Pop quiz! The picture below is a solar power facility wherein light from the sun is collected by mirrors and focused onto the top of a collecting tower. Fluid within the tower is heated by this light and the hot fluid is used to generate power. We won’t care about that in this quiz though; we’re just assuming that all the energy goes into heating the tower until its own radiant heat output is equal to that coming in from the mirrors.
Here’s the quiz setup. There’s nothing stopping you from adding as many mirrors as you want to this installation – for the purposes of this question you can put it in space and use a million square miles of mirrors, all focused onto the tower. As you dump more and more energy into the tower, it will eventually reach some high equilibrium temperature as it emits its own radiant heat just like the heating element in a toaster.
So the question is this: how hot can this equilibrium temperature be, if you add as many mirrors as you want? Is there any limit? If not, how are you not breaking the laws of thermodynamics by spontaneously transferring energy from a colder body (the sun) to a hotter one (the tower)? If so, why?
As a hint, there is a simple and unambiguous answer, but it’s not necessarily one you heard in thermodynamics class.