# can heat radiate from a cold to hot body?

if you have 2 bodies (A,B), with Temperature of B>A, can you have heat transfer from A to B through radiation? In particular if A reflects the wavelengths that B is emitting the radiation at would this be possible? And if so is this process independent of the temperature of B (since A is reflective) or does A radiate as a function of the temperature difference with its surroundings (in this case B).

I was thinking of how this applies to radiative sky cooling: the process by which you use the radiation of object A to disperse heat, and create A reflective of the Sun's radiation to not heat up from that. The universe is about 3K, if it was 200K, would this process differ?

• Are you asking if objects with $T>0$ radiate, or are you asking if there is a net flow of radiative energy from the cooler to the warmer, i.e., will the warmer object increase in temperature? Jul 12, 2018 at 15:20
• I want to isolate a body from convection and conduction from its surroundings, but not radiative isolation. Imagine this body in a double dewar that isolates it thermaly, but light passes through it. Now if this object is reflective, it will cool down since its radiating heat to outside the sistem, but not absorbing it. I want to know the limit of this process ans whether it depends on the outside temperature or not.
– Leo
Jul 12, 2018 at 17:55

Yes, some times it is possible This is happening in refrigerator. In this case some energy must be supplied to complete this transaction

• I was thinking more specifically of 'radiative sky cooling' and whether the heat of the universe affects the rate of radiation emitted of if it doesn't matter.
– Leo
Jul 12, 2018 at 12:57
• @DDleo : Is your question inspired by any chance from the video 'How outer space could cool buildings' uploaded by bloomberg on YouTube. I watched this video recently, your question seems similar. Jul 12, 2018 at 14:04
• yeah, from the Ted talk about 'radiative sky cooling' form the same people.
– Leo
Jul 12, 2018 at 14:11

if you have 2 bodies (A,B), with Temperature of B>A, can you have heat transfer from A to B through radiation?

Yes, for instance, if radiation from A is focused on B, while radiation from B is directed elsewhere. The relevant statement of the second law of thermodynamics says:

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

While heat is transferred from A to B, B is radiating into universe, which should cause "other changes". So, there is no violation of the second law of thermodynamics.

In particular if A reflects the wavelengths that B is emitting the radiation at would this be possible?

Yes, it is possible. It could be viewed as a variation of the first scenario.

And if so is this process independent of the temperature of B (since A is reflective) or does A radiate as a function of the temperature difference with its surroundings (in this case B).

Yes, it should be independent of the temperature of B. It could be affected by the temperature of B indirectly though, for instance, if B heats A to the extent that the radiating efficiency of A decreases, but that is unlikely considering that A reflects most of the radiating energy.

The universe is about 3K, if it was 200K, would this process differ?

No, for the same reason, i.e., as long as the radiating efficiency of A is not affected by it being heated too much by the universe, which should not be the case with the universe at 200K.

• thank you, so if you have a reflective coated body A, conduction and convection isolated from its surrounding (like in a glass chamber kept in a vacuum). The system only exchanges heat via radiation with the outside world. Does then this system cool down to approaching 0 by radiating its heat outwards and not absorbing? or is there a limit to this process?
– Leo
Jul 12, 2018 at 14:17
• @DDleo These two qualities you are asking for i.e perfect emitter and perfect reflector cannot be present simultaneously in one body. Perfect Emittance would mean releasing all the thermal energy within. Perfect Reflectivity would mean not absorbing any of the incident light/energy. Now, a white body in theory is able to reflect all the radiations that fall on it. So that means it never absorbed any radiation and hence has nothing to emit. Whereas a black body can be both a perfect absorber and a perfect emitter, but has zero reflecting power. Therefore it can emit all the radiation it absorbs Jul 12, 2018 at 14:56
• So we can only arrive at the best possible compromise between emissive power and reflecting power. We cannot have the best of both worlds. Jul 12, 2018 at 14:57