09/09/09
Professor Philip S. Marcus
ME106
Homework Problem Set 2  Pressure
Do Problems in Chapter 2 (6
th
edition): 2.29, 2.34, 2.58 and 2.61. (or equivalently,
in the 3
rd
edition: 2.25, 2.34, 2.52, and 2.64).
O2.1) Find expressions for the density
ρ
(
z
) and entropy
S
(
z
) of an isothermal at
mosphere as a function of height z and the density
ρ
0
and entropy
S
0
at sea level
(assumed to be at
z
= 0.) Now make a plot (use MATLAB or any other program
ming tool you want) of the density as a function of height assuming that the pressure
at sea level is 14.7 pounds per square inch and that the temperature is 310 K. Start,
by using
P
=
ρ R T
and the value of
R
for air from Lecture
1
by finding the value
of
ρ
0
. What is the functional form of the entropy as a function of height (i.e., ex
ponential, logarithmic, powerlaw, linear, cubic, quadratic, etc.)? In an isothermal
atmosphere does the entropy increase or decrease with increasing height?
O2.2) If the density of the atmosphere were in hydrostatic equilibrium and
ρ
(
z
) =
ρ
0

α z
, what are
T
(
z
),
P
(
z
), and
S
(
z
) in terms of
α
,
ρ
0
,
g
,
P
0
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 Fall '08
 Morris
 Thermodynamics, Atmosphere, Fundamental physics concepts

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