Course Outline

Statistical and thermal physics describe systems that contain large numbers of individual constituents. Typical examples are gases and solids, which contain large numbers of identical atoms or molecules. The goal of thermal physics is to describe these systems in terms of bulk macroscopic quantities, such as temperature and pressure. The goal of statistical physics is to relate the bulk description to microscopic descriptions of the system constituents. Averaging over microscopic properties such as kinetic energies or dipoles moments of individual molecules or atoms can yield bulk properties such as temperature or magnetization.

Statistical physics and thermodynamics have been developed to the point where a wide range for phenomena can be described using the same small set of general principles. These subjects form a cornerstone of current physics and are frequently used in condensed matter physics, atomic and molecular physics, astrophysics, chemistry and elsewhere.

Phys 362 will introduce you to the framework and techniques of statistical and thermal physics as well as illustrating its applications throughout the physical sciences.

The course will cover the following topics subject to minor modifications.

  1. Microscopic and macroscopic systems, thermodynamic systems and states, thermodynamic equilibrium.
  2. First law of thermodynamics, energy, heat capacities, enthalpy.
  3. Thermodynamic processes, entropy, heat engines.
  4. Fundamental thermodynamic relation.
  5. Probability, microstates/macrostates, thermodynamic ensembles.
  6. Magnetic systems.
  7. Classical ideal gases, Bose and Fermi gases.
  8. Chemical potential.

Homework Assignments

There is an extensive supplementary web page for the text. This includes a large collection of simulations, some of which will be used for assignments throughout the semester. The best way to access all of these is via the launcher at the STP Package page. This contains a java program which you should download, save and run. If the website is unavailable, there is another copy of the launcher at alternative location at CMU.

Due: 21 January 2016 Homework 1
Due: 26 January 2016 Homework 2
Due: 28 January 2016 Homework 3
Due: 2 February 2016 Homework 4
Due: 4 February 2016 Homework 5
Due: 9 February 2016 Homework 6
Due: 11 February 2016 Homework 7
Due: 16 February 2016 Homework 8
Due: 23 February 2016 Homework 9
Due: 25 February 2016 Homework 10
Due: 1 March 2016 Homework 11
Due: 8 March 2016 Homework 12
Due: 10 March 2016 Homework 13
Due: 22 March 2016 Homework 14
Due: 24 March 2016 Homework 15
Due: 29 March 2016 Homework 16
Due: 31 March 2016 Homework 17
Due: 5 April 2016 Homework 18
Due: 7 April 2016 Homework 19
Due: 12 April 2016 Homework 20
Due: 14 April 2016 Homework 21
Due: 26 April 2016 Homework 22
Due: 3 May 2016 Homework 23
Due: 5 May 2016 Homework 24

Exams

There will be two hour long exams during class on the following dates: Thursday 3 March 2016 and Thursday 14 April. There will be a comprehensive final exam on Tuesday 10 May 2016.

Exams and solutions from previous semesters.

Spring 2014 Class exam 1
Spring 2014 Class exam 1: Solutions
Spring 2014 Class exam 2
Spring 2014 Class exam 2: Solutions
Spring 2014 Final exam
Spring 2014 Final exam: Solutions
Spring 2015 Class exam 1
Spring 2015 Class exam 1: Solutions
Spring 2015 Class exam 2
Spring 2015 Class exam 2: Solutions
Spring 2015 Final exam
Spring 2015 Final exam: Solutions

Exams and solutions from this semester.

Solutions will be posted after each exam has been graded.

Spring 2016 Class exam 1
Spring 2016 Class exam 1: Solutions
Spring 2016 Class exam 2
Spring 2016 Class exam 2: Solutions

Supplementary Reading

There are many additional texts which are potentially suitable for this course. The following is a selection.

  1. Thermodynamics

    1. D. V. Schroeder, Thermal Physics Addison-Wesley (2000). Accessible and written in conversational style. A greater focus on applications of thermodynamics to various physical situations, including everyday phenomena. Many interesting applications within the problems.

    2. K. Stowe, An Introduction to Thermodynamics and Statistical Mechanics Cambridge (2007). Mixes the statistical and traditional thermodynamic approaches. Many problems and exercises.

    3. R. Baierlein, Thermal Physics Cambridge (1999).

    4. F. Mandl, Statistical Physics Wiley (1988). Perhaps the most accessible text for undergraduates that strives to lay out axioms and foundations of statistical physics. If the origins of the idea of free energy mystify you and you like some abstraction, then this is the place to look.

