PHYS 445 Lecture 7  Ensembles and averages
7  1
© 2001 by David Boal, Simon Fraser University.
All rights reserved; further resale or copying is strictly prohibited.
Lecture 7  Ensembles and averages
What's Important:
•
ensembles and averages
•
heat, work, energy
Text
: Reif
Demo
: mechanical equivalent of heat
Further reading
: Secs. 210, 211.
Ensembles and averages
Suppose we have a group of hard spheres confined to a container.
The spheres have
no other interaction with each other beyond their hardcore potential: when they
collide, they exchange energy and momentum according the usual conservation laws.
Suppose that we now want to find the probability of a sphere having a given speed
s
.
Few spheres are moving either very slowly or very fast. The probability density
distribution might look like:
where
P
(
s
)
ds
is the probability of finding a sphere with speed between
s
and
s
+
ds
.
We can imagine two ways of measuring this distribution:
measure all spheres at once
make repeated measurements
on a single sphere
P
(
s
)
s
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© 2001 by David Boal, Simon Fraser University.
All rights reserved; further resale or copying is strictly prohibited.
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 Spring '08
 DavidBoal
 Physics, Thermodynamics, Energy, Work, Heat, David Boal

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