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Thermodynamics and Statistical Mechanics

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Thermodynamics and Statistical Mechanics Winter 2012 Chemistry 223B: Thermodynamics and Statistical Mechanics Instructor: Alex Levine Office Hours: Office: Young Hall 3044A Monday 1:30 – 2:30 pm Phone: 794-4436 Wednesday 1:30 – 2:30pm Email: [email protected] And by appointment if necessary Teaching Assistant: Christian Vaca Office Hours: Office: Geology 4607 TBA Email: [email protected] And by appointment if necessary Class Meetings: 1) Lectures will be held on Mondays and Wednesdays from 10:00am to 11:50am in Young Hall 3069. 2) Christian Vaca will hold a discussion section on Fridays at 10:00am to 10:50 am in Young Hall 3069. Homework: Typically, homework will be assigned on Mondays and will be due on the following Monday unless specified otherwise All assignments will be found online at the course website. Books: Below I list a number of useful textbooks for the course roughly in order of importance to the class. I would like you to purchase the main two texts for our course and I strongly recommend that a few of the other ones, particularly if you are interesting in pursuing this field further. The principal text for the thermodynamics part of the course. This is a classic textbook in the field Thermodynamics and an Introduction to and presents thermodynamics in a concise and Thermostatistics, 2nd Edition, Herbert Callen, John axiomatic approach. Over the two-quarter sequence, Wiley & Sons, New York (1985). we will cover most of the first eleven chapters. The principal text for the statistical physics part of the course. This book provides an excellent Elementary Statistical Physics, Charles Kittel, introduction to the subject and provides one of the Dover Publications Inc., New York, (1958). best discussions of fluctuations, correlations, and the relaxation kinetics towards equilibrium. 1 A strongly recommended supplementary text for the course. This book does an excellent job of Fundamentals of Statistical and Thermal Physics. F. discussing elementary kinetics and quantum Reif. McGraw Hill Book Co., New York (1965). statistical mechanics. Some homework problems will come from this book. A recommended supplementary text for the Statistical Physics 3rd Edition Part 1 L.D. Landau course. If this subject is important to you, this text and E.M. Lifshitz Pergamon Press, Oxford (1980). will be an important addition to your library. The Elements of Classical Thermodynamics, A.B. A classic discussion of thermodynamics. Pippard Cambridge University Press (1964). Lecture notes from a brilliant but idiosyncratic Statistical Mechanics: A set of lectures R.P. course on statistical mechanics. Somewhat more Feynman Addison-Wesley, Redwood City (1988). advanced than most of the course. An overview of the statistical mechanics and Principles of Condensed Matter Physics P.M. structure of matter in various condensed phases Chaikin and T.C. Lubensky Cambridge University emphasizing the role symmetries as an organizing Press (1995). principle. Again, a more advanced discussion than what we will cover. Prerequisites: Chemistry 110B and Math 33A/B. I assume that all students are already proficient with multivariable calculus, differential equations, and some complex analysis. Nevertheless, we will review some of the mathematics as it comes up in the course. Exams and Grading: There will be one midterm exam given in class. These will be given on: Midterm In class, Monday, February 6, 2012 Final Exam 11:30am – 2:30pm Friday, March 23, 2012 If you have an excused absence from midterm exam, you may either take a separate exam, or have your final exam score count for both the final and midterm. Grading: Your final grade in the course will be determined as follows: Homework 25% Midterm 35% Final 40% 2 Material to be covered: Statistical mechanics is a broad and active research area. We cannot expect to cover the field exhaustively in one or two quarters, but I hope to be able to give you an introduction to the field and to prepare you to take more advanced courses if you choose to do so. Due to our reorganization of the curriculum to accommodate new interdivisional specializations, e.g. materials chemistry or biophysics, the first quarter is required to act as both the beginning of a two-quarter sequence and as a stand-alone class for those students intending to take only one quarter (223A) of the two offered (223A & 223B). For that reason, we will cover the material in a new way. In the fall quarter (223A) we will overview both thermodynamics and its connection to statistical physics, while in the second quarter will return to some of these topics to cover them in more depth, focusing in particular on more sophisticated treatments of statistical mechanics. We will also introduce entirely new ideas, e.g. kinetic theory, irreversible processes, and transport. More specifically in Chemistry 223A, I intend to review the fundamentals of thermodynamics, to introduce the basic concepts of statistical mechanics, and to discuss measurable correlation functions in physical systems. Throughout the course, I hope to illustrate these basic principles using physical examples drawn from both classical results of the previous century and current research in this department and elsewhere. I hope you will enjoy the subject as much as I do. Course Outline: This is a rather general outline of topics to be covered. The proposed timing is merely a rough guide; we may adjust the schedule based on your input over the quarter. I. Weeks 1 – 4: A brief review of thermodynamics from an axiomatic approach a. Heat and work b. Entropy maximum principle, energy conservation and the 0th law. The formal structure of thermodynamics c. Thermodynamic potentials, Legendre transforms, and derivative relations II. Weeks 5-6: Fluctuations, thermodynamic stability and phase transitions a. Examples of first- and second-order phase transitions, broken symmetries b. Fluctuations, correlation functions, and thermodynamic stability III. Weeks 7-10: An introduction to Statistical Mechanics a. Statistics: The binomial distribution and random walks b. Classical statistical mechanics: Microcanonical, canonical, and grand canonical ensembles. c. The statistical meaning of entropy and the connection of statistical mechanics to thermodynamics d. Applications of statistical mechanics in classical systems, equilibrium fluctuations 3 .
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