    5. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, Wiley (1985). Lays out postulates and axioms for thermodynamics and develops the subject from these. One of the more mathematically sophisticated texts for undergraduates.

    6. F. Reif, Fundamentals of Statistical and Thermal Physics McGraw-Hill (1965). Long standing classic undergraduate text. Starts with statistical physics and develops thermodynamics from this.

    7. C. Kittel, Thermal Physics Wiley (1969). Another long-standing classic undergraduate text.

    8. H. A. Buchdahl, The Concepts of Classical Thermodynamics Cambridge (1966). Want an axiomatic approach to thermodynamics? It exists. This is heavy in mathematics and light in applications but gives a great treatment of the conceptual and mathematical structure of thermodynamics.

  2. Velocity Distributions in Gases

      Maxwell produced his result for the distributions of velocities within a gas in the 1860's. The first attempts to verify this directly were done by Otto Stern in the 1920s. The following is selected early literature which presents confirmation of Maxwell's results.

    1. O. Stern, Eine direkte Messung der thermischen Molekulargeschwindigkeit, Z. Physik 2,, pg 49 (1920).

    2. O. Stern, Nachtrag zu meiner Arbeit: "Eine direkte Messung der thermischen Molekulargeschwindigkeit", Z. Physik 3,, pg 417 (1920).

    3. John A. Eldridge, Experimental test of Maxwell's Distribution Law, Phys. Rev. 30,, pg 931 (1927).

    4. I. F. Zartman, A Direct Measurement of Molecular Velocities, Phys. Rev. 37,, pg 383 (1931).

    5. R. C. Miller and P. Kusch, Velocity Distributions in Potassium and Thallium Atomic Beams, Phys. Rev. 99,, pg 1314 (1955).

  3. Thermal Properties of Solids

    1. P. Debye, Zur Theorie der spezifischen Warmen, Ann. Phys. 344,, pg 789 (1912).

    2. A. H. Compton, The Variation of the Specific Heat of Solids with Temperature, Phys. Rev. 6,, pg 377 (1915).

    3. William S. Corak, M. P. Garfunkel, C. B. Satterthwaite, and Aaron Wexler, Atomic Heats of Copper, Silver, and Gold from 1K to 5K, Phys. Rev. 98, pg 1699 (1955).

    4. G. T. Furukawa, W. G. Saba, M. L. Reilly, Critical Analysis of the Heat-Capacity Data of the Literature and Evaluation of Thermodynamic Properties of Copper, Silver, and Gold from 0 to 300 K, U.S. Dept. of Commerce, National Bureau of Standards (U.S. Government Printing Office, Washington, D.C., 1968)

    5. K. A. Rogers, The Behavoir of Heat Capacity at Low and High Temperatures, Submitted as part of a Stanford University course (2007).

Links and Animations

  1. Reference Sources
    1. Physlink. Reference information and data, including decimal system notation, physical constants, math constants, astro-physical constants, etc,....
    2. Eric Weinstein's World of Physics. Encyclopedia of Physics maintained by Wolfram Research. Entries at a variety of technical levels.
    3. Science and Engineering Encyclopedia: Physics Encyclopedia of Physics with a somewhat cumbersome interface. Includes conversion calculators.
    4. Periodic Table of Elements. WebElements site.
    5. NIST Databases. Administered by the National Institute for Standards and Technology. The final word in physical data. Intended for professionals.
  2. Animations
    1. Math and Physics Simulations. A great collection of excellent simulations from Paul Falstad.
    2. PhET. University of Colorado PhET simulations.
    3. Physclips. From the University of New South Wales, Australia.
    4. LTU Applets. Collection of simulations provided by Scott Schneider, Lawrence Technological University.
    5. PSU Schuylkill Animations. Provided by Michael Gallis, Penn State University Schuylkill.
  3. Thermal Physics
    1. Gas Properties. PhET simulation from the University of Colorado. Alternative link here.
    2. Free Expansion of a Gas. Animation from Pennsylvania State University, Schuylkill.
    3. Simplified MRI. PhET simulation from the University of Colorado. Alternative link here.
    4. Smashing Racquet Ball. From North Carolina State University.
    5. Gas Thermometer. From University of Iowa.
    6. Kinetic Theory. From Oklahoma State University.
    7. Kinetic Theory. From LON-CAPA.
    8. Fire Syringe. From University of Iowa.
  4. Thermal Physics of Solids
    1. Normal Modes. PhET simulation from the University of Colorado.