# 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

• I'd like to point out that the fusion experiments at NIF (National Ignition Facility at Lawrence Livermore) use mirrors and lenses (and nonlinear optical crystals) to make a small target very hot. Explain that! – DarenW Oct 17 '13 at 19:09
• Laser light is coherent, it's not at a certain temperature. – Bubble Oct 17 '13 at 19:14
• The reason is quite simple: Absorbing bodies also emit thermal radiation. Once the object is hot, it shines back at the sun. To prove the symmetry microscopically you need to consider the entendue of the light path, the object's spectral characteristics, and so on. Or, you can simply appeal to the second law of thermodynamics that if the object were to get any hotter than the sun, you could build a heat engine using the object as heat source and the sun as the cold sink, and extract energy for free. – Nanite Oct 17 '13 at 19:19
• I have come to agree that E is the correct answer. Second law dictates that you cannot transfer heat from a colder to a hotter body, but the other way round. – mcodesmart Oct 18 '13 at 0:21