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PHYSICS 420
THERMAL PHYSICS
J. D. Maynard
READING ASSIGNMENT:
Reif, Chapter 5
Homework #6
Due Lecture 33
You are on your honor to work on this on your own, or get hints from Professor Maynard or
the Teaching Assistant only.
1.
In a temperature range near absolute temperature
T,
the tension force
F
of a stretched
plastic rod is related to its length
L
by the expression
F
=
aT
2
(
L

L
0
)
where
a
and
L
0
are positive constants,
L
0
being the unstretched length of the rod. When
L
=
L
0
,
the heat capacity
C
L
of the rod (measured at constant length) is given by the
relation
C
L
=
bT,
where
b
is a constant.
(a)
Write down the fundamental thermodynamic relation for this system, expressing
dS
in
terms of
dE
and
dL.
(b)
The entropy
S
(
T, L
) of the rod is a function of
T
and
L.
Compute (
∂S/∂L
)
T
.
(c)
Knowing
S
(
T
0
, T
0
)
,
Fnd
S
(
T, L
) at any other temperature
T
and length
L.
(It is most
convenient to calculate Frst the change of entropy with temperature at the length
L
0
where
the heat capacity is known.)
(d)
If one starts at
T
=
T
i
and
L
=
L
i
and stretches the thermally insulated rod quasi
statically until it attains the length
L
f
,
what is the Fnal temperature
T
f
? Is
T
f
larger or
smaller than
T
i
?
(e)
Calculate the heat capacity
C
L
(
T, L
) of the rod when its length is
L
instead of
L
0
.
(f)
Calculate
S
(
T, L
) by writing
S
(
T, L
)

S
(
T
0
, L
0
) = [
S
(
T, L
)
S
(
T
0
,
0
, L
)] + [
S
(
T
0
, L
)

S
(
T
0
, L
0
)]
and using the result of part (e) to compute the Frst term in the square brackets. Show that
the Fnal answer agrees with that found in (c).
1
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The fgure illustrates a soap flm (shown as
crosshatched) supported by a wire Frame. Because
oF surFace tension the flm exerts a Force 2
σl
on the
cross wire. This Force is in such a direction that it
tends to move this wire so as to decrease the area
oF the flm.
The quantity
σ
is called the surFace
tension oF the flm and the Factor 2 occurs because
the flm has two surFaces. The temperature depen
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