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One model that estimates the properties of an electron gas at absolute zero in metals is the Fermi gas.
The electrons, being Fermions, have to be in different quantum states, which leads the electrons to get very high typical velocities, even at absolute zero.
The maximum energy that an electrons can have at absolute zero is called the Fermi energy.
The Fermi temperature is defined as this maximum energy divided by Boltzmann's constant, and is of the order of 80, 000 K for typical electron densities found in metals.
For temperatures significantly below the Fermi temperature, the electrons behave in almost the same way as at absolute zero.
This explains the failure of the classical equipartition theorem for metals that eluded classical physicists in the late 19th century.

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