Blackbody radiation with frequency filter

[novop]

Let's say there's a perfect blackbody inside a box (at room temperature) composed of material such that only x-rays are able to enter and leave. If the absorption and emission of the x-rays weren't the same, the box would heat up above room temperature, and this would contradict thermodynamics.

So, if this blackbody is being bombarded with x-rays, all the x-rays are absorbed (a perfect blackbody). Then the blackbody would emit radiation in accordance with Planck's law, which suggests that the radiation would be largely in the infrared region for an object at room temperature. This radiation is not allowed to leave the material since it isn't x-rays, so the box heats up. But obviously this can't be so. The black body HAS to emit x-rays in order for it not to heat up above room temperature.

So my question is, how can this blackbody emit x-rays in order to avoid heating up, when Planck's law suggests that it emits radiation only in much higher wavelengths (~infrared at room temp)?

 

[Drakkith]

Hold on. Is the object itself able to absorb and emit only x-rays, or also other radiation?

 

[Drakkith]

Actually, I don't see how absorbing x-rays and emitting infrared radiation contradicts thermodynamics. Why are you requiring the object to not rise above room temperature?

So my question is, how can this blackbody emit x-rays in order to avoid heating up, when Planck's law suggests that it emits radiation only in much higher wavelengths?

This is incorrect. Plancks law is based on temperature, not what it is absorbing. If I shot x-rays at the object it MUST heat up if it absorbs them. Radiation is emitted as long as the object is above absolute zero.

You are calling this a perfect black body, but it cannot be if it only absorbs and emits x-rays.

 

[novop]

Hold on. Is the object itself able to absorb and emit only x-rays, or also other radiation?

All radiation. The screen just prevents all radiation but x-rays from passing through.

I didn't base the emission of any radiation on what it is absorbing, I based it on the temperature. On that note, I think I see my mistake; there's no reason for me to require that the blackbody stays at room temperature.

 

[sardar]

I would like to clarify a few points in this scenario. Firstly, a perfect blackbody is an idealized concept that does not exist in reality. However, we can use materials with high absorptivity and low emissivity to approximate a blackbody.

Secondly, the statement that a blackbody can only emit radiation in the infrared region at room temperature is incorrect. According to Planck's law, the intensity of radiation emitted by a blackbody is a function of its temperature and the wavelength of the radiation. At room temperature, a blackbody can emit radiation in the infrared region, but it can also emit radiation in other regions, including x-rays.

Thirdly, the idea that a blackbody can only emit x-rays in order to avoid heating up is also incorrect. A blackbody will emit radiation of all wavelengths, including x-rays, as long as it is at a non-zero temperature. The intensity of the emitted radiation in each wavelength region will depend on the temperature of the blackbody.

In this scenario, the blackbody is being bombarded with x-rays, which are all being absorbed. This will cause the temperature of the blackbody to increase, and it will emit radiation in accordance with Planck's law. This radiation will include x-rays, but the intensity of the x-rays may be much lower compared to the infrared radiation emitted at room temperature.

In conclusion, the blackbody will emit x-rays as well as other wavelengths of radiation in order to maintain thermal equilibrium and avoid heating up. The intensity of the x-rays emitted may be lower compared to the infrared radiation emitted at room temperature, but they will still be present. This does not contradict thermodynamics, as the blackbody is still following the laws of thermodynamics by emitting radiation and maintaining thermal equilibrium.