Physics 363 Previous Announcements
Spring, 2011

• Solutions to Assignment 10 are available to download.

• Answers to 1-minute questionnaires are available to download. These include questionnaires spanning April 4 through April 21. Some answers help to clarify recent lectures so I would encourage everyone to look through these answers.

Friday, April 22

• Assignment 11, the last assignment, is now available to download. It is due on Thursday, April 28 by 5pm, in the folder just outside my office.

• I scheduled recitations in Room 090 next week on
  1. Tuesday, April 26, 4-5 pm.
  2. Wednesday, April 27, 3-4 pm.
  3. Thursday, April 28, 3-4 pm.
  and I will be glad to meet with you outside these times as my schedule permits. However, I may need to go out of town next Monday or Tuesday and I'll email the class as soon as I know more.

Thursday, April 21

• Today's lecture notes are available to download.

• Reading: Section 7.4 and Section 5.3.

Tuesday, April 19

• Today's lecture notes are available to download.

Monday, April 18

• Solutions to Assignment 9 are now available.

• Quiz 5 solutions are now available.

• Reading:
  • In Chapter 7: Sections 7.1 and 7.2, pages 271-278 of Section 7.3, and all of Section 7.4.
  • In Chapter 5, Section 5.3 on phase transitions.
  Note: this is the reading through the end of the semester.

• Recitations this week have been set up for:
  • Tuesday, April 19, from 2:30-3:30 PM.
  • Wednesday, April 20, from 2:00-3:15 PM.
  • Friday, April 22, from 2-3 PM.
  These are all in Room 090 in Physics.

Thursday, April 14

• Today's lecture notes have been posted.

  If you would like to see the details of how to derive the Fermi-Dirac and Bose-Einstein distributions (occupation numbers) more carefully and rigorously, see the book Statistical and Thermal Physics by Reif that is on reserve for the course in Perkins library. In particular, Reif shows how to handle the case of a finite number of particles for a boson system.

Wednesday, April 13

• Assignment 9 is now available and is due a week from today, in the folder outside my office.

• Reading:
  • In Chapter 7: Sections 7.1 and 7.2, pages 271-278 of Section 7.3, and all of Section 7.4.
  • In Chapter 5, Section 5.3 on phase transitions.
  Note: this is the reading through the end of the semester.

Tuesday, April 12

• Lecture notes for April 12 have been posted.

• Quiz 6 has been canceled to free up time for a lecture on phase transitions.

Tuesday, April 5

• April 5 lecture notes have been posted.

• Solutions to Assignment 8 have been posted.

• Quiz 5, the second to the last quiz of the semester, will be given this Thursday at 10:05 AM sharp. (The last quiz is scheduled for two weeks from Thursday, on April 21.) As usual, please come a few minutes early to settle in: bookbags to the side, only writing utensils on the desk, spread the desks so that there is plenty of space around you.

  Quiz 5 will cover lectures, reading, and homeworks since Quiz 4 (March 24), up to and including today's Tuesday lecture (April 5). All key equations and data will be given, your job will be to show that you know how to use the appropriate equations and can answer appropriate conceptual questions. Key topics you should know for Quiz 5 are:

  • Approximating a partition function by an integral in the high-temperature limit, as we did for the energy levels of a rotating heteronuclear diatomic molecule.

  • Working with probability densities, which include skills like:
    • how to normalize a non-negative function f(x,y) to obtain a probability density D(x,y).
    • how to use a probability density to obtain the average value of some expression X(x,y).
    • how to obtain lower-dimensional probability densities from a multidimensional probability density by integrating over certain variables.
    • how to obtain the probability density for a new variable p=p(q) from a probability density for a variable q by a change of variables, e.g, changing Cartesian coordinates to polar or spherical coordinates.

  • How to calculate the probability density for the velocity of a molecule in an equilibrium gas, and then use that density to calculate the Maxwell speed distribution in two or three spatial dimensions.

  • How to apply the Maxwell speed distribution to properties of molecules (e.g., how to calculate the most likely, average, and rms speeds), and apply the speed distribution to kinetic theory, e.g., to effusion or the cold plate problem.

