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Final Exam for Physics/ECE 176
Professor Greenside
Wednesday, May 4, 2011
Please read the following before starting the test:
1. This exam is closed book and will last the entire exam period.
2. No calculators or other electronic devices are allowed.
3. Look over the entire exam and get a sense of its length, what kinds of questions are being asked, and
which questions are worth the most points.
4. Answer the truefalse and multiple choice questions on the exam itself, answer all other questions on
extra blank pages. If you need extra pages during the exam, let me know.
5. Please write your name and the problem number at the top of each extra page.
6. Unless otherwise stated, you must justify any written answer with enough details for me to understand
your reasoning.
7. Please write clearly: if I can not
easily
understand your answer, you will lose credit.
8. If you are not sure about the wording of a problem, please ask me during the exam.
1
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Problems That Require Writing
1.
(8 points)
A germ can be approximated as a rigid sphere of radius about a micron (10

6
m) that
is filled with water (density
≈
10
3
kg
/
m
3
). To the nearest power of ten and in units of microns per
second (i.e., body lengths per second), estimate the magnitude of the germ’s speed that arises from
the germ being in equilibrium with pond water at room temperature.
2.
(12 points)
During the semester, you learned two paradoxical facts: that “it is not possible to boil
water with boiling water” but “it is possible to boil water with ice”. Explain briefly how to demonstrate
these statements experimentally, and also discuss briefly the physics that explains these facts.
3.
(8 points)
What is the generalization of the Gibbs factor
e

β
(
E
s

μN
s
)
for the case of a small system
like a porous balloon that can exchange energy
E
s
, particles
N
s
, and volume
V
s
with some reservoir?
4.
(a)
(5 points)
Describe precisely what is meant by “Einstein’s model of a solid”.
(b)
(20 points)
Assume that an Einstein solid that consists of
N
identical atoms is in equilibrium
with a reservoir whose temperature has the constant value
T
. Derive an expression for the heat
capacity
C
(
T
) of the Einstein solid.
Next, plot
C/
(
Nk
) qualitatively versus
kT/
, where
is the constant spacing between energy
levels, and give some numerical values on the horizontal and vertical scales to indicate the scales
involved. Also discuss briefly how your plot relates to the equipartition theorem and to the third
law of thermodynamics.
(c)
(10 points)
Motivated by Einstein’s model, the Dutch scientist Peter Debye obtained a more
accurate description of the heat capacity
C
(
T
) of a solid by using more realistic assumptions
than those of Einstein. His theory led to the following result for the thermal energy
U
of a solid
consisting of
N
atoms in a volume
V
at temperature
T
:
U
=
9
NkT
4
T
3
D
Z
T
D
/T
0
x
3
e
x

1
dx,
(1)
where the socalled Debye temperature
T
D
is given by
T
D
=
hc
s
2
k
6
N
πV
1
/
3
,
(2)
where
c
s
is the speed of sound waves in the solid, and is assumed to be a constant.
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 Spring '08
 Behringer
 Physics, Thermodynamics, photon gas, equilibrium photon gas

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