Why do bodies absorb and radiate heat in the same proportion?

[Bassalisk]

In fact, we can be much more precise: a body emits radiation at a given temperature and frequency exactly as well as it absorbs the same radiation. This was proved by Kirchhoff: the essential point is that if we suppose a particular body can absorb better than it emits, then in a room full of objects all at the same temperature, it will absorb radiation from the other bodies better than it radiates energy back to them. This means it will get hotter, and the rest of the room will grow colder, contradicting the second law of thermodynamics. (We could use such a body to construct a heat engine extracting work as the room grows colder and colder!)

If I may dare to ask the question: WHY are bodies absorbing and radiating heat in same proportion?

I can't find the answer anywhere on the internet. And why are bodies radiating heat in the first place? And why whole spectrum of wavelengths?

 

[alxm]

If I may dare to ask the question: WHY are bodies absorbing and radiating heat in same proportion?

For the reason stated in the quote you supplied? If something is a net absorber or emitter of radiation, then it's gaining or losing energy relative its surroundings, meaning it's getting hotter or colder. As the quote says, something at the same temperature as its surroundings can't spontaneously heat up or cool down without violating the second law of thermodynamics.

I can't find the answer anywhere on the internet. And why are bodies radiating heat in the first place?

Because the electromagnetic field is coupled to all the other forms of energy in the system. A vibrating molecule can give off its vibrational energy as EM radiation, and absorb EM radiation as vibrational energy (or rotational or other degrees of freedom).

And why whole spectrum of wavelengths?

It's not the whole spectrum; it follows the Planck distribution, so the probability of very high energy radiation quickly becomes negligible.

 

[Bassalisk]

Thanks, I understand now.