  • How to evaluate various Gaussian integrals related to the Maxwell speed distribution, e.g., by differentiating with respect to a parameter, by integration by parts, by making a variable substitution, or by evaluating the Gamma function.

  • Understand how one can use the speed distribution for effusing molecules to test whether a gas satisfies the Maxwell speed distribution.

  • How to identify a thermodynamic potential that depends on certain experimental thermodynamic variables, how to derive the thermodynamic identity for that potential, and how to express various thermodynamic quantities in terms of the potential.

  • How to show that the thermodynamic potential for a small system in contact with some reservoir decreases monotonically until the system attains thermodynamic equilibrium.

  • How to calculate the pressure, entropy, and chemical potential of a system in terms of the partition function Z of the system.

Monday, April 4

• Assignment 9 is now available. It is due outside my office by 5pm this Friday.

  Note: This is a relatively short assignment, especially if you have been keeping up with the recommended reading since, with the exception of the effusion problem, I chose straightforward problems that are closely related to the assigned reading.

• Reading: Finish the assigned reading in Chapters 5 and 6 and start reading Sections 7.1 and 7.2 in Chapter 7.

• Recitation will be this Wednesday, from 2-3 PM in Room 090. If you can't make this time or want to discuss the problems at some other time, I will be glad to meet with you as my schedule permits.

• Quiz 4 grades and scores have been posted on Blackboard, the graded quizzes will be returned to you this Tuesday. The updated grade statistics Mathematica file has also been updated so you can see the class score distribution and how grades were assigned.

  I will be glad to meet with you if you have questions about the grading, about the answers, or if you want to discuss how to do better. Again, the Quiz 4 solutions have been posted and it is worth your time to make sure you understand the solutions.

Thursday, March 31

• March 31 lecture notes are available to download.

• Solutions to Quiz 4 have been posted. I have not yet finished grading all the quizzes but hope to post the scores and grades by Friday afternoon.

Wednesday, March 30

• March 29 lecture notes are now available for download.

• Answers to the March 29 1-minute questionnaires have been posted.

• Reading: Please read Schroeder sections 6.3-6.7 and pages 149-152, 156-158, and 161-166 from Chapter 5.

• Recitation: I will hold recitation this Wednesday from 2-3 PM in Room 090 but am glad to meet with you at other times as my schedule permits.

Monday, March 28

• Quiz 5 will be on Thursday, April 7, and will cover all material since Quiz 4.

• Two applets for studying the Maxwell-Boltzmann distribution in a 2D ideal gas:
  • Maxwell speed distribution applet, can run in reverse.
  • Maxwell speed distribution applet, multiple particles possible

• Answers to March 21 and March 17 1-minute questionnaires are available to download. The answers discuss a bit further where the Earth's magnetic field comes from and also include a more detailed explanation of why the heat capacity of a substance decays as 1/T² for large temperatures T if the microscopic components have a finite number of energy levels.

Saturday, March 26

• Reading: Please read Schroeder sections 6.3-6.7 and pages 149-152, 156-158, and 161-166 from Chapter 5.

• Assignment 8 is available to download, it is due by the beginning of class this Thursday.

• Recitation: I will hold recitation this Wednesday from 2-3 PM in Room 090 but am glad to meet with you at other times as my schedule permits.

Thursday, March 24

• The Duke Chapter of the Society of Physics Students (SPS) is holding an Astronomy Night at the Duke Forest observatory, led by Physics Professor and string theorist Ronen Plesser. You will have a chance to learn something about the spring night sky, see various stars, planetary nebulas (stars that have shed their outer atmosphere after dying), stellar clusters, galaxies, and other objects, and finish the evening looking at Saturn, its rings, and some of its moons. If you want to come, be outside Physics around 7:45pm and dress warmly(!), people will be carpooling from Physics to the site about 10 minutes away. If you have a car and are willing to drive, please bring your car and park in front of Physics around 7:45pm.

