Homework #6
— PHYS 603 — Spring 2007
Deadline:
Tuesday, May 1, 2007, in class
Professor Victor Yakovenko
Office: 2115 Physics
Web page: http://www2.physics.umd.edu/˜yakovenk/teaching/
Textbook: Gregory H. Wannier,
Statistical Physics
Dover 1987 reprint of the 1966 edition, ISBN 048665401X
Do not forget to write your name and the homework number!
Each problem is worth 10 points.
Ch. 7 Thermodynamic Exploitation of the Second Law;
Mass Transfer Problem
1. UMD qualifier problem, August 2002: Boiling and freezing of water at high
elevation.
(a)
Near Earth, the pressure in a liquid or gas decreases as we move away from the
earth. Show that, for a small vertical displacement
dz
, the change of pressure
dP
is
dP
=

ρ g dz
(1)
where
ρ
(
z
) is the mass density of the fluid.
(b)
Assuming that the air near Earth can be treated as a perfect gas in equilibrium
with a constant temperature
T
, show that Eq. (1) yields the Boltzmann distri
bution for the variation of the number density
n
(
z
) with the height
z
. (It is also
called the barometric distribution.)
(c)
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 Spring '08
 V.Yakovenco
 Thermodynamics, Work, Statistical Mechanics, DP, Professor Victor Yakovenko

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