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.