Homework #8
— PHYS 603 — Spring 2008
Deadline:
Thursday, April 17, 2008, in class
Professor Victor Yakovenko
Office: 2115 Physics
Web page:
http://www2.physics.umd.edu/
~
yakovenk/teaching/
Textbook: Silvio Salinas,
Introduction to Statistical Physics
Springer, 2001, ISBN 0387951199
Do not forget to write your name and the homework number!
Each problem is worth 10 points.
Ch. 9 The Ideal Fermi Gas
1. Problem 9.1. Compressibility of the Fermi gas. [10 points]
The compressibility is defined in Eq. (3.43). Only derive an equation for the compress
ibility and do not calculate a numerical value for metallic sodium.
2. Entropy and spin susceptibility of the Fermi gas at
T
¿
ε
F
. [20 points]
(a) Entropy of the Fermi gas.
As discussed in Problem 3 of Homework 7, the entropy of the Fermi gas is
S
=
γV
Z
dε D
(
ε
)
s
(
ε
)
,
s
(
ε
) =

f
(
ε
) ln
f
(
ε
)

[1

f
(
ε
)] ln[1

f
(
ε
)]
,
(1)
where
f
(
ε
) = [
e
β
(
ε

μ
)
+ 1]

1
is the Fermi distribution function,
γ
is the number
of fermion species (
γ
= 2 for spin 1/2), and
D
(
ε
) is the energy density of states.
Sketch the function
s
(
ε
) in the case
T
¿
ε
F
. Indicate the position, the width,
and the height of the peak in this function.
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 Fall '08
 V.Yakovenco
 Physics, Work, Statistical Mechanics, Fundamental physics concepts, Fermi gas

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