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On reading Chapter 1-2 (Thermal Radiation) of Quantum Physics of atoms, molecules, solids, nuclei and particles by Robert Eiberg and Robert Resnick

It stated that

The details of the spectrum are almost independent of the particular material of which a body is composed, but they depend strongly on the temperature.

Further down,

Generally speaking, the detailed form of the spectrum of the thermal radiation emitted by a hot body depends somewhat upon the composition of the body. However, experiment shows that there is one class of hot bodies that emits thermal spectra of a universal character. These are called blackbodies, that is, bodies that have surfaces which absorb all the thermal radiation incident upon them. One example of a (nearly) blackbody would be any object coated with a diffuse layer of black pigment, such as lamp black or bismuth black.

While discussing cavity radiation,

Radiation incident upon the hole from the outside enters the cavity and is reflected back and forth by the walls of the cavity, eventually being absorbed on these walls. If the area of the hole is very small compared to the area of the inner surface of the cavity, a negligible amount of the incident radiation will be reflected back through the hole.

All good, but this is where I have my confusion

Now assume that the walls of the cavity are uniformly heated to a temperature $T$. Then the walls will emit thermal radiation which will fill the cavity. The small fraction of this radiation incident from the inside upon the hole will pass through the hole. Thus the hole will act as an emitter of thermal radiation. Since the hole must have the properties of the surface of a blackbody, the radiation emitted by the hole must have a blackbody spectrum; but since the hole is merely sampling the thermal radiation present inside the cavity, it is clear that the radiation in the cavity must also have a blackbody spectrum. In fact, it will have a blackbody spectrum characteristic of the temperature T on the walls, since this is the only temperature defined for the system.

So after absorbing the incident thermal radiation through that minute hole, it bounces on the walls on the cavity until it's absorbed by the walls of the cavity (The hole is too small compared to the surface area of the cavity, therefore there are less chances for the radiation to escape).

After absorbing the incident thermal radiation the system tends to go to thermal equilibrium by emitting thermal radiation. Won't that radiation escape out the object instead of emitting in the cavity of the object?

However even if the object emits thermal radiation in the cavity won't it get absorbed by successive reflections in the walls of the cavity, and as a result nothing or a very very tiny amount of radiation escapes out of the hole right? Then how can we say that the hole merely samples the radiation present inside the cavity and thus act as a black body? (The hole absorbs almost all radiation and then emits a very tiny bit of radiation)

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  • $\begingroup$ We usually only care about the case where the inside of the cavity is heated to a temperature much higher than the outside. In that case the emitted radiation flux is much higher than the absorbed flux. Having said that, the text is correct that even radiation that comes from the outside is quickly thermalized in the walls, so it doesn't matter. $\endgroup$ Jan 18 at 13:05
  • $\begingroup$ There are no perfect black bodies. In 1900 Planck considered a dark hole, such as the entrance of a coal mine with the lights off, to be a good enough approximation. Why are high school students still taught about holes as black bodies and Bohr atoms? $\endgroup$
    – my2cts
    Jan 18 at 13:07

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However even if the object emits thermal radiation in the cavity won't it get absorbed by successive reflections in the walls of the cavity, and as a result nothing or a very very tiny amount of radiation escapes out of the hole right? Then how can we say that the hole merely samples the radiation present inside the cavity and thus act as a black body?(The hole absorbs almost all radiation and then emits a very tiny bit of radiation)

The radiation is in equilibrium with the wall of the cavity, that is as much radiation is absorbed by the walls of the cavity as is emitted by them. The hole should be indeed very small - only to sample the radiation inside, without significantly perturbing the thermal equilibrium inside.

This indeed is often realized in real life - e.g., the spectrum of stars (including the Sun) is well approximated by the Planck's curve (i.e., the black body radiation spectrum), even though the stars are clearly not in equilibrium with the surrounding vacuum - all the emitted radiation escapes and never returns (e.g., the Sun surface temperature is 6000K, while the surrounding vacuum is a few Kelvins.) However, the fraction of the radiation escaping through the surface of a start is only a tiny part of the radiation wondering inside, constantly reabsorbed and re-emitted by the matter composing the star.

Related: How does radiation become black-body radiation?

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