endgroup$
    – Roger V.
    Jan 10, 2023 at 19:51
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    $\begingroup$ Yeah, I've read that discussion now. And even though you find it hard to believe, Vladimir F is right. I think the key insight for you is that the ground is not only in thermal contact with the air above: The air is (semi-)transparent to large regions of thermal radiation frequencies to which the ground is much, much darker. That's why the thermal environment of the ground always includes space unless it's cloudy, and why the ground's equilibrium temperature is between those of the air (warm) and space (cold). As such, this equilibrium is colder than the air above. $\endgroup$ Jan 11, 2023 at 6:48
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A prima facie example of cooling below the air temperature due to evaporation is the wet-bulb temperature, that is, the temperature of a thermometer surrounded by a wet cloth or similar material. As the water keeps evaporating, the thermometer indicates a lower temperature than a thermometer without such wet material.

The measured temperature difference is used to measure air humidity in meteorological stations. If the air is saturated with water vapour (100% humidity), the temperature difference will be zero because no evaporation and cooling happens.

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    $\begingroup$ Yes. Mass transfer in evaporation for say water is driven by the difference between the saturation pressure of the liquid at the temperature of the liquid, and the partial pressure of vapor in the air (humidity). This can compete with heat transfer due to temperature difference. $\endgroup$
    – John Darby
    Jan 9, 2023 at 21:56
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    $\begingroup$ @JohnDarby In atmospheric sciences we say that the latent heat flux competes with the sensible heat flux. Hence also the Bowen ratio and similar. $\endgroup$ Jan 10, 2023 at 6:39
  • $\begingroup$ While this is an effect that can cool the ground below freezing while the air above is above, this is not the main effect, afaik. It is the radiative loss of heat to space that allows the ground to a) become colder than the air above, and b) drop below the wet-bulb temperature, allowing water to resublimate as ground frost. The later effect cannot be achieved with evaporative cooling. $\endgroup$ Jan 10, 2023 at 19:48
  • $\begingroup$ @cmaster-reinstatemonica Sure, every undegrad knows that (or at least our undergrads at their final exams, hopefully). See my more thorough comments under other answers. This answer demonstrates a very direct demonstration and application of using the temperature difference to measure the humidity. $\endgroup$ Jan 10, 2023 at 20:23

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