MAE 216, Advanced Thermodynamics
Winter Quarter, 2014
: T/H 10:00-11:50am 1007 Geidt Hall

  • Prof. Raissa D'Souza, Office Hours: Tues 2:10-3pm, 3057 Kemper Hall
  • Mr. Vikram Vijayaraghavan, Office Hours: Thurs 3:10-4:30pm, 2341 Academic Surge
  • Dr. Pierre-Andre Noel, Office Hours by appt: noel.pierre.andre "at"

  • Overview
  • There is no required text. Content will be based on lectures.
  • Here is a brief syllabus.
  • Here is an extended course outline.
    Course Requirements
  • Approximately 6 problem sets. (To be posted below)
  • A research paper on a modern area of statistical thermodynamics. (More details below)
  • Final Exam, Tues, Mar 18, 1:00-3:00pm.
  • Grade breakdown: HWs 70%, Final exam 30%.
    Useful Textbooks
  • R. E. Sonntag, G. J van Wylen, Fundamentals of statistical thermodynamics. John Wiley and Sons, 1966.
       (You can find some version of this text used on
  • C. E. Hecht, Statistical Thermodynamics and kinetic theory. Dover Publications, 1990.
  • M. Kardar, Statistical Physics of Particles, Cambridge University Press, 2007.
       Avaialble for free via the MIT Open Courseware!
  • A. Huan, Statistical Mechanics
    Useful Web Pages
  • Brief bio of Ludwig Boltzmann, who largely developed statistical mechanics.
  • The 15th Annual Berkeley Mini-Stat Mech Meeting, Jan 10-12, 2014.
  • Heat and Thermodynamics, from "HyperPhysics"
  • Equipartion of energy
  • Specific heats, incl diatomic gas
  • Table of specific heats for many real substances
  • Quantum particle in an infinite square well (i.e. a box)
  • Boltzmann, Fermi-Dirac and Bose-Einstein statistics
  • Bose-Einstein condensation; (Could enable a quantum computer)
  • Electronic states: Lennard-Jones potential
  • The Hydrogen Atom (wikipedia)
  • The Hydrogen Atom (from hyperphysics)
  • Periodic Table of Elements
  • Ideal Quantum Gas
  • Ideal Quantum Diatomic gas
  • Additional topics:

  • Wikipedia page on electric grid
  • Wikipedia page on chemical thermodynamics
  • Chemical Thermodynamics
  • Statistical mechanics of chemical reactions
  • Thermodynamics of Chemical equilibrium

  • Homeworks
  • Homework 1. Due Fri Jan 17 (HW1 Solution)
  • Homework 2. Due Thurs Jan 30 (HW2 Solution)
  • Homework 3. Due Fri Feb 7 (HW3 Solution)
  • Homework 4. Due Weds Feb 19 (HW4 Solution)
  • Homework 5. Due Fri Feb 28 (HW5 Solution)
  • Homework 6. Due Fri Mar 14 (HW6 Solution)
  • (Gradebook will be maintained on smartsite)

    Extra Credit Research Paper, Due Friday Mar 21

    Format: A 3 to 4 page review paper, double-spaced. You should choose some modern area of statistical thermodynamics to explore on your own. Choose a topic and find 3 to 4 compelling references which are books or journal articles (note, you might refine or change topics as you start doing the research and finding out what prior work is available). Give an overview of the topic, including what are the big-picture issues addressed by the area. Give a quick review of the literature you have found. Give some open questions/next steps to explore in the area.

    Potential Topics:

  • Thermal ratchets
  • Single molecule thermodynamics
  • Biological applications of statistical physics
  • Photovoltaics
  • Photoelectrics
  • Phase Transitions: superconductivity, Currie Magnetism, Ising model (magnetic systems).
  • See also: The 15th Annual Berkeley Mini-Stat Mech Meeting, Jan 10-12, 2014.
  • ....

    Sample papers:

  • Turbulence and non-extensive stat mech
  • Thermal Ratchets
  • Thermodynamics of DNA (longer than necessary, but impressive)

    Lectures (Schedule subject to change)

    1/7Course Overview and Review of Classical Thermodynamics (Example Steam Tables)
    1/9Review: Phase diagrams, First and Second Laws, Open vs Closed systems
    1/14Review: Cycles, Carnot cycles, Ideal Gas. (Video of a real reversible system)
    1/16TA lead lecture: Maxwell's relations and discussion. (HW1 due Jan 17)
    1/21Maxwell's relations, Response functions, microstates versus macrostates (pdf notes from MIT course)
    1/23Counting: permutations versus combinations
    1/28Boltzmann probability for microstates, Partition function
    1/30Partition function (see e.g. Sec 2.2 of Statistical Mechanics) (HW2 due Jan 30)
    2/4Probability (see Kardar text): One random variable; Many random variables;
    Maxwell Boltzmann Distribution (see Wallace text and slides)
    2/6Equipartition of energy; Ideal diatomic gas -- vibration and rotation (HW3 due Feb 7)
    2/11Quantum mechanics: Wave/particle duality; de Broglie wavelength;
    (See Double slit experiment, Wave equation, plane wave, Video of double-slit and wavefunciton collapse)
    2/13Uncertainty relations; Schrodinger's equation; QM for 1) Particle in a box
    2/18QM for 2) Rigid Rotator; 3) Harmonic Oscilator; (approx anharmonic oscillator) (HW4 due Feb 19)
    2/20Modifying Boltzmann statistics: Fermi-Dirac statistics: Bose-Einstein statistics
    (See Wikipedia entry, Textbook chapter, Bose Einstein condensation(BEC) )
    (Videos on BEC: Nova (theory), Nova (experiment), Slowing down light & Quantum Computing,)
    2/25Electronic states/Atomic energy levels
    2/27Ideal Quantum Gas: Monoatomic (See Ideal Quantum Gas)
    3/4Band structure and semi-conductors; Diatomic, polyatomic gas (See Ideal Quantum Diatomic gas)
    3/6Next steps: Chemical reactions, phase transtions, Monte Carlo simulation
    3/11 In-class office hours with TA -- HW 6 discussion
    3/13Review (Interesting further reading: Connections to information theory);
    A Table showing how to get thermodynamic quantities from z.