Tuesday, March 22

• Reading: To prepare for the next few lectures, please read Schroeder sections 6.3-6.5 and pages 149-152, 156-158, and 161-166 from Chapter 5.

• Today's lecture notes are available to download.

• Solutions to Assignment 7 are available to download.

• Office hours on Wednesday will be 3-4 pm in Room 090.

• Thursday's Quiz 4 will cover material since the midterm: Sections 6.1 and 6.2 of Schroeder, my lecture notes up to and including today (Tuesday), and any material addressed in Assignment 7.

  Some things you do not need to study:

  • You can ignore the few comments I made in my notes about thermodynamic potentials (pages 3 and 4 of my March 15 lectures notes). I will discuss those ideas next week.

  • You can ignore pages 234-236 of Schroeder regarding rotation of diatomic molecules, I will discuss that material on Thursday, after the quiz.

  Concepts you should especially think about:

  • The assumptions, logic, and technical details of how the Boltzmann factor and partition function were obtained when calculating the probability for a small system, in equilibrium with a reservoir, to be in a state s with energy E_s. I would recommend the discussion I gave in class and in my notes over what Schroeder gave.

  • From a knowledge of the states and their energies for some system, how to use the Boltzmann factor and partition function to calculate physically important features of a system such as:
    1. the probability of finding the system in a certain state;
    2. the relative probabilities of two states;
    3. statistical averages such as the mean and standard deviation of some quantity X_s that varies from state to state.
    4. how to relate statistical averages to derivatives of the Boltzmann factor.
    5. the heat capacity from the average energy.

  • The low- and high-temperature behaviors of the Boltzmann factor and partition function.

Saturday, March 19

• Sunday's recitation will be held 5-6pm in Room 090. I have also set aside 4:30-5:30pm this Monday for office hours, if you want to come by and ask questions.

Thursday, March 17

• Today's lecture notes have been posted.

Wednesday, March 16

• Answers to the 1-minute questionnaires of March 15 and February 14 have been posted.

• The three remaining quizzes are scheduled on these dates:
  1. Quiz 4: Thursday, March 24
  2. Quiz 5: Thursday, April 7
  3. Quiz 6: Thursday, April 21

• Midterm scores and grades have been posted on Blackboard. You can download the Mathematica notebook containing the grade statistics to see the score distribution and how grades were assigned. As usual, I am glad to meet with you if you have any questions whatsoever about how your exam was graded or about the answers to the exam questions.

Tuesday, March 15

• Solutions to the midterm exam have been posted. Graded midterms will be returned Thursday, with scores and grades posted on Blackboard.

• Reading: Sections 6.1 and 6.2 of Schroeder.

• Today's lecture notes have been posted.

• Assignment 7 is now available and is due on Tuesday, March 22.

• Inner Life of a Cell, 3-minute version. You can find the full video with a narrative description at the BioVisions site.

Tuesday, March 1

• Solutions to Quiz 3 are available to download.

• Solutions to Assignment 6 are now available.

• NY Times article Remapping Computer Circuitry to Avert Impending Bottlenecks about severe implications of energy consumption for improving the capacity of future computers. If you didn't think that the material in Physics 363 matters, this should help change your mind.

Sunday, February 27

• A reminder that I will have official office hours tomorrow (Monday) from 2-3pm in Room 090, and Wednesday from 2-3:15pm in Room 090. If you can not make these times and want to meet, please email me what days, and times on those days, you are free I will do my best to meet with you during one of those times.

• The midterm will cover all material discussed so far this semester, up to and including last Thursday's lecture of Feb 24, including all recommended reading in Schroeder, and including material addressed in all the homework assignments, including Assignment 6. The exam will have the format of a long quiz: a mix of multiple choice questions, true-false questions, and questions where you have to write up answers showing scientific insight and technical competence. Roughly 75% of the total points will derive from the written questions. All key formulas and physical parameters will be provided for you.

  Here are some previous midterms and some previous quizzes, with solutions, so you can get a feeling for the kinds of questions I have asked in the past.

