Second Law of Thermodynamics....confusion over an example By the second law of thermodynamics, you shouldn't be able to use any amount of mirrors/lenses to focus sunlight onto an object and heat it past the surface temperature of the sun (approximately 5800K). 
In principle this makes sense to me, but I'm more concerned with the mathematics behind this. Whenever I stop to think about energy, things seem to break down in my mind. I just can't get past the fact that the more rays of light your focus (ie, the more photons), the more energy that would be passing into your system. If you increase the energy of your system, is seems like the average energy of the molecules in your system will continue to increase. 
Can anybody show me a mathematical counterexample? I guess I just don't understand all of the equations that necessarily go into this calculation, because I keep getting that the energy of your system increases with each photon that passes into your system. Thanks!
If you believe my statement is incorrect, please look at problem 91 here and explain why I'm incorrect and how the answer is E http://www.physics.ohio-state.edu/undergrad/greStuff/exam_GR9677.pdf
 A: The picture in the GRE problem is misleading (probably deliberately) as it shows all rays coming out of the oven as being parallel.  Light coming from a thermal source will be distributed in direction as well as frequency, so only a fraction gets focused at the desired spot.  There is something in optics called the "etendue" (look it up) which describes how light is distributed in angle as well as in space.  The fact that the etendue is conserved in optics (basically Louiville's theorem, conservation of volume in phase space) means that a passive optical system cannot increase the temperature of light.  So E is the correct answer.
Let me explain further, since I know this will be controversial.  When you go outdoors you are exposed to a 5000 degree thermal radiation source, however that source is limited in solid angle (the solid angle subtended by the sun) which is why you are not burnt to a crisp.  If you set up a bunch of parabolic mirrors or lenses or whatever, you can increase the solid angle subtended, but only up to a point.  There are only 4 pi sterradians available.  If you manage 4 pi sterradians then you have the full 5000 degree thermal distribution, but you can't go beyond that.
What the etendue tells us is that if we want to squeeze the radiation in space (focusing) we spread it out in angle.  It is the distribution in both space and angle which characterizes the thermal distribution, not simply the intensity.  
