268 Problems €4 Solutions on Thermodynamics €4 Statistical Mechanics
where
2096
For Na metal there are approximately 2.6 x conduction electrons/
cm3, which behave approximately as a free electron gas. From these facts,
(a) give an approximate value (in eV) of the Fermi energy in Na,
(b) give an approximate value for the electronic specific heat of Na at
(UC, Berkeley)
room temperature.
Solution:
(a) The Fermi energy is
h2 312
EF = - (3r2 F)
2m
N
V
We substitute h = 6.58 x
1022/~m3 into it and obtain EF w 3.2 eV.
eV.s, m = 0.511 MeV/c2 and - = 2.6 x
(b) The specific heat is
where me = 9.11 x kg is the mass of the electron, k = 1.38 x
J/K is Boltemann’s constant, and kT w - eV at room temperature.
We substitute EF and the other quantities in the above expression and
obtain C M 11.8 J/K.g.
1
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