# Black Body in empty space

Let's say we have a body of spherical shape with a temperature T > 0 Kelvin for our purposes. It's supposedly in empty space. Completely empty space, no other radiation, no far away stars nothing.

So this body will be radiating EM waves of some wavelength related to it's temperature with most of the around a wavelength $$\lambda_{max}$$ as given by Planks radiation formula.

Will this Black Body at some point reach a temperature of absolute 0 ? Does it depend on what material it is composed off which the minimum temperature will be reached?

Temperature is related to the kinetic energy of molecules, atoms and subatomic particles of a medium or body. In a profound consideration, the motion - or more precisely - the acceleration of particles is accompanied by the emission and absorption of photons. These energy quanta are involved in every change of direction of the particles in a body.

In your case, a body somehow has a temperature in an otherwise empty space. There are no other bodies radiating and therefore a temperature increase of your body is impossible.

Your body has an outer surface. The surrounding empty space is the only condition for photons to escape from your body. Once emitted towards the empty space, the photon is lost to the body.

In the end nothing can stop the dissipation of energy (photons) inside the body. The cooler surface area (which emits photons and becomes cooler) is fed by the inner area. A condition to stop this process is unknown. Cooling down to zero Kelvin is unavoidable.

• Your last sentence contradicts the third law of thermodynamics. – Hartmut Braun Sep 26 '20 at 6:12
• @HartmutBraun Why you think this way? – HolgerFiedler Sep 26 '20 at 6:36
• third law of thermodynamics states that zero Kelvin is impossible. – Hartmut Braun Sep 26 '20 at 6:38
• @HartmutBraun In reality 0K is impossible because around are innumerable sources of heat and the interact. The question was about a very theoretical case of an empty universe. Tell me, how the escaping photons will get back from space? How phonons of the body will not dissipate and end as photons? And if they will stay phonons forever, how one will measure it? (Without measuring process no statement about temperature). At last, I agree, it is speculative, because empty universe with only one body is impossible and hard to abstract from the reality) – HolgerFiedler Sep 26 '20 at 7:16
• I’m not an expert in that matter, thus I didn’t make the following speculation an answer: when the matter that makes up the black body reaches ground state it cannot radiate photons away anymore. But still there is energy left in the ground state. Thus zero degree can never be reached. – Hartmut Braun Sep 26 '20 at 9:06

No, the black body are not going to lose whole energy because energy is quantized. The lowest level of energy will stay anyway. $$E_n=\hbar\omega \left( n+\frac{1}{2}\right)$$