I read this article on xkcd.xom, from its spin-off blog "What If?" and that answer made me wonder.
It was mentioned in that article that a very hot but indestructible box would eventually be able to instantly superheat the air around it, which would then cause massive drafts that lift it high up into the atmosphere.
My question is, although he did mention 18.7 GW of energy inside the 1x1x1 box, how hot would a sphere have to be to do the same, and what is the relation of its size and shape to be able to superheat the air in one big burst (at 1 atm at the surface, and then I imagine it would have to fall back down into the ground)?
And how hot would a disc have to be to do the same, but remain stable? What factors in real life (aside from the massive amounts of energy required) would cause this to be unsustainable/wobbly?