  That being said, you do not need to master every little detail that has been discussed so far. Instead, make sure you know basic definitions and concepts (equilibrium, relaxation time, heat, work, macrostate, microstate, multiplicity, entropy, heat capacity, equipartition, extensive vs intensive, paramagnet, magnetization M of a paramagnet, the three laws of thermodynamics, reversible vs irreversible processes, etc), and that you can solve representative problems of the sort that you have seen emphasized in lecture, in Schroeder, and in the homeworks. For example, on the midterm you may see problems that ask you to

  • analyze some process of an ideal gas, in which you have to calculate the change in internal energy, change in temperature, work done on the gas, heat transferred to the gas, and change in entropy. If the process is cyclic, you may be asked to calculate the efficiency of the process as a heat engine, by calculating the ratio W/Q, of "sum of work done by the gas during the cycle" to the "sum of heat transferred to gas during the cycle", and compare that efficiency to the maximum possible allowed by the second law of thermodynamics.

  • identify macrostates and accessible microstates for some novel system, calculate the multiplicity, then calculate the entropy, temperature, heat capacity, or other appropriate quantity of interest. (The discussion about paramagnets and Problem 3.34 on pages 114-115 of Schroeder are good examples of what you should be able to do.) You should be able to deduce the qualitative form of U(T) and C(T) from the qualitative form of S(U).

  • use Taylor series or Stirling's formula or a combination to get some insightful approximation to some physical expression.

  • calculate the total entropy change for some process involving substances (not necessarily gases) coming into equilibrium with one another, e.g., by using the relation of entropy to heat capacity.

  • use kinetic theory, say for particles with isotropic velocities, to calculate the rate with which some quantity is delivered to the wall of a container per unit time and per unit area.

  • estimate the value of some expression to one significant digit or to the nearest power of ten and think about the physical meaning of your estimate.

  • calculate the temperature, pressure, and chemical potential of a system from knowledge of the entropy S(U,V,N) as a function of energy, volume, and particle number, and use these expressions to derive an equation of state analogous to PV=NkT that describes how the key thermodynamic variables are related to one another.

  • use the thermodynamic identity of some system to derive relations between thermodynamic variables when other thermodynamic variables are held constant. For example, dU=TdS - PdV + μ dN can be used to show that dN/dV=P/μ for a system in which the energy and entropy are held constant (dU=dS=0).

  I will not be asking any detailed questions about chemical potentials beyond using the basic definition and the fact that equilibrium requires equality of the chemical potential for each interacting subsystem, and I will not be asking any technical questions about paramagnets although you need to understand the key qualitative properties of paramagnets, such as how the entropy, heat capacity, and magnetization vary with temperature and with external magnetic field.

  The lists of topics to focus on for previous quizzes (see the Previous Announcements webpage remains a useful summary of points you should now, you should also look those over when preparing for the midterm.

Friday, February 25

• Quiz 3 scores and grades have been posted on Blackboard. I will put the graded quizzes in an envelope marked "363 Quizzes" outside my office door, in the journal rack to the left of my door, so you can pick up your quiz at your convenience (and I will bring the quizzes to class on Tuesday). I will post solutions to Quiz 3 later this weekend.

Thursday, February 24

• Today's lecture notes are available for download.

  I also updated the February 22 lecture notes, to include the missing pages 2-4.

• As discussed in lecture, next Tuesday's class will be a recitation rather than lecture during which you can work on your homework, practice quiz and midterm problems from previous years, or just ask me or your classmates questions that you might have about the material. I would recommend that you bring your copy of Schroeder and a laptop so you can look up previous quiz and exam files.

• The 363 midterm exam will be given on Thursday, March 3. It will start at 10:05 AM and last the entire class period. The format will be similar to a long quiz: some written questions, some multiple choice questions, and some true-false questions.

  Sometime this weekend, I will post topics since Quiz 3 that you should especially focus on for the midterm as well as some topics you will not have to study since they were introduced so recently before the midterm.

  The lists of topics to focus on for earlier quizzes are still valid for what to think about for the midterm, you can find these on the Previous Announcements webpage.

Tuesday, February 22

• Answers to today's 1-minute questionnaires are available to download.

