Table Of Content-
PHYSICS 7B
WORKBOOK
CUSTOM EDITION FOR THE UNIVERSITY OF CALIFORNIA, BERKELEY
2007 REVISIONS BY AUSTIN HEDEMAN
PEARSON
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TABLE OF CONTENTS
• WORKSHEETS
THERMODYNAMICS
Tl Ideal Gases: The Ideal Gas Law and Internal Energy.................................... 3
T2 Thermal Expansion, Kinetic Theory, and Calorimetry ................................. 9
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T3 Heat Transfer: Conduction and Radiation .. . .. .. .. .. .. . . . . . .. . . .... .... . .. . . .. . . . . . . . . . . . .. . . 13
~ T4 The First Law of Thermodynamics . . . . . . . . . . . . . . . . . .. . . .. . . . . . .. . . . ... . . ..... .. .. .. ... .. . . . . . . . . 19
TS Engines and Efficiency ................................................................................. 25
T6 Entropy and the Second Law ........................................................................ 31
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T7 Entropy: Other Topics ................................................................................... 39
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ELECTRICITY
El Coulomb's Law ............................................................................................. 45
E2 Electric Fields ............................................................................................... 49
E3 Gauss's Law .................................................................................................. 55
E4 Conductors .................................................................................................... 63
E5 Electric Potential ......................................................................................... 67
E6 Capacitance .................................................................................................. 73
E7 DC Circuits ................................................................................................... 81
MAGNETISM
Ml Introduction to Magnetism ........................................................................... 85
M2 The Lorentz Force Law ................................................................................. 87
M3 Magnetic Fields ............................................................................................ 93
M4 Ampere's Law.............................................................................................. 99
M5 Faraday's Law ............................................................................................. 107
M6 Inductance................................................................................................... 115
M7 Displacement Current and Maxwell's Equations ...................................... 121
TIME DEPENDENT CIRCUITS
Cl RC Circuits ................................................................................................. 125
C2 LR Circuits ................................................................................................. 129
C3 LRC and AC Circuits ................................................................................. 133
C4 AC Circuits - Impedance ........................................................................... 137
SUPPLEMENTAL HANDOUTS
Supp 1 Free Expansion of an Ideal Gas .................................................................. 141
Supp 2 Entropy of the Ideal Gas . . . . . . . ........ .. ... . . .. . . .. . . . .. . . . . . . . . . . . . .. .. ... .. . . .. . . . . .. . . . . . . . . . . . . 145
Supp 3 Vectors and Right Hand Rules in Magnetism . . . . . ....... .. . .. . .............. .. .. .. .. .. . . 14 7
Supp 4 Differential Equations for Circuit Problems .............................................. 149
T-S 1 Ideal Gas Transformation ........................................................................... 153
T-S2 Efficiency of the Carnot Engine ................................................................. 155
•LABS
Lab 1 Thermodynamic Cycles and Engines ... . ...................... ....... ........ .. .. .. .. . . . . . . . 161
Lab 2 Equipotential Lines and Electric Fields . .. .. .. .. . . .. . .. .............. .. . . .. . . .. .. .. ..... ... . 171
Lab 3 DC circuits . . . . . . . . . . . .. . . . . . . . . . . .. .... .. .. .. . . . . . . . . . . . . . . . . . . . . . . . . .. ... . .. .. .. .. .. .. .. .. ... .. ........... 177
Lab 4 Charge-to-Mass Ratio of Electron ............................................................. 181
Lab 6 Oscilloscope and Time Dependent Circuits ............................................... 191
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Physics 7B
Worksheets
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Physics 7B WS Tl (rev. 2.0) Page3
T-1. Ideal Gases:
The Ideal Gas Law and Internal Energy
Part 1: The Ideal Gas Law and the p-V Diagram
Questions for discussion (Part 1)
1. An ideal gas confined to a box exerts pressure on the walls of the box. Where does this pressure
come from? (In other words, what is going on microscopically?)
2. How could you measure the pressure of a gas? ("Use a pressure gauge" is not an answer, unless
you also explain how a pressure gauge works. The same goes for barometers, etc.)
