Part of my question on Can a low-energy source/object heat a higher-energy object via radiative heat transfer? asked if a 100W lightbulb could heat a blackbody in a vacuum indefinitely, presuming the blackbody is perfectly insulated against the radiation it emits (which insulation lets the flashlight's energy through).
The up-voted answer was "Yes, the blackbody's temperature should rise indefinitely (or at least until the system melts down into a liquid)."
I'm trying to reconcile this with the fact that, contrary to this, a flame can't heat something hotter than itself (see: can a flame raise the temperature of an object higher than itself?).
What's the distinction? And, if both are true, couldn't we "hack" it with a system like this:
- Have a flame continuously heat a piece of metal.
- The flame will reach equilibrium with the metal at some point, e.g. when flame temperature equals metal temperature.
- At this point (as well as throughout the process) the metal will be emitting thermal electromagnetic radiation, as all hot things do. It will be emitting energy some amount of watts of energy.
- Direct this radiation towards the same apparatus as in the first question. Now we have an equivalent situation (the 'flashlight' being replaced by 'the EM emissions of a heated piece of metal'). Therefore the target blackbody will heat up indefinitely, i.e. hotter than the flame.
This feels like cheating, and from what I understand, you can't cheat the thermodynamic Gods. My question then is where does this break down?
EDIT: to clarify my question is, if both are true it seems we can rig the flame to a system that emits radiative energy and then heats a black body to hotter than the flame itself. Can it really be so? If yes then why doesn’t this violate any laws, and if no then why not?