I was reading this question: Concentrating Sunlight to initiate fusion reaction and some of the comments, as well as an answer, suggest that thermodynamics second law prevents what I ask in the title. I was wondering if that is really the case because: 1) The sun and a small target (eg deuterium pellets) are not equal amounts of gas in equilibrium. 2) Even if equal amounts of gas aren't required, it's still more like focusing light from one side of the box onto a smaller region on the other side. 3) There is mass being converted into energy in the center of the sun which can flow from place to place and drive an engine.. in other words this set up wouldn't make perpetual motion or free lunch.
And here is my attempt at a calculation: The largest parabolic reflector I know about is 500 meters wide (area ~ 500*500*3.14 = 785000 m^2). The earths surface receives 1000 watts per square meter, so 785000*1000=785,000,000 J/s it was also pointed out in the other question that you can't focus onto an arbitrarily small point. So lets dump the energy into a cup of water no? Specific heat of water: 4.18 joules per gram per degrees c. grams, one cup of water weighs about 236 grams
So if we throw all those together we get: (785,000,000 J/s)/[(4.18 J/gc)(236 g)] = 795759 c/s
If the surface of the sun is 5505 degrees then ignoring losses how long would it take to heat the water that high from room temperature or 25 degrees c? (x seconds)(rate)=5505-25=5480
x~6.9*10-3 seconds
So in order to prevent the cup of water from exceeding the temperature at the surface of the sun it'd have to cool off quicker that that fraction of a second, of course it's going to boil and plasmafy and rapidly expand, but keep in mind that I'm using a relatively small telescope parabola we could do the same calculation but with a much larger diameter and get a much smaller x seconds. Also the more sunlight you capture the higher pressure it's going to put on the target which prevents cooling. I can't see why exceeding the surface temperature wouldn't be possible.
Edit:
I'm confident that the assertion in the above linked question (that you can't make the target hotter than the surface of the sun) is wrong. So basically my question is what is the theoretical problem, and how is the real problem different from the theoretical? Alternatively, if I'm wrong, and the real problem doesn't deviate significantly from the theoretical, then why is the above calculation misleading? In the above calculation I show that there is a relation between the square meters of cross section of the focusing optic (e.g. reflective parabola) and the number of seconds it would take to raise the target to the suns surface temperature. Some number of orders of magnitude more area, and it becomes inconceivable to me that the target would be able to cool off fast enough to not heat up higher than the specified temp. So is there some missing piece of physics that would forbid that?
As I understand it the theoretical problem stems from second law of thermodynamics. One statement of that is as follows - you can't use a colder body to spontaneously heat a hotter body. In other words you can't make a perfect refrigerator. Or refrigeration requires work to be done on the system. Perhaps the optics are doing the work? Which gives me an idea, if the system was just the reflector, target, and star, then perhaps the solar radiation pressure would push everything apart fast enough.
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