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So I read this xkcd, and thought it was kind of cool. However, I showed it to my engineer father and physics undergrad brother and neither seem to find the explanation very convincing (though they don't dispute the conclusion; I'm in computer science hence my deference to their opinion). Specifically they think that the reference to the second law is misleading, and that conflating light and heat/energy is leading to bad arguments. How valid are the arguments presented in the blog and is the conclusion valid?

In case of bad link etc, the question at hand is what it would take to burn things with moonlight like you can do with a magnifying glass and sunlight. The author claims that you couldn't heat anything over 100 degrees Celsius with just lenses and moonlight.

Edit: Thanks to my conversation with Rodrigo, I basically want a slightly more technical explanation that I can show to someone with a scientific background, but that I should at least be able to follow the math in if possible for the claim that you cannot use lenses to heat something hotter than its celestial source (sun/moon)

Edit 2: I think the comments and answers so far have covered most of the points, but there's still one sticking point about how there's a one to one relationship between the surface temp of the moon and the temperature that the moonlight can heat things up to. I.e. it's understood that the total energy reflected by the moon is a limit on the amount of energy that can be harnessed, but why can that energy not be used directly to heat an object above 100 deg C? Shouldn't it be a relative temperature caused by the energy? I.e. isn't the amount of energy required to heat the moon's surface to 100 degrees sufficient to heat something smaller hotter? To be clear, isn't temperature relative, how is it that knowing what temperature the energy heats the moon to tells you the temperature that energy will heat a leaf on earth to?

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    $\begingroup$ I don't see how they think that Munroe "conflates light and energy." The answer deals with the available energy, and the fact that the energy is carried by light is irrelevant. $\endgroup$
    – Asher
    Commented Feb 13, 2016 at 23:51
  • $\begingroup$ I think their point is that you should be able to focus light from multiple points on the moon/sun's surface to reach a higher temp, while Munroe seems to say it's only energy from a single point? Like they think in his final analogy (surrounded by surface) you could use lenses to focus the energy to get a hotter temperature? $\endgroup$
    – Adam Martin
    Commented Feb 14, 2016 at 0:00
  • $\begingroup$ Specifically, the author claims that you cannot heat anything with optic systems to a temperature hight than the light source. $\endgroup$
    – rodrigo
    Commented Feb 14, 2016 at 0:02
  • $\begingroup$ They're saying that energy is additive, so you should be able to use a system of mirrors and lenses to get above the surface temperature at a single point $\endgroup$
    – Adam Martin
    Commented Feb 14, 2016 at 0:05
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    $\begingroup$ No, using multiple points will not reach a hight temperature. Imagine warming your house with a red hot stone, you may think that two red hot stones will heat your house faster, and you'd be right. But once your whole house has reached the temperature of the stones, bringing one hundred more stones to your house will not make it any hotter. $\endgroup$
    – rodrigo
    Commented Feb 14, 2016 at 0:05

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In short, the answer is no: you cannot heat an object to a temperature higher than that of the source of the light.

This follows from the thermodynamic rules that were described in the article, but more fundamentally it depends on the Brightness Theorem of classical optics, and related theorems.

For the full analysis, in excruciating detail, see "Intensity, Brightness and Etendue ´ of an Aperture Lamp": http://www.physics.princeton.edu/~mcdonald/examples/lamp.pdf

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