Course Prerequisites: PHYS 3313 and MATH 2326, or instructor s consent.

Transcription

1 1 Course: PHYS Thermodynamics and Statistical Mechanics Semester, Year: Fall 2012 Days/Time: Tu, Th 2:00 3:20 pm Building, Room: Science Hall, Rm. 105 Instructor: Dr. R. S. Rubins Office: Science Hall, Rm. 107F Office Hours: Tu-Th 3:40 4:40 pm, or by appointment. Phone: (817) Course Prerequisites: PHYS 3313 and MATH 2326, or instructor s consent. Required Textbook: Classical and Statistical Thermodynamics by Ashley H. Carter (Prentice Hall, 1 st ed. 2001). Instructor PowerPoint slides are on-line at Description of Course The topics to be treated in this course may be separated into the three categories described below. 1. Classical thermodynamics A standard and concise approach to thermodynamics will include all basic definitions and problem types relating to the laws of thermodynamics. The definition of heat leads to the 1st law of thermodynamics and its consequences, such as thermodynamic work, heat and internal energy. Isothermal, adiabatic and free expansion processes are to be studied in detail. The second law of thermodynamics is introduced through heat engines, and expressed in terms of entropy changes, which are calculated for a variety of processes. A discussion of exact and inexact differentials leads to the fundamental thermodynamic relation and then to Maxwell s relations. Other subjects covered include the following: phase transitions, heat capacities, the Joule and Joule-Thomson processes, phase diagrams, the Clausius-Clapeyron equation, and the entropy of EM radiation.

2 2 2. Statistical thermodynamics This, the central part of the course, starting from the fundamental postulate of equal a priori probabilities, shows the statistical nature of classical thermodynamics, and leads to the definition of the partition function Z. Subjects covered in detail include the harmonic oscillator and Einstein s specific heat model, the entropy of an ideal monatomic gas, the equipartition theorem, the Maxwell velocity distribution, photon statistics and Planck s radiation law, the grand partition function, Fermi-Dirac and Bose-Einstein statistics (calculated by two methods), and applied to free electron theory and Bose-Einstein condensation. 3. Additional topics A variety of topics vary between those normally taught in a thermodynamics course, such as an introductory kinetic theory, and less conventional material. The latter include introductions to black-hole thermodynamics, superfluidity in liquid helium, and an experimentally oriented review of practical Bose-Einstein condensation. Tentative Topic Schedule: Part 1: CLASSICAL THERMODYNAMICS: 1. Thermal concepts and definitions 2. Ideal gas temperature scale 3. Equations of state 4. The first law of thermodynamics 5. Differential form of first law, exact and inexact differentials 6. Reversible and irreversible processes 7. Enthalpy and change of phase 8. Heat capacities: definitions, difference and ratios 9. The fundamental thermodynamic relation 10. The Joule and Joule-Thomson effects 11. Inversion temperature and the Linde liquefaction process 12. Heat engines, refrigerators, and the second law of thermodynamics 13. Entropy changes for various processes 14. Maxwell s relations and applications 14. Conditions for equilibrium 15. Phase-equilibrium in a one-component system 16. The Clausius-Clapeyron equation 17. The third law of thermodynamics and its consequences 18. The entropy of blackbody radiation

3 3 Part 2: STATISTICAL MECHANICS 1. Statistical weight (or thermodynamic probability) 2. Fundamental postulate of equal a priori probabilities 3. Equilibrium between two parts of an isolated system 4. The Boltzmann distribution and the partition function Z 5. Calculations mean values from Z 6. Ensembles and the relationship between entropy and probability 7. The entropy of an ideal monatomic gas 8. Free expansions and Gibbs paradox 9. The partition function of an ideal monatomic gas 10. The equipartition theorem and applications 11. Spin ½ paramagnet in a magnetic field and Curie s law 12. Adiabatic cooling 13. The harmonic oscillator and the heat capacities of solids 14. The Maxwell velocity distribution and its applications 15. Quantum gases: symmetrical and antisymmetrical wavefunctions 16. Photon statistics and blackbody radiation 17. The grand partition function 18. Fermi-Dirac and Bose-Einstein statistics 19. Bose-Einstein condensation 20. Free-electron theory of metals Part 3: ADDITIONAL TOPICS A: KINETIC THEORY 1. Assumptions of kinetic theory 2. Molecular effusion B: SUPERFLUIDITY IN LIQUID HELIUM 1. Zero-point energy 2. Lambda specific heat transition 3. Two-fluid model 4. Thermodynamic properties: the fountain effect C: BOSE-EINSTEIN CONDENSATION (BEC) 1. Introduction to BEC 2. Experimental preparation of a BE condensate 3. Photographing the condensate D: INFORMATION THEORY 1. Missing information and entropy 2. Shannon s calculation E: BLACK-HOLE THERMODYNAMICS 1. Entropy of a black hole 2. Space at the Planck level

