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 1 
Physics 2213 HW #2 — Solutions
Fall 2008
18.30
[Mixed Gases]
a)
All gases in the mixture are at the same temperature. The average kinetic energy of a molecule in a
gas depends only on the temperature, not on the molecule’s mass, so the average kinetic energy is the
same for the molecules of each element.
b)
Equation (18.19) shows that for constant temperature, the rms speed is proportional to the inverse
square root of the mass, and so
rms Kr
rms Rn
rms Ne
rms Ne
20.18
20.18
0.491,
0.301 and
83.80
222.00
v
v
v
v
=
=
=
=
rms Rn
rms Kr
83.80
0.614.
222.00
v
v
=
=
18.37
[Oxygen Molecules]
a)
.
J
10
6.21
K)
K)(300
J
10
381
.
1
)(
2
3
(
21
23


×
=
×
=
kT
K
2
3
ave
=
b)
21
5
2
2
ave
ave
3
23
2
2(6.21 10
J)
2.34 10 m s .
(32.0 10 kg mol) (6.023 10 molecules mol)
2
K
(v )
m


×
=
=
=
×
×
×
c)
s,
m
2
3
10
84
.
4
mol)
kg
10
(32.0
K)
K)(300
mol
J
3(8.3145
3
×
=
×
⋅
=
=

M
RT
v
rms
which is of course the square root of the result of part (b).
d)
s)
m
2
23
3
10
84
.
4
(
mol)
molecules
10
(6.023
mol)
kg
10
(32.0
×
×
×
=
=

rms
A
rms
v
N
M
mv
=
2.57
×
10

23
kg
⋅
m s
This may also be obtained from
mol)
molecules
10
(6.023
mol)
kg
10
J)(32.0
10
2(6.21
2
23
3
21
×
×
×
=
=


ave
mK
p
rms
e)
The average force is the change in momentum of the atom, divided by the time between collisions.
The magnitude of the momentum change is twice the result of part (d) (assuming an elastic collision), and
the time between collisions is twice the length of a side of the cube, divided by the speed. Numerically,
2
21
19
rms
rms
ave
ave
rms
2
2
2(6.21 10
J)
1.24 10
N.
2
(0.100m)
mv
mv
K
F
L v
L
L


×
=
=
=
=
=
×
f)
2
17
ave
ave
1.24 10
Pa.
p
F
L

=
=
×
g)
( 29 ( 29
5
17
21
ave
1.013 10 Pa
1.24 10
Pa
8.15 10 molecules.
p p

=
×
×
=
×
h)
A
A
N
RT
pV
N
n
N
=
=
=
1.00 atm
(
29
1.00 L
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This note was uploaded on 10/25/2008 for the course PHYS 2213 taught by Professor Perelstein,m during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 PERELSTEIN,M
 Magnetism, Energy, Kinetic Energy, Mass, Heat

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