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Unformatted text preview: N noninteracting spin1/2 fermions in an area A with nonrelativistic energy dispersion E ( k ) = ¯ h 2  k  2 / (2 m ). (a) Find an expression for the Fermi energy, E F , of this gas expressed as a function of n = N/A , m , and fundamental constants. (b) Obtain an exact expression for the chemical potential, μ , of this gas valid at arbitrary temperature. (c) Show that in the limit T → 0 the expression for μ obtained in Part (b) becomes equal to the Fermi energy obtained in Part (a). (d) For k B T ¿ E F the speciﬁc heat of this gas is C V = π 2 3 Nk B ˆ k B T E F ! , (you do not need to show this). In one or two sentences explain qualitatively why this speciﬁc heat is so much lower than the speciﬁc heat of a classical 2D monatomic gas ( C cl . V = Nk B ). Hint : For Part (b) you may ﬁnd the following integral useful: Z ∞ 1 z1 e y + 1 dy = ln(1 + z ) . 2...
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 Spring '09
 Bonesteel
 Thermodynamics, mechanics, Energy, Statistical Mechanics, Fundamental physics concepts, 2m

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