4 4 Learning Outcomes By the end of the course the student should be able to do the following: a. explain the contents of the ideas presented in the Topic schedule ; b. work thermodynamic and statistical mechanics problems given in the homework sets; c. understand in principle how the whole edifice of Statistical Mechanics can be built from the fundamental postulate. Specific Course Requirements with Descriptions 1. POINTS will be allotted roughly as follows: Two tests (110 points each) 220 Final 130 Homework (scaled down to) 250 TOTAL 600 points 2. Proposed TEST DATES* and material to be covered. TEST 1 (Carter, class notes) Thursday, Sept. 27. TEST 2 (Carter, class notes) Tuesday, Oct. 30. FINAL (Carter, class notes) Tuesday, Dec. 11, 2:00 4:30 pm 3. The test points will be about 60% MULTIPLE CHOICE questions (mostly qualitative, and 40% CONVENTIONAL PROBLEMS, which, for full credit, need to be written out carefully, with all important steps shown. 4. A detailed breakdown of the MATERIAL to be COVERED on each test will be given about a week before each test. 5. The tests will be CLOSED BOOK, but relevant equations will be given to you. If you are stuck on a problem, you may get help at the expense of some points. 6. In the case of a test missed without an official reason, a MAKE-UP TEST may be taken within a week of the test, with a 10 % PENALTY. 7. There is no make-up for the Final, so try not to oversleep or get the day wrong.

5 5 8. Your HOMEWORK should be largely done and definitely written out on your own. I shall give hints in class. If you cannot get started on a problem, please come to me for help. 9. Your final grade will be based on the total numbers of points. There will be NO SPECIAL PROJECTS for extra credit. 10. The LAST DROP DATE is Wednesday, Oct There will be a PENALTY of 10% per working day for the late arrival of Homework, so try not to throw points away by finishing it late. 12. Your COMPLAINTS and SUGGESTIONS should be made known to me as early as possible, so that changes may be made during the semester. * While this schedule will be followed as far as possible, it may be necessary on occasion to make changes in dates and/or material covered. In particular, if the weather is especially bad on the test date, the test may be postponed until the next class. General University Notices Final Review Week A period of five class days prior to the first day of final examinations in the long sessions shall be designated as Final Review Week. The purpose of this week is to allow students sufficient time to prepare for final examinations. During this week, there shall be no scheduled activities such as required field trips or performances; and no instructor shall assign any themes, research problems or exercises of similar scope that have a completion date during or following this week unless specified in the class syllabi. During Final Review Week, an instructor shall not give any examinations constituting 10% or more of the final grade, except makeup tests and laboratory examinations. In addition, no instructor shall give any portion of the final examination during Final Review Week. Academic Dishonesty It is the philosophy of The University of Texas at Arlington that academic dishonesty is a completely unacceptable mode of conduct and will not be tolerated in any form. All persons involved in academic dishonesty will be disciplined in accordance with University regulations and procedures. Discipline may include suspension or expulsion from the University. "Scholastic dishonesty includes but is not limited to cheating, plagiarism, collusion, the submission for credit of any work or materials that are attributable in whole or in part to

6 6 another person, taking an examination for another person, any act designed to give unfair advantage to a student or the attempt to commit such acts." (Regents Rules and Regulations, Part One, Chapter VI, Section 3, Subsection 3.2, Subdivision 3.22). E-Culture Policy The University of Texas at Arlington has adopted the University address as an official means of communication with students. Through the use of , UT-Arlington is able to provide students with relevant and timely information concerning registration, financial aid, payment of bills, and graduation may be sent to students through . All students are assigned an account, available at and information about activating and using it. New students (first semester at UTA) are able to activate their account 24 hours after registering for courses. There is no additional charge to students for using this account, and it remains active as long as a student is enrolled at UT-Arlington. Students are responsible for checking their regularly. Americans With Disabilities Act The University of Texas at Arlington is on record as being committed to both the spirit and letter of federal equal opportunity legislation; reference Public Law The Rehabilitation Act of 1973 as amended. With the passage of new federal legislation entitled Americans With Disabilities Act - (ADA), pursuant to section 504 of The Rehabilitation Act, there is renewed focus on providing this population with the same opportunities enjoyed by all citizens. As a faculty member, I am required by law to provide "reasonable accommodation" to students with disabilities, so as not to discriminate on the basis of that disability. Student responsibility primarily rests with informing faculty at the beginning of the semester and in providing authorized documentation through designated administrative channels. Student Support Services Available The University of Texas at Arlington supports a variety of student success programs to help you connect with the University and achieve academic success. These programs include learning assistance, developmental education, advising and mentoring, admission and transition, and federally funded programs. Students requiring assistance academically, personally, or socially should contact the Office of Student Success Programs at for more information and appropriate referrals. Grade Exclusion or Replacement You may use the grade made in this course if and only you fill in the necessary forms found in the Registrar s office by the Census date (Monday, Sept. 10). If you do not fill out the forms the University will not honor the replacement. Students who wish for a Grade Exclusion or Grade Replacement to impact their grade point average for the current term and beyond will be required to file for use of those policies by the Last Drop Day for the semester. Pass-fail Requests

7 7 All Pass/Fail request must be completed and returned to the Physics Office before the Census Date (Monday, Sept. 10) or you will not be able to take the class as a pass fail. Drop for Non-payment of Tuition If you are dropped from this class for non-payment of tuition, you may secure an Enrollment Loan through the Bursar s Office. You may not continue to attend class until your Enrollment Loan has been applied to outstanding tuition fees. DISCLAIMER This syllabus is subject to change. If you have concerns about any of the Information shown here, please let me know as early in the semester as you are able.