Homework #5
— PHYS 404 — Fall 2011
Deadline:
Thursday, October 13, 2011, in class
Professor Victor Yakovenko
Oﬃce: 2115 Physics
Web page:
http://www2.physics.umd.edu/
~
yakovenk/teaching/
Textbook: Daniel V. Schroeder,
An Introduction to Thermal Physics
Addison Wesley Longman, 2000, ISBN 0201380277
Do not forget to write your name and the homework number!
Total score is 35 points.
Ch.3 Interactions and Implications
1. Problem 3.5, 10 points.
The energy
U
of an Einstein solid at low
T
.
First, express the entropy
S
(
U,N
) of an Einstein solid from Problem 2.17 in terms of
the total energy
U
=
q±
and the number of oscillators
N
. You should have found the
multiplicity Ω = (
eN/q
)
q
in Problem 2.17.
Second, introduce the temperature
T
using the equation 1
/T
=
∂S/∂U
and the expres
sion for
S
(
U,N
) from the ﬁrst step. Solve this equation to express the energy
U
(
T,N
)
as a function of
T
and
N
.
Additional Question:
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 Fall '11
 Anlage
 Thermodynamics, mechanics, Work, Statistical Mechanics, Entropy, Black hole, NJ, ej, Professor Victor Yakovenko

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