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I'm specifically looking at the case of the Sun's corona emitting light that then heats up other bodies on Earth. These bodies can never attain a higher temperature than the Sun's corona.

I know the obvious answer as to why this is is that the second law of thermodynamics says so. But the fact that the light emitted somehow encodes within it the temperature of the thing that emits it is what is strange to me. Are there not bodies of different temperatures that emit the same frequencies of light? Is there some deeper set of statistical mechanics taking place such that the second law of thermodynamics holds?

It makes sense for bodies directly interacting to end up at the same temperature, and at the microscopic scale this would seem to happen because of electrostatic interactions between the bodies. Whichever atom in an atom-atom interaction has a greater kinetic energy will impart kinetic energy on the atom with a lower kinetic energy until equilibrium. A bit of handwaving, I'm sure, because we are considering classical atom-atom interactions, but it makes quite good sense and probably isn't completely off. However, light seems to somehow encode the temperature of what emitted it, and I can't explain how the second law of thermodynamics holds with it.

Why is it that the light emitted by a body of a certain temperature will not heat up a body of the same or greater temperature? Answers I'd like would sort of explain the interactions taking place such that the second law makes some sort of sense, perhaps with Newton's laws, statistical mechanics, Maxwell's equations... whatever else makes sense would be appreciated, really.

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  • $\begingroup$ Is that truly the case? Any source? I think using a lens large enough, you'll be able to obtain local temperatures higher than at the source. $\endgroup$ – SF. Dec 22 '16 at 13:34
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    $\begingroup$ "the fact that the light emitted somehow encodes within it the temperature of the thing that emits it is what is strange to me." That is what the black body radiation spectrum represents. $\endgroup$ – Lewis Miller Dec 22 '16 at 14:07
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    $\begingroup$ @SF. Doesn't your statement violate second law? $\endgroup$ – Deep Dec 23 '16 at 5:16
  • $\begingroup$ @Zero: Entropy in the whole system increases. Localized decreases of entropy are not violating second law of thermodynamics. (otherwise existence of life would be violating it) $\endgroup$ – SF. Dec 23 '16 at 15:44
  • $\begingroup$ @SF. I asked that only because your statement sounds like it is possible to transfer heat from colder to hotter body, without any external input of work. $\endgroup$ – Deep Dec 24 '16 at 14:16
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Let's take a simple example of the Sun heating some body e.g. the Earth.

The key point to remember is that light ray trajectories are symmetric i.e. for every light ray that leaves the Sun and hits the Earth a light ray from the Earth can move along the same path in the opposite direction and hit the Sun. So at the same time that the Sun is heating the Earth the Earth is heating the Sun.

This symmetry means that for any pair of bodies there will be a net flow of radiant energy from the hotter one to the colder one. So the Sun cannot heat the Earth, or anything else, to a higher temperature than its own surface.

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Look into black body radiation. https://en.wikipedia.org/wiki/Black-body_radiation#Explanation

The body being heated is radiating too, so for it to increase in temperature radiation in must be greater than radiation out. (possible, but doesn't tend to occur in naturally - e.g. in astronomy).

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