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Ph 111.01
December 10, 2008
PS 14b (37)
n, T, V
R
A
Problem 1 = Walker P. 1726.
A
390
mL spherical flask contains
0.075 mol of an ideal gas at a temperature of
237
K. What is the
average force exerted on the walls of the flask by a single molecule?
N
Solution.
From the volume we can get the radius of the
sphere:
()
1
1
3
3
63
3 390 10
3
0.0453 m
44
xm
V
R
ππ
−
⎛⎞
⎜⎟
=
=
=
⎝⎠
3
4
3
VR
π
=→
And from
R
we can calculate the area:
2
22
A=4 R
4
0.0453 m
0.0258 m
==
Now, we can easily calculate the pressure per molecule from the idealgas equation of state
in the form
PV
NkT
=
The pressure per molecule is thus
23
18
1.38 10
J/K
237
8.386 10
Pa/molecule
390 10
xK
T
x
−
−
−
=
Pk
NV
And, multiplying by the area,
(
)
18
2
19
8.386 10
Pa/molecule 0.0258 m
2.164 10
N/molecule
Ax
x
−−
=
F
L
0
Δ
L
d
FP
NN
Problem 2 = Walker P. 1727.
A rock climber hangs freely from a nylon rope that
is 12 m long and has a diameter of
6.7
mm. If the rope stretches
6.4
cm, what is the
mass of the climber?
kg
Solution.
The stretch of the rope is related to the stress by
0
L
Am
g
L
Δ
FY
Solving for the mass
m,
we find
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 Fall '08
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