• Today's lecture notes are available to download.

• Reading: All of Chapter 3, Section 4.1, and pages 144-147.
  We will cover Chapter 3 rather quickly since we have already discussed many of its points, such as how the condition of maximum entropy of an isolated system leads to the temperature, pressure, and chemical potential being uniform throughout a system (Sections 3.1, 3.4, and 3.5). The two sections with substantial new material are Section 3.2, on how one can compute the entropy change during some process via some integral involving a heat capacity, and Section 3.3 on the paramagnet. I plan to finish Chapter 3 by February 24 and then start Chapter 6.

Friday, February 25

• Quiz 3 scores and grades have been posted on Blackboard. I will put the graded quizzes in an envelope marked "363 Quizzes" outside my office door, in the journal rack to the left of my door, so you can pick up your quiz at your convenience (and I will bring the quizzes to class on Tuesday). I will post solutions to Quiz 3 later this weekend.

Sunday, February 20

• Answers to the 1-minute questionnaires of last Thursday's class are available to download.

• Answers to Assignment 5 are available to download.

Saturday, February 19

• Assignment 6 is now available.

  Note that this assignment is due a week from this Tuesday, on March 1 in class, and it will be the only assignment before spring break. No late assignments will be accepted since I will be making the solutions available on March 1, so you will have the answers in time to review for the midterm exam on Thursday, March 3.

• Office hours I will have office hours on Wednesday, Feb 23 from 2-3pm and Monday, Feb 28 from 2-3pm in Room 090 near my office. If you can't make these times, send me an email and we can try to meet at another time.

• Solutions to Assignment 4 have been posted. Solutions to Assignment 5 will be posted later this weekend.

• Quiz 3 will be this Tuesday at 10:05 AM so please come five minutes early to be ready by 10:05. Some topics to especially focus on:
  • The fundamental assumption of statistical physics, all accessible microstates are equally likely, and why this implies that some macrostates are much more likely to be observed than other macrostates.

  • The entire chain of reasoning related to Einstein solids: how to compute the multiplicity for a single solid, how to compute the multiplicity for two coupled Einstein solids, how to derive the high-temperature approximation to the multiplicity (page 63 of Schroeder), how to show that the multiplicity has a sharp peak of width 1/sqrt(N), and how to extract physically useful quantities like the entropy and heat capacity from various expressions. Problem 2 of Assignment 5 is important here.

  • How to calculate the multiplicity of an ideal gas and how to derive the Sackur-Tetrode equation from that multiplicity.

  • How to deduce the qualitative behavior of U(T), C(T), and S(T) from a given qualitative curve S(U).

  • Various technical skills:
    • How to use Stirling's formula to simplify binomial coefficients and other expressions involving factorials.
    • How to carry out Taylor series approximations to second order.
    • The trick of differentiating a definite integral with respect to a parameter to get the value of a new definite integral.
    • The definition of the Gamma function and how to compute new values from known values using the recursion relation Eq. (B.14)
    • How to make sense of and use the formula for the surface area of a d-dimensional hypersphere.
    • How to show that a high power of a function f(x) is approximated by a particular Gaussian.

Thursday, February 16

• Quiz 3 will be given next Tuesday so please come a few minutes early so you can be prepared to start at 10:05 AM.

  Sometime this weekend, I will post some topics to especially focus on. As before, it will cover all material discussed since Quiz 2 including homeworks, lectures (up to and including today's lecture), and related reading in Schroeder.

• Today's lecture notes are available to download.

• Reading: All of Chapter 3 We will cover Chapter 3 rather quickly since we have already discussed many of its points, such as how the condition of maximum entropy of an isolated system leads to the temperature, pressure, and chemical potential being uniform throughout a system (Sections 3.1, 3.4, and 3.5). The two sections with substantial new material are Section 3.2, on how one can compute the entropy change during some process via some integral involving a heat capacity, and Section 3.3 on the paramagnet. I plan to finish Chapter 3 by February 24 and then start Chapter 6.

Tuesday, February 15

• Quiz 2 solutions are available to download.

