PHYS 445 Lecture 18  MaxwellBoltzmann distribution
18  1
© 2001 by David Boal, Simon Fraser University.
All rights reserved; further resale or copying is strictly prohibited.
Lecture 18  MaxwellBoltzmann distribution
What's Important:
•
mean speeds
•
molecular flux
Text
: Reif
Mean speeds
The MaxwellBoltzmann speed distribution that was derived in the previous lecture
has the appearance
where
F
(
v
)
dv
is the number of particles per unit volume with a speed between
v
and
v
+
dv
.
Now, there are three common measures of the velocity distribution
v
2
1/2
≡
v
rms
(
root mean squarespeed
)
v
≡
(
mean speed
)
˜
v
≡
(
most likely speed
)
.
These quantities are straightforward to calculate, and the details can be found in Reif.
Root mean square
One can work through the integral of
F
(
v
) to obtain
v
rms
, or
just invoke the equipartition theorem in three dimensions:
3
2
k
B
T
=
[
mean kineticenergy
]
=
1
2
mv
2
or
v
rms
=
3
k
B
T
m
.
(18.1)
Mean
Evaluate the integral
v
=
1
n
v F
(
v
)
dv
=
8
π
k
B
T
m
0
∞
∫
(18.2)
Most likely
Determine the derivative
dF
(
v
)
dv
=
0
⇒
˜
v
=
2
k
B
T
m
(18.3)
0
v
F
(
v
)
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PHYS 445 Lecture 18  MaxwellBoltzmann distribution
18  2
© 2001 by David Boal, Simon Fraser University.
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 Spring '08
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 Physics, David Boal

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