Exercise #3
Astronomy Ranking Task:
The Seasons
Description: In the figure below parallel beams of sunlight are projected through equal sized
cutouts of a screen and then strike a spherical globe at locations A - D. Note that A and C are at
the same latit
PHYSICS 112
Homework 1 Solutions
1. (a) From g (U ) = CU 3N/2 we have, with S = kB ln g ,
S
U
1
=
T
= kB
N
3N 1
,
2U
(1)
and hence
3
U = N kB T .
2
This is the form of the energy of an ideal gas, as we will discuss later in the course.
(b) Dierentiating E
PHYSICS 112
Homework 4 Solutions
1. The specic heat, per unit volume of a crystal at low temperature is given by
Cphonon
12 4 n
=
kB
5
T
D
3
,
while the specic heat per unit volume of a photon gas is
Cphoton
4 2
( kB T ) 3 ,
=
kB
15( c)3
h
which can be ob
PHYSICS 112
Homework 3 Solutions
1. As shown in class (see also handout) the allowed values of k in k -space form a regularly space grid
with spacing /L (where the system is of size L in each direction) and kx , ky etc. are taken to be
positive.
[Note: Th
PHYSICS 112
Homework 2 Solutions
1. (a) If the two states have energy 0 and , the partition function is given by
Z = 1 + e ,
where = 1/kB T , and so the free energy is given by
F = kB T ln Z = kB T ln 1 + e .
(b) The energy is given by
U=
1
(F ) =
.
e +1
PHYSICS 112
Homework 5 Solutions
1. We have
f ( + ) =
1
1
=
,
exp[ ( + )] + 1
exp[ ] + 1
and similarly (with replaced by )
f ( ) =
Now
1
.
exp[ ] + 1
1
ex
1
=
=1
,
x+1
x
e
1+e
1 + ex
and so, with x = , we have
f ( + ) = 1 f ( ) .
Hence the probability tha
PHYSICS 112
Homework 6 Solutions
1. (a) The thermodynamic identity is
T dS = dU + P dV.
If the volume changes by a small amount dV , and the temperatures by dT at constant entropy
we have 0 = dU + P dV . Now dU = CV dT since the energy of an ideal gas onl
PHYSICS 112
Homework 9 Solutions
1. As discussed in class the (Helmholtz) free energy of the van der Waals gas is given by
F = N kB T
n Q ( V N b)
N
+ 1 N a,
N
V
ln
where
mkB T
2 2
h
nQ =
3/2
.
(a) The entropy is given by
S=
F
T
V ,N
= N kB l n
=
N kB l n
PHYSICS 112
Homework 8 Solutions
1. (a) In the reaction
e + H + H
we have e = 1, H + = 1, H = 1 and so the law of mass action gives us
nQe nQH +
1
ne nH +
=
nH
nQH ZH (int)
(1)
where ZH (int) = e E is the internal partition function of the hydrogen atom (
PHYSICS 112
Homework 7 Solutions
1. Since
n
L
where n = 1, 2, 3, the number of states with wavevector between k and k + dk is (L/ )dk , If
the corresponding (innitesimal) range of energy is d then we have
k=
L
() d = 2 dk,
(1)
where the factor of 2 comes
Comins DEU 3e Ch 01 Quiz 1 completed
The correct answers are written in bold, italic and underlined.
The most important questions to study for the exam are highlighted.
1. We know that stars in our local region of the universe are moving
relative to one a
Comins DEU 3e Ch 03 Quiz 2 completed
The correct answers are written in bold, italic and underlined.
The most important questions to study for the exam are highlighted.
1. Which way does the light ray bend when it passes obliquely (i.e., at an angle to th
Comins DEU 3e Ch 03 Quiz 3 completed
The correct answers are written in bold, italic and underlined.
The most important questions to study for the exam are highlighted.
1. In the periodic table of elements, elements that have similar chemical properties
Comins DEU 3e Ch 03 Quiz 1 completed
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The most important questions to study for the exam are highlighted.
1. Violet light differs from red light in that
violet light has a longer wavelength t
Comins DEU 3e Ch 02 Quiz 3 completed
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The most important questions to study for the exam are highlighted.
1. The two most common substances in the universe are
carbon and oxygen.
hydrogen an
Comins DEU 3e Ch 02 Quiz 1 completed
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The most important questions to study for the exam are highlighted.
1. One of the aims of the scientific method is
to establish a faith system about the
Comins DEU 3e Ch 02 Quiz 2 completed
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The most important questions to study for the exam are highlighted.
1. A planet moving in an ellipse with the Sun at one focus will have a speed that is
Comins DEU 3e Ch 04 Quiz 1 completed
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The most important questions to study for the exam are highlighted.
1. How many molecules of nitrogen will there be in a sample of air at the Earth's surf
Comins DEU 3e Ch 04 Quiz 2 completed
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The most important questions to study for the exam are highlighted.
1. The fundamental process that shaped the Moon's surface was
heat from the Moon's in
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) On which of the following dates is Earth closest to the Sum?
A) July 31
B) Jan. 3
C) June 21
1)
D) Dec. 21
2) At which phase (s) of the Mo
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) When a planet is at conjunction, it will
A) be at the farthest position from the Sun in the sky, as seen from the Earth.
B) set at the sam
Comins DEU 3e Ch 05 Quiz 4 completed
The correct answers are written in bold, italic and underlined.
The most important questions to study for the exam are highlighted.
1. Observation of clouds and structure in Jupiter's atmosphere
demonstrate that this p
Comins DEU 3e Ch 05 Quiz 3 completed
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The most important questions to study for the exam are highlighted.
1. Which of the following descriptions best characterizes the surface of
Mars?
More-o
Comins DEU 3e Ch 05 Quiz 1
The correct answers are written in bold, italic and underlined.
The most important questions to study for the exam are highlighted.
1. The planet with the shortest year is
Mercury.
Venus.
Mars.
2. A colleague tells you that a
Comins DEU 3e Ch 05 Quiz 2 completed
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The most important questions to study for the exam are highlighted.
1. Venus appears to be very bright in our sky at certain times because
it is covered
PHY 206
SPRING 2012
Lab Text: J. Rollino. Laboratory Notes for Phy 205-206 revised ed.
WEEK of:
Experiment
1/16
Labs do not meet. Students obtain lab
manuals and USB storage device (Flash key).
1/23
Electrostatics I (Notes on Blackboard)
1/30
Electrostati