I've constructed a 25cm x 25cm hot plate out of an aluminum plate with flat nichrome wire under it as a resistive element.
I blackened the top with a pitch black spray paint, and placed it at the base of a 23cm x 23cm x 23cm styrofoam box. I lined the inside walls and ceiling of the box with aluminum foil, but the top of the hot plate remains black.
At room temperature the plate is 24.4C or so. According to the Stefan Boltzmann Law, it's thus emitting 23.513W of thermal radiation.
However, when I run 13.997W of current through it and let it attain a steady state, the steady state temperature is 77.6C. According to the same law, it's now emitting 45.4W of radiation.
So I've increased the rate of energy input into the system by 13.997W, but now it's radiating 21.89W more energy as a result! That's about a 1.56x multiplier effect.
How does this not violate the laws of physics? It seems to violate the first law of thermodynamics in that it's generating more energy than I put in, or perhaps the second law as it's being heated more by its own heat reflected from within the box?
However, it actually happened, so I know that it must not be!