# Why must black bodies in thermal equilibrium emit the amount of radiation absorbed?

I'm studying black bodies for IB Physics and I'm having trouble understanding the full concept of black body radiation. I understand that a black body in thermal equilibrium with its surroundings will emit all radiation that is incident upon it. My question is, why must this radiation be emitted at all? Why can't the object continue to heat up from the absorbed radiation? If energy is transferred to the black body, why can't it's temperature increase rather than the energy being emitted? I'm barely starting to cover quantum mechanics, so my knowledge on the subject is bare which is probably the source of my confusion. Any help would be greatly appreciated. Thank you in advance.

• I guess maybe the electron can't contain the excitement for long... Aug 13, 2016 at 7:29
• Because if they don't then they aren't in equilibrium. That's what thermal equilibrium is. Oct 3, 2016 at 9:35

The definition of thermal equilibrium is that at equilibrium there is no net transfer of heat, so it is this requirement that forces the blackbody to emit as much energy as it absorbs.

In general an object can heat up (or cool down) by absorbing (respectively emitting) radiation, but then the object is not in thermal equilibrium and will have a lower (respectively higher) temperature than its surroundings.

• So is my intuition backwards? I thought a black body emitted the same amount of radiation absorbed because it was in thermal equilibrium, but is it actually the case that a black body is in thermal equilibrium because it absorbs the same amount of radiation it emits? Aug 13, 2016 at 7:31
• Its simpler than that. Saying "a blackbody is in thermal equilibrium" is just a fancy way of saying "its emitting the same amount of heat as it is absorbing". there is no real difference between the 2 statements. Aug 13, 2016 at 7:35
• I see. I'm used to thinking of heat transfer as merely convection and conduction, so I hadn't thought of it that way. Aug 13, 2016 at 7:39
• @BySymmetry Does the radiation comes from transitions in mircoscopic level? Apr 4, 2020 at 18:02

I understand that a black body in thermal equilibrium with its surroundings will emit all radiation that is incident upon it.

This is true when interpreted correctly, but it is not the best thing to begin with when trying to understand what is going on.

All bodies reflect some part of radiation that is directed at them and absorb the rest. They also emit their own radiation. All at the same time.

In thermodynamic equilibrium, the energy of body is constant, so if there are above processes going on, they must balance each other: