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If the size of the penny was reduced to just a few atoms, wouldn't changing the number of atoms in the penny affect the rate at which the penny itself could emit radiation through blackbody emission? If so, I would expect there would be a size at which the penny could be small enough that it's temperature could grow arbitrarily large once the heat flux in = heat flux out from the penny.

I don't know very much thermodynamics, but I'm not sure that thermodynamic temperature is well-defined for a system consisting of "just a few atoms".

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