Consider an ensemble of M localized atoms, each having only two energy levels ɛ1 = +ɛ and ɛ2 = −ɛ. Each single particle

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Consider an ensemble of M localized atoms, each having only two
energy levels ɛ1 = +ɛ and ɛ2 =
−ɛ. Each single particle energy level may accommodate up to 2
electrons with spin 1/2 (i.e. it is 2-fold degenerate). Find
the chemical potential corresponding to a total number of
electrons, N = 2M (i.e. 2 electrons per atom). Find the
corresponding total energy E(T) and heat capacity C(T). Calculate
the low (kBT << ɛ) and high (kBT
>> ɛ) temperature limit and sketch it.