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If the "internal energy" of an object is thermal photons and thermal
phonons and electron band energy and chemical bond energy and nuclear bond
energy and everything else, then as I understand it, the usual meaning of
"heat" is "thermal photon energy plus thermal phonon energy." Heat is
blackbody radiation within an object, plus the hypersonic white-noise of
thermal vibrations of the lattice. (Uh, do we need to add the energy
contained in the electrons of hot metals?) As long as chemical or nuclear
reactions or phase changes aren't adding or subtracting thermal
photons/phonons within the object, then "heat" is conserved because energy
is conserved.