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I am interested in finding out whether the term 'Internal Energy' can be used in both of the following cases:

  • In the case of a macroscopic body upon which light is incident, the internal energy would designate the total energy absorbed by the body, causing it to heat up (in the absence of other heating mechanisms)

  • In the case of a low-density system of atoms upon which light is incident and absorbed, the internal energy would designate the total amount of energy absorbed by the atoms and therefore would relate to the sum of the excitation and kinetic energies of the atoms.

Are both uses of the term 'Internal Energy' correct, or would it only apply to one of the cases? In both cases it would refer to the total energy absorbed by the system from radiation, but how the energy is distributed in the system (kinetic vs excitation) would depend on the type of system.

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Internal energy refers to all the energy you don't care about (or can't distinguish) macroscopically. It's totally unimportant in what form it is present as all forms of energy are equal.

More precisely, by Boltzmann statistics the probability of a microstate with energy $E$ is $p \sim \exp(-E / k_B T)$ law. $E$ here refers to total energy of the microstate which of course consists of both kinetic and interaction terms. The internal energy of a macrostate is then a thermal average of energies of individual microstates.

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At least in mechanics, internal energy covers all forms of energy except bulk kinetic (mass time velocity squared over two (including rotational)). It could be elastic energy, thermal energy, gravitational potential energy, and/or chemical energy. The individual energies of random atomic motion, are usually defined to be part of the thermal energy, which is part of internal, rather than kinetic energy, which applies only to bulk motion.

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