Show that (8.11.8) and (8.11.13) both follow from (8.11.12) for an electron gas with two degenerate spin

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Show that (8.11.8) and (8.11.13) both follow from (8.11.12) for an electron gas with two degenerate spin states, in the two limits of a T = 0 electron gas with a Fermi level, and in the high-temperature, Maxwell–Boltzmann limit.

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