3. If you cause an ideal gas to contract, does the temperature go up or down? Explain.
Page4 WS Tl (rev. 2.0) Physics 7B
Problems (Part 1)
You should complete your work for the "Problems" on separate sheets of paper. Do not work in the
margins below; you'd like to be able to make sense of your work later when you review for.the exams!
1. A box of length 1 meter and cross-sectional The number of particles on the left is N1 =
area A has a moveable partition inside it. 3xl023. The number of particles on the right
There is some gas on either side of the is N2 = 2x 1023• The gas on both sides is in
partition. thermal equilibrium at the same temperature
T. When the partition settles down to its final
lm position, find the lengths L1 and L2 of the left
<E---------;>
and right sides of the box. ❖
2. Your baby brother is toddling around the a) If the temperature inside your house is 25°
house, playing with a toy balloon. You decide Celsius, while the temperature inside the
to teach him something about physics, so you freezer is -10° Celsius, then by what
take the balloon away from him and hide it in percentage will the volume of the balloon
the freezer. (His cries are enough to convince change? We will take the pressure inside the
you that he is excited about this learning balloon as constant.
experience.)
c) Sketch a p-V diagram for the gas inside the
When you put the balloon in the refrigerator, balloon as it cools inside the regrigerator.
it will shrink. (Try it and see!) Label the axes as completely as possible
according to the given information. ❖
3. A canister with thin metal walls is immersed Then, using the piston that forms the lid of
in water with temperature T. (See figure.) the canister, you compress the air until it
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Initially the canister holds air at atmospheric occupies half of its original volume.
pressure.
a) Assuming that the water maintains the air at
temperature T throughout the process, what
will be the final air pressure in the canister?
b) Sketch this process on a p-V diagram. Label
the axes as completely as possible according to
the given information. ❖
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Physics 7B WS Tl (rev. 2.0) Page5
4. Now would be a good time to look back over b) Does your answer to Discussion Question 3
your answers to the Discussion Questions still make sense, in light of your answers to
above. Problems 3 and 4? ❖❖
a) Do any of the diagrams on this worksheet
suggest answers to Discussion Question 1?
Part 2: Energy Contained in an Ideal Gas
Summary
The total energy of a system of particles is called the "internal energy" of the system, Einternal.
Equipartition theorem: If a system is in thermal equilibrium at temperature T, then each
. independent quadratic term (or degree of freedom) in its energy has average value equal to (1/2)kT.
1 1 1
For a single particle of any type (KE translational)= (2 mvx2) + (2 mvy2) + (2 mvz2)
(KE translational) = 23 kT
(d degrees of freedom) Einternal = dNkT
2
For a system of monatomic particles Einternal = N<KEtranslationaJ>
3
2
Einternal = NkT
1 1
For a system of diatomic particles Einternal = N<KEtranslationaJ>· + N(2 Ixoox2) + N(2 !y0ly2)
5
(at medium temperature) Einternal = 2 NkT
For a system of particles with
d
d degrees of freedom Einternal = - NkT
2
Page 6 WS Tl (rev. 2.0) Physics 7B
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Questions for discussion (Part 2) '
1. A box with total volume Vo is divided in half by a partition. On the left-hand side of the
partition, there is a sample of monatomic ideal gas with initial pressure po and initial temperature
To. On the right-hand side of the partition, the box is empty.
The partition is then suddenly removed, and the gas expands freely to fill the entire box. Soon
the gas is in thermal equilibrium again.1
a) What is the final temperature of the gas? Explain.
b) What is the final pressure of the gas?
c) Can you explain why the pressure has changed? (Note: "pV = NkT'' is not an explanation!)
Hint: Think about where the pressure comes from: When the box suddenly doubles in size, what
can you say about the particles' collisions with the walls?
2. I have two samples of ideal gas, identical except that sample A is at temperature TA= 100 K,
while sample B is at temperature TB = 400 K. (Both samples are in thermal equilibrium at their
respective temperatures.) If you could somehow become microscopically tiny, and could see the gas
particles close up, then what difference would you observe between the particles of A and the
particles of B? (Try to answer both qualitatively and quantitatively.)
1 Note: For further discussion of this situation, see "Free Expansion of an Ideal Gas," in the
Supplementary Material at the end of the workbook.
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