• Answers to today's 1-minute questionnaires are available to download.

• Today's lecture notes are available to download.

• Scores and grades for Quiz 3 have been posted on the 363 Blackboard webpage, and detailed answers will be posted on Tuesday. The statistics of the quiz scores and how grades were assigned can be obtained from this Mathematica file.

Saturday, February 12

• Reading: Sections 2.1-2.6 and Appendixes B.1-B.4 about Gaussian integrals, the Gamma function, Stirling's formula, and area of a hypersphere. You do not need to understand the derivations in these appendices, but do need to know the definitions and some elementary manipulations using the definitions..

• Answers to the 1-minute questionnaires of last Thursday's class are now available.

• Assignment 5 is now available. Note the due date and place: Friday at 3pm, at my office. I will place a folder in the journal rack just to the left of my office door where you can drop your homework off.

  Most of the problems are in the form of guided tutorials so the time to complete the assignment should not be too bad but two of the problems will involve a fair amount of algebra. Also, do start this assignment early so that you have time to ask questions if questions arise. To the extent my schedule is free, I will be glad to meet with you during the week.

  Please email me if you reach 8 hours before completing the assignment. If enough students need more time, I will give an extension.

  Besides the usual office hours on Wednesday from 2-3:15pm in Room 090, I will keep some time free on Thursday and Friday afternoons.

Thursday, February 10

• The lecture notes for today's class are now available.

Wednesday, February 9

• Answers to the 1-minute questionnaires from yesterday's class have been posted.

• I will hold office hours in Room 090 today from 2-3:15pm if you have questions about the homework or course material. If you can't make this time, email me and I can try to meet with you at another time.

Tuesday, February 8

• Reading: Sections 2.1-2.5 and Appendixes B.1-B.4 about Gaussian integrals, the Gamma function, Stirling's formula, and area of a hypersphere.

• Today's lecture notes are available for download.

• Today's lecture slides are available for download. Clicking on pictures and links will bring you to webpages where you can view animations, e.g., the convection simulations and spiral defect chaos convection state that I showed in class.

• Mathematica notebook coupled-einstein-solids.nb generates Figures 2.4 and 2.5 in Schroeder, you can modify this to explore coupled Einstein solids on your own.

Sunday, February 6

• Solutions to Assignment 3 have been posted.

• Answers have been posted for the 1-minute questionnaires of February 3.

Friday, February 4

• Reading: Read Sections 2.1 through  2.4 in Schroeder for next week.

  For those of you who have not taken Physics 143 or 211, you may find it helpful to browse through Appendix A of Schroeder on quantum mechanics, especially pages 364-366 about the uncertainty principle, pages 370-372 about the quantum harmonic oscillator, and pages 377-379 about spin. The latter is especially useful as we discuss a spin-1/2 paramagnet.

• Assignment 4 is now available. Because the previous homework was longer than average, this assignment is shorter than average.

• Solutions:
  • The solutions to Quiz 1 have been updated to include the answers to the true-false questions.
  • Solutions to Assignment 2 have been posted.

• Quiz 2 will be this Tuesday, February 8 and will cover material since Quiz 1 and through Thursday's lecture (February 3) as well as what you have read in Schroeder and learned through the homework assignments up to and include Assignment 3. Please make sure to come a few minutes early to class, the quiz will start promptly at 10:05 AM.

  As before, some example 363 quizzes and exams with solutions can be found here. The first midterm from 2009 also has questions (with solutions) that can help you prepare for the quiz.

  The following are topics that you should focus on:

  • The concepts of thermal energy, heat, and work.

  • How thermal energy, heat, and work are related by the first law of thermodynamics, Eq. (1.24) of Schroeder.

  • How to calculate the change in energy ΔE, heat Q transferred, and work W transferred for some process represented by a curve in the PV diagram of an ideal gas, including isobaric, isochoric, isothermal, and adiabatic processes. The key equations are Eqs. (1.23), (1.24), and (1.29) in Schroeder.

  • The concept of heat capacity and specific heat, and that the heat capacities at constant pressure and at constant volume are related by Eq. (1.45) of Schroeder.

