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If the missing energy is not radiated away, then there are two
remaining explanations:
1) Some of the energy "goes" into some other form.
2) The law of conservation of energy is wrong.
Lacking *any* reason whatsoever to think otherwise, I'm going to
place my money on the "radiated away" option, but you are certainly
free to try to do the experiment and see for yourself. In contrast,
however, to the previously suggested calorimetry experiment (which
you showed little interest in doing) *this* would be a difficult
experiment to perform.