Homework #9
— PHYS 404 — Fall 2011
Deadline:
Tuesday, November 10, 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 30 points.
Ch. 5 Free Energy and Chemical Thermodynamics
1. Problem 5.22, 5 points.
μ
(
P
) for a gas.
Additional question:
In Problem 1.16, you derived how the pressure
P
(
z
) changes
with the height
z
. Substituting
P
(
z
) into Eq. (5.40), prove the formula for
μ
(
z
) given
in Problem 3.37.
Hint:
In general, the constant of integration in Eq. (5.40) may depend on
z
:
μ
(
T, P, z
) =
μ
0
(
T, z
) +
kT
ln(
P/P
0
)
.
(1)
Eq. (1) gives the chemical potential of a gas at the given temperature
T
, pressure
P
,
and height
z
.
Atmosphere is in diffusive equilibrium (molecules can move anywhere), so the chemical
potential must be constant at all heights
z
, i.e.
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 Fall '11
 Anlage
 Thermodynamics, mechanics, Work, Statistical Mechanics, Professor Victor Yakovenko, ClausiusClapeyron relation

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