[Physics] In a vacuum can a cooler body radiate Infrared radiation to a warmer body

radiationtemperaturethermodynamicsvacuum

I mentioned vacuum, because I want to discount the effects of conduction or convection. I simply want to know if some of the infrared radiation(IR) goes from the cooler body to the hotter body? How does each body know how much to radiate at any particular time? I assume that it ultimately comes down to temperature difference but how does the hotter body know what the temperature is of the cooler body and vice versa? We all know that both bodies will radiate IR at the 4th power of its temperature and obviously they will be eventually in equilibrium with each other, each of them then radiating an equal amount to each other.

Best Answer

Yes, both bodies radiate, including the cooler one. The warmer one puts out more power in its radiation, proportional to $T^4$ just as you say. The amount of radiation depends on absolute temperature, not temperature difference. But since the colder body has a lower absolute temperature, it radiates less than the hot one and the net result is that heat flows from the warmer body to the cooler one.