Word Count : 414

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In the Sommerfeld free electron theory, the electrons in a metal are treated as a degenerate Fermi gas. At finite temperature (T), the chemical potential (\mu) and electronic specific heat (c_v) can be obtained using the Fermi–Dirac distribution. The total number of electrons is: [ N = \int_0^\infty g(\varepsilon) f(\varepsilon) d\varepsilon ] where (g(\varepsilon) = \frac{3N}{2\varepsilon_F} \sqrt{\frac{\varepsilon}{\varepsilon_F}}) is the density of states and (f(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/k_B T}+1}) is the _______ _________ ___ ____ ________ ___ ________ ______ ______ ___.
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