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Can solar furnace achieve higher temperature than sun surface?

I guess not, but I'm not sure about that. Can you check my reasoning:

-------- My reasoning -----------

Consider Sun as a black body and (almost) Lambertian radiator. If there would be an optical system which can focus all radiation from one black body to an other body in such way, that you achieve higher temperature, it would be possible to make a Maxwell daemon, because you can than produce useful work by using one body as heater and the second body as cooler in an heat engine.

I think there is some theorem in optics which say that you cannot increase radiance by any focusing without loss of power.

However, I'm not quite sure how this theorem is called, and what is a background. As well I'm not able to make rigorous reasoning, how this limit the temperature of solar furnace.

Only what I can say that two black bodies of different size in elliptical cavity does not create Maxwell daemon, because of this radiance limit (You actually does not focus all the light from the bigger body to the smaller one ).

But what if I don't have to use all the light power from sun? For example you can limit the aperture by diaphragm. In this case you can increase radiance without braking second law of thermodynamics nor the radiance invariant. I'm not sure if in this case (if you sacrifice some power) you can get higher temperature?

If so, is it possible to formulate equation which connect power efficiency and temperature difference for this "optical heat pump"

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marked as duplicate by Chris White, Qmechanic Jul 1 '13 at 19:46

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Possible brought on by comments on And certainly relevant to it. –  dmckee Jul 1 '13 at 14:27
essentially a duplicate: But no one actually wrote out the thermodynamic reason in the answer. I will do it on this question, and it can be moved if this questioned is closed. –  BebopButUnsteady Jul 1 '13 at 18:59

1 Answer 1

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We can certainly use the Sun to heat things up hotter than Sun, such as by using solar cells to generate electricity and using that to run a furnace. However to ensure that entropy increases we must perform additionally perform an irreversible process. Otherwise we are simply taking heat out of a cold body and moving it to a hot body. Optics are a reversible process, and therefore you cannot use them alone to make a heat pump.

The reversibility manifests itself in the fact every optical path from the Sun to the object can be traversed backwards. Recall as well that the probability to absorb and the probability to emit must be related by thermodynamics. Therefore once you object reaches the same temperature as the Sun your object must be emitting as much radiation at the Sun as the Sun is emitting at you object. So its temperature cannot increase past the temperature of the Sun.

Note that the Sun is not a perfect blackbody. Therefore, one may be able to heat a furnace slightly beyond the usual stated "surface temperature of the sun". Although this would all be practically indistinguishable, the correct quantity to use is the entropy of the radiation.

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