As you can tell, conservation of energy is a fundamental physics principle. Assumptions of "perfect conversion and no entropic losses" aren't applicable, and anyone who mistakenly thinks they are should read through those examples to learn about conservation of energy.
Utter nonsense. They are perfectly applicable in the kind of THOUGHT EXPERIMENT we were discussing, which is the ONLY context relevant to this discussion. Your own equations were proof of this... nowhere did you factor in conversion inefficiences. NOT ONCE.
Stop being a goddamned hypocrite, and go away.
But net radiative power out of a boundary around the source = "radiative power out" minus "radiative power in", so the equation Jane just described also says:
NO!!!!!
As I have explained to you innumerable times now, you can also consider your heat source, by itself, that "sphere". The only NET radiative power out comes from the electrical power in.
Further, the cooler walls do not contribute any of that NET power out. That's what net means.
If the sphere under consideration is the spherical power source itself, and no NET radiative power is absorbed from the cooler outside objects (a requirement of thermodynamics), then the only NET radiative power out ultimately comes from the electrical power in.
Power in = power out.
You don't understand what NET means. That is your failure, not mine. As I have explained to you many, many times now, you are counting some radiation twice, which is simply bad math.
END. You are wrong. You were proved wrong long ago. GO AWAY and stop bothering me with your nonsense.