  • How to use heat capacities to estimate the final temperature of objects that are placed in contact with one another (Problem 1.41 of Schroeder).

  • How to estimate the heat capacity of a molecular gas and of a crystalline solid using the equipartition theorem. In particular, you should know how to calculate the number of translation, rotational, and vibrational degrees of freedom for a molecule using the arguments given in class, see pages 14-15 of my January 27 lecture notes.

  • The qualitative and quantitative features of the two experimental figures of heat capacities on page 30 of Schroeder.

  • The definition of the latent heat of a substance (pages 32-33 of Schroeder) and how to use this concept.

  • How to use dimensional analysis to deduce the formula for some expression of interest in terms of a product of powers of physical parameters (as in Problem 1.55(d) of Schroeder).

  • The assumptions and details of the derivation given in lecture of how the fact that entropy S(U,V,N) is a maximum when an isolated system is in thermodynamic equilibrium implies that there is a temperature (defined by 1/T=dS/dU) and other quantities that must be the same for all subsystems. You should also understand how the fact that the entropy increases monotonically over time for a nonequilibrium system, dS/dt > 0, implies that heat transfers from a high temperature subsystem to a low temperature subsystem.

  • The concept of the macrostate of some macroscopic system, the concept of a microstate, and the concept of the multiplicity Ω of a macrostate, which is the number of microstates consistent with a specified macrostate. You should also be able to identify these states and compute Ω for some simple examples, e.g., involving coins, playing cards, etc.

  • The factorial of an integer, n!, the definition of a binomial coefficient B(n,m) = n!/[m!(n-m)!], and how to compute a binomial coefficient for simple cases, for example B(5,2) and B(8,6).

  Thursday, February 3

  • Today's lecture notes have been posted.

  • Solutions to Assignment 2 have been posted.

  Tuesday, February 1

  • Answers to today's one-minute questionnaires have been posted.

  • Today's lecture notes are available for download.

  Monday, January 31

  • Reading: Finish Chapter 1 (pages 1-33 and page 41-42 on the mean free path) and start reading Sections 2.1 and 2.2 in Schroeder.

  • Quiz 2 will be on Tuesday, February 8 and will cover all material since Quiz 1 and through Thursday's lecture (February 3). As before, a few days before the second quiz, I will post a list of topics that you should especially focus on understanding.

  • I have posted your quiz scores and grades on Blackboard and will return your graded quizzes tomorrow in class.
    You can see the class distribution of scores and how grade thresholds were assigned by downloading and opening this Grade Statistics Mathematica notebook.
    I will be glad to discuss your quizzes with you if you have questions about the answers or how the problems were graded.

  Sunday, January 30

  • Assignment 3 is now available.

    Note: As of 11:20 PM, I updated this assignment with a short extra problem about degrees of freedom, and a discussion of what is meant by "dimensional analysis" for Problem 1.55 on page 36 of Schroeder. So if you downloaded the homework before this time, please download the newer version.

  • Answers to the 1-minute questionnaires of Thursday's class have been posted.

  Thursday, January 27

  • Lecture notes for today have been posted on the course webpage.

  • Scores for the first homework have been posted on the course Blackboard webpage.

  • Reading: finish reading Chapter 1 (pages 1-33 only) and read Section 2.1 in preparation for next Tuesday's lecture, when we will start Chapter 2 in Schroeder.

  • Quiz and midterm dates:
    • Quiz 2: Tuesday, February 8
    • Quiz 3: Tuesday, February 22.
    • Midterm: Thursday, March 3.

  Tuesday, January 25

  • Answers to today's 1-minute questionnaires have been posted.

  • Lecture notes for today's lecture have been posted.

  Monday, January 24

  • Reading: finish reading Chapter 1. The material we will discuss is Sections 1.1-1.6, up to page 33. We will not discuss enthalpy until later in the semester, and we will not discuss Section 1.7 on "Rates of Processes" (but pages 41-42 have a brief discussion of mean free path that you should read).

