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PHYS 445 Lecture 15  Equipartition theorem
15  1
© 2001 by David Boal, Simon Fraser University.
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Lecture 15  Equipartition theorem
What's Important:
•
equipartition theorem
•
applications: ideal gas, harmonic oscilator, 3D lattice
Text
: Reif
Skip Secs. 7.1 to 7.4
Cheap tricks: equipartition theorem
A simple expression for the mean energy per degree of freedom arises when the total
energy of a system
•
is quadratic in its variables;
e.g.
K
=
p
2
/2
m
or
V
=
kx
2
/2
•
separates into singlevariable expressions, such as
K
=
p
1
2
/2
m
1
+
p
2
2
/2
m
2
.
For a given degree of freedom (labeled by an index
i
), let us write the energy as
i
=
b p
i
2
where
p
i
could be a coordinate or its time derivative.
Then
i
=
∫
i
exp(

ß
[
E
rem
+
i
])
dq
1
..
dq
f
dp
1
..
dp
f
∫
exp(

ß
[
E
rem
+
i
])
dq
1
..
dq
f
dp
1
..
dp
f
where
E
rem
is the remaining energy in the system, other than
i
:
E
rem
=
E

i
.
Because the energy separates into a piece that depends on
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This note was uploaded on 09/07/2009 for the course PHYS 445 taught by Professor Davidboal during the Spring '08 term at Simon Fraser.
 Spring '08
 DavidBoal
 Physics

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