# Can solar furnace achieve higher temperature than sun surface? [duplicate]

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. http://en.wikipedia.org/wiki/Spectral_radiance

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"

• Possible brought on by comments on physics.stackexchange.com/q/69652. And certainly relevant to it. Jul 1 '13 at 14:27
• essentially a duplicate: physics.stackexchange.com/q/2679. 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. Jul 1 '13 at 18:59