Thread by @gro_tsen

These cool images remind me of a physics question I have: I've been told before that “for thermodynamical reasons”, it's not possible to achieve a temperature greater than that of the surface of the sun (~6000K) in a solar furnace. Several questions: … •1/3

https://twitter.com/UrbanFoxxxx/status/1351511804955013120

Is this correct? What exactly is the thermodynamical argument in question? (It sounds superficially reasonable, but I can't figure out how to formalize it.) Can we reformulate it in the context of geometrical optics? What would it then say? And, more importantly: … •2/3

… what, exactly, are the assumptions used in the reasoning? (Clearly we can use solar panels and electric heating to produce a temperature far beyond 6000K, so I'd like to know exactly what the “solar furnace” hypothesis means. Something like “no cold sink involved”?) •3/3

✵︎Update:✵︎ I got a number of interesting answers. The xkcd ‘what if’ page whatif.xkcd.com/145/ is very good. The key notion from geometrical optics is that of “étendue” (which I see as the natural measure on the Grassmannian) and its conservation. •4/(3+7)

The key idea from thermodynamics is, of course, that heat must flow from hot to cold. But of course, thermodynamics alone does not prohibit heating something above the temperature of the hot source! We can do this with a heat engine and a cold sink. •5/(3+7)

So I'm 99% satisfied, but still not quite 100%: I have yet to understand the precise link between the idea of conservation of étendue in geometrical optics and the “you can't create a cold sink using optics” part (presumably) of the thermodynamical argument. •6/(3+7)

(I mean, geometrical optics and étendue don't speak about temperature, and thermodynamics alone doesn't forbid something reversible from creating heat beyond the hot source, so we still need a bit of reasoning to link the two together.) •7/(3+7)

This is maybe a mathematician's kind of bickering, but I really like to make sure, when presented with a reasoning, that all the required assumptions have been used somewhere in the reasoning — or it can't be correct — and that I know where. •8/(3+7)

If the reasoning doesn't say something about geometrical optics, it would seem to apply to using a solar panel and electricity to heat something above 6000K, which is possible: so the reasoning should make it clear why it doesn't apply to this situation. •9/(3+7)

In other words, my question is now: what's the precise property of optical systems, NOT applicable to thermodynamical systems in general, which guarantees that it is thermodyn.‌ly impossible to produce a temperature higher (or I guess, lower) than those given as input. •10/(3+7)