Problems and Solutions on Thermodynamics and Statistical Mechanics

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.

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