Floating Mirror & Its Unusual Focus Heat

[AbhiNature]

Scenario:

Entropy of the system or say the Universe is at its maximum, and there's a parabolic mirror floating in space with an object at its focus.

Due to CMBR the object at focus will heat above the CMBR.

Oh! Is there something wrong?

 

[jfizzix]

The important thing to consider is that almost all of thermodynamics deals with systems in thermal equilibrium. The Universe is not at maximum entropy, since its entropy is increasing pretty much all the time, so the universe as a whole is not in a thermal equilibrium, though small parts of it can be.

Incidentally, when the universe reaches thermal equilibrium, it's known as the heat death of the universe.
http://en.wikipedia.org/wiki/Heat_death_of_the_universe

By creating a parabolic mirror, and putting some object at its focus, that object will indeed end up having a larger temperature than the CMBR. This would be due to starlight and other forms of light which can be focused by a parabolic mirror.

This is because it will heat up to the point where the energy it radiates away as heat equals the energy it absorbs from the environment. With the mirrors in place. That is when that object will be in a thermal equilibrium.

If the mirror went away, the object will cool down until again the rate that it radiates energy away is the same as it's absorbing.

Hope that helps:)

 

[AbhiNature]

I was considering a hypothetical scenario where entropy is at its maximum. Instead of Universe it could be any isolated system where entropy is at its maximum and there's a parabolic mirror floating with an object at its focus. The object's temperature will be above that of the bacground radiation?

 

[jfizzix]

Consider an alternative situation:

Let's say you have an elliptical cavity with the walls kept at constant temperature, and you wait long enough so the radiation inside has maximum entropy. Would you expect the energy density at the foci to be the same as everywhere else in the cavity?

Or better yet, what if you have a spherical cavity? Would you expect the energy density in the center to be the same as everywhere else in the cavity?

If the system is in thermal equilibrium, then its temperature everywhere inside must be the same. Putting an object anywhere in that cavity would result in it eventually reaching the same temperature as the rest of the cavity.

At this point my knowledge gets a little fuzzy in that I'm not certain if there are some cavity shapes that simply cannot reach thermal equilibrium, where the radiation will keep oscillating and evolving forever.

In any case, if the system you're thinking about can reach thermal equilibrium, you can be certain the temperature will be the same throughout your system.

Hope this helps:)

 

[russ_watters]

Parabolic mirror.

The mirror blocks exactly as much radiation as it focuses on the object.