9  1
© 2001 by David Boal, Simon Fraser University.
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Lecture 9  Temperature and specific heat
What's Important:
•
thermal equilibrium
•
temperature
•
zeroth law of thermodynamics
•
equipartition theorem
•
specific heat of an ideal gas
Text
: Reif
Approach to equilibrium (thermal)
Let's return to the problem of two systems
A
and
A'
being brought into thermal (but not
mechanical) contact.
Notes
:
•
After contact, averages are made over the energies because the systems can
exchange energy.
•
The most probable energies are very close to the average energies.
By conservation of energy:
E
f
+
E
'
f
=
E
i
+
E
'
i
Note that no averages need be performed over the initial states, as they are in
isolation and their energies are constant.
Defining
Q
as the energy
absorbed
by
A
, (and
Q'
by
A'
) then
Q
=
E
f

E
i
=
E
'
i

E
'
f
= 
Q
'
or
Q
+
Q'
= 0.
(9.1)
What about the entropy?
Recall that the probability in the combined system is given by
P
(
E
) = const •
(
E
)
'
(
E'
)
The probability of being in the final state is always greater than, or equal to, the
probability of being in the initial state, reflecting the number of accessible states:
(after) ln
f
(
E
f
) + ln
'
f
(
E'
f
)
≥
ln
i
(
E
i
) + ln
'
i
(
E'
i
)
(before)
But we know that entropy is related to
by
S
=
k
B
ln
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 Spring '08
 DavidBoal
 Physics, Heat, Zeroth Law Of Thermodynamics

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