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.

Homework Assignments

There is an extensive supplementary web page for the text. The text provides simulations that we will use. These can be accessed at Statistical and Thermal Physics Programs page. This page contains browser based versions of the programs. Details of these programs and Java or Python source codes are at OSP Statistical and Thermal Physics Programs.

Due: January 23, 2026 Homework 1
Due: January 27, 2026 Homework 2
Due: January 30, 2026 Homework 3
Due: February 3, 2026 Homework 4
Due: February 6, 2026 Homework 5
Due: February 10, 2026 Homework 6
Due: February 13, 2026 Homework 7
Due: February 17, 2026 Homework 8
Due: February 20, 2026 Homework 9
Due: February 24, 2026 Homework 10
Due: February 27, 2026 Homework 11
Due: March 3, 2026 Homework 12
Due: March 13, 2026 Homework 13
Due: March 24, 2026 Homework 14
Due: March 26, 2026 Homework 15
Due: March 31, 2026 Homework 16
Due: April 3, 2026 Homework 17
Due: April 7, 2026 Homework 18
Due: April 10, 2026 Homework 19
Due: April 14, 2026 Homework 20
Due: April 21, 2026 Homework 21
Due: April 28, 2026 Homework 22
Due: May 1, 2026 Homework 23
Due: May 5, 2026 Homework 24

Exams

There will be two hour long exams during class on the following dates: Thursday March 5, 2026 and Thursday April 23, 2026. There will be a comprehensive final exam on Tuesday May 12, 2026.

Exams and solutions from previous semesters.

Spring 2019 Class exam 1
Spring 2019 Class exam 1: Solutions
Spring 2019 Class exam 2
Spring 2019 Class exam 2: Solutions
Spring 2019 Final exam
Spring 2019 Final exam: Solutions
Spring 2020 Class exam 1
Spring 2020 Class exam 1: Solutions
Spring 2020 Class exam 2
Spring 2020 Class exam 2: Solutions
Spring 2020 Final exam
Spring 2020 Final exam: Solutions

Exams and solutions from this semester.

Solutions will be posted after each exam has been graded.

Spring 2026 Class exam 1
Spring 2026 Class exam 1: Solutions
Spring 2026 Class exam 2
Spring 2026 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 Behavior 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. Periodic Table of Elements WebElements site.
    4. NIST Standard Reference Data Administered by the National Institute for Standards and Technology. The final word in physical data. Intended for professionals.
  2. Animations
    1. PhET. From the University of Colorado.
    2. oPhysics Physics simulations provided by Tom Walsh.
    3. LTU Applets. Collection of simulations provided by Scott Schneider, Lawrence Technological University.
    4. Animations for Physics and Astronomy. Collection of simulations from Dr. Michael R. Gallis, Penn State University, Schuylkill. Youtube channel
    5. Physclips. Collection of simulations from the University of New South Wales, Australia.
  3. Thermal Physics
    1. Gas Properties. PhET simulation from the University of Colorado.
    2. Free Expansion of a Gas. Animation from Pennsylvania State University, Schuylkill.
    3. Simplified MRI. PhET simulation from the University of Colorado.
    4. Gas Thermometer. From University of Iowa.
    5. Fire Syringe. From University of Iowa.
  4. Thermal Physics of Solids
    1. Normal Modes. PhET simulation from the University of Colorado.