    Most introductory physics books have good discussions of the topics Schroeder covers in Chapter 1 (heat, work, first law of thermodynamics, ideal gas law, etc). I encourage you to read the related chapters of your intro text to complement Chapter 1.

  • Office hours: will be this Wednesday from 2-3:15pm in Room 090 of Physics. If you can't make these office hours or just want to meet with me to talk about the course, you can send me an email and I can try to meet with you at another time.

  Sunday, January 23

  • Answers to the 1-minute questionnaires of the January 20 lecture can now be downloaded.

  • Solutions to the first homework assignment are available for you to download. The graded homeworks will be returned to you in class this Thursday, your homework scores will be posted on the 363 Blackboard webpage.

  • The first quiz is this Tuesday, January 25. Some comments:
    • The quiz will start promptly at 10:05 AM so you should come a few minutes early to class so you can settle in and be ready to start at 10:05. Please put your backpack at the side wall (away from your desk). The only item that you are allowed on your desk are writing utensils (pen, pencil, pencil sharpener); no cellphones, no calculators, no other electronic devices.

    • The quiz will cover all material discussed in lecture, in the first homework assignment, and the parts of Schroeder relevant to the lectures and homeworks (pages 1-9 and Eq. (1.21) on page 13). Particular topics you should focus on are:
      1. The several informal meanings of temperature.
      2. The operational ways to test whether a system is in thermodynamic equilibrium.
      3. Several length scales: the de Broglie length, the average interparticle spacing, and the mean free path.
      4. The concept of a relaxation time and how to estimate the time for a system to reach equilibrium, e.g., that Siberian mammoth.
      5. The idea of a random walk and of an ensemble average.
      6. Mathematica notation and commands at the level of the tutorial. In particular, you should be able to answer all the questions in the last cell of that tutorial, with title "Summary of Mathematica functions and syntax mentioned".

      I scanned my lecture notes for the last two lectures which you can find here. You can also find examples of previous quizzes here.

  Friday, January 21

  • The second homework assignment is now available.

    Note: Problem 2 of this assignment you will likely not be able to do until after this Tuesday's lecture, when I show you how to use an elementary kinetic theory to calculate various fluxes.

  Tuesday, January 18

  • Answers to today's 1-minute questionnaires have been posted here.

  • Office hours: this Wednesday, January 18, I'll be in my office (Physics 097) from 2-3:15 pm if you would like to drop by and ask questions about the homework or material. If enough students come by, we'll meet in Room 090, which is just down the hall from my office. I'll also try to be in my office from 5:15-6pm if you can't make the earlier time.

  • I have posted the OpenOffice files for my first two lectures and my scanned notes for Tuesday's lecture on the Lectures webpage.

  • The first quiz will be on Tuesday, January 25. I will post specific topics to review for the quiz a few days before the quiz. The quiz will began promptly at 10:05 AM so come to class a few minutes early, to settle in.

  Sunday, January 16

  • You can download answers here to your 1-minute questionnaires. I also posted some related journal articles.

  Friday, January 14

  • Relativity powers your car battery, Physical Review Focus article about a recent theoretical calculation which shows that about 80% of the power provided by a lead car battery comes from the relativistic motion of the lead valence electrons. Not something you learn in your average high school chemistry class. :)

    This article is related to a point I made in class, that even at absolute zero, atoms, molecules, and solids have parts that have significant momentum and so it is not correct to say that all motion comes to a halt at absolute zero. In fact, zero motion is forbidden by the Heisenberg uncertainty principle since at absolute zero a motionless electron would have a precise position and precise momentum.

  Thursday, January 13

  1. Reading:
     • Please read twice carefully the course syllabus, especially the part concerning grading.

     • Please read Sections 1.1-1.3 of the Schroeder book in preparation for next week's lectures.

  2. The first assignment is now available. Please hand in your homework (except for Problem 1 which you will email me directly by this Sunday) no later than the beginning of class on Thursday, January 20. If you have any questions or run into any difficulties, I will be glad to meet with you.

     A suggestion: start this assignment several days before it is due so you will have plenty of time to ask questions if questions arise.

  
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