- PHYSICS 7B WORKBOOK CUSTOM EDITION FOR THE UNIVERSITY OF CALIFORNIA, BERKELEY 2007 REVISIONS BY AUSTIN HEDEMAN PEARSON C'llstorn . Publbhiug ~ Cover Art: Chicago 86 by Patrick Linehan Copyright © 2008, 2007 by Pearson Custom Publishing All rights reserved. Permission in writing must be obtained from the publisher before any part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system. All trademarks, service marks, registered trademarks, and registered service marks are the property of their respective own ers and are used herein for identification purposes only. Printed in the United States of America ,.\ . :t- ISBN 0-536-51128-4 2007100043 1 MC Please visit our web site at www.pearsoncustom.com ' ---- PEARSON Custom PEARSON CUSTOM PUBLISHING Publishing 501 Boylston Street, Suite 900, Boston, MA 02116 A Pearson Education Company TABLE OF CONTENTS • WORKSHEETS THERMODYNAMICS Tl Ideal Gases: The Ideal Gas Law and Internal Energy.................................... 3 T2 Thermal Expansion, Kinetic Theory, and Calorimetry ................................. 9 ~ 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 ,-""\ T7 Entropy: Other Topics ................................................................................... 39 ,-""\ 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 ' ' ' ' Physics 7B Worksheets ' 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 ' 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. ❖ ' ' 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 ' 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. '