PHYS*4240 Statistical Physics II Fall 2018 Course Outline

PHYS*4240 Statistical Physics II
                       Fall 2018 Course Outline
                                Department of Physics
                                 University of Guelph

Course Objectives
Two years ago, PHYS*2240 introduced you to the central role that entropy and the
second law play in thermodynamics. The entropy concept originates from our lack of
precise knowledge about which of the many, many microscopic states a system is
actually in, despite our imposition of constraints on the system at a macroscopic level.
This statistical perspective on entropy motivated the second law. We explored the
consequences of the second law for equilibrium, for phase transitions, and for various
applications and measurable quantities. PHYS*4240 continues the discussion begun
two years ago.

We will follow the topic selection and structure in the textbook Thermal Physics by
Daniel V. Schroeder. PHYS*4240 begins with a brief review of thermodynamics. This
covers Chapters 1-3 and selected topics from Chapter 5. We will generalize the
thermodynamic formalism from the isolated systems we considered in PHYS*2240,
which have constant energy, volume, and particle number, to systems with other
constraints, such as fixed temperature, fixed pressure, and/or fixed chemical potential.
Free energies and extremum principles, which are ultimately connected to the entropy
and the second law, are key concepts in these situations. The overall structure, and
universal nature, of thermodynamics will be emphasized.

The central portion of the course (Chapter 6) develops convenient statistical methods
for calculating free energies and other thermal-average properties of materials by
counting ensembles of appropriately-weighted microstates. Systems we will consider
include the ideal gas, the van der Waals fluid, the paramagnet, and the Einstein solid.

The final part of the course is devoted to the statistical mechanics of systems that are
described by the laws of quantum mechanics (Chapter 7). We will resolve several
issues with the classical treatment of the ideal gas that are related to the counting of
microstates when the particles are indistinguishable. We will discuss the distinct
statistics of fermions and of bosons. Topics include the quantum ideal gas, the heat
capacity of the free electron gas in metals, blackbody radiation and the photon gas,
Bose-Einstein condensation, and finally the treatment of quantized lattice vibrations
(phonons) of a solid.

You will refine your analytical and problem-solving skills through regular written
assignments.

Class Schedule and Location
Monday, Wednesday, and Friday 11:30 am - 12:20 pm, MCKN 305
First Lecture: Friday, September 7th
Last Lecture: Friday, November 30th

The course runs for 12 weeks (36 lectures); there is no lecture on Thanksgiving
(Monday, October 8th). Friday, November 30th is a Thanksgiving make-up lecture.

Course Instructor
Name: Rob Wickham
Office: MacNaughton 448
Phone: (519) 824-4120 ext. 53704
Email: rwickham@uoguelph.ca

Office Hours
Monday, 2:00 pm - 3:00 pm and Tuesday, 1:00 pm - 3:00 pm. Assignments will be due
on (alternate) Wednesdays. Please send me an email if you can't find me and wish to
schedule a meeting.

Course Website
CourseLink: Login via https://courselink.uoguelph.ca/

Required Textbook
An Introduction to Thermal Physics, by D. V. Schroeder (Addison Wesley Longman,
2000).

Other, optional resources:
A typed set of related notes by Eric Poisson which can be found on his web site (see
faculty link on the departmental web site).
  Some of the Classic References

      F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill,1965,QC
      175.R43).
      F. Mandl, Statistical Physics, Second Edition (Wiley,1988,QC174.8.M27).
      D.L. Goodstein, States of Matter (Prentice Hall, 1975; Dover, 1985, QC
      173.3.G66).
      K. Huang, Statistical Mechanics, Second Edition (Wiley,1987,QC174.8.H83).
      C. Kittel and H. Kroemer, Thermal Physics, Second Edition (Freeman, 1980, QC

311.5.K52).
       L.D. Landau and E.M. Lifshitz, Statistical Physics, Third Edition, Part 1
       (Pergamon, 1980, QC 175.L32).
       R.K. Pathria, Statistical Mechanics (Pergamon,1972,QC175.P35).

At this stage of your education, you should be consulting more than one text to enhance
your learning and understanding of the material. No particular book is perfect in all
respects and scientists regularly refer to several books and papers to understand a
concept.

Evaluation

Assessment                % of Grade                          Due Date
Assignments (5)                30%          Sept. 26, Oct. 10, Oct. 24, Nov. 14, Nov. 28
Midterm Test                   30%          Monday, October 29th, 7-9 pm, place TBD
Final Exam                     40%          December 7h, 7:00 - 9:00 pm, place TBD

A medical certificate is required if the exam is missed.

Assignments are due at the beginning of class; late assignments will receive a grade of
zero.

Physics is not done in a vacuum. (OK, sometimes it is...) Students may discuss
assignments amongst themselves but their written solutions must not be shared with
anyone (this would be an example of plagiarism).

Plagiarism is the act of appropriating the ``...composition of another, or parts or
passages of his [or her] writings, or the ideas or language of the same, and passing
them off as the product of one's own mind...'' (Black's Law Dictionary). A student found
to have plagiarized will receive zero for the work concerned. Collaborators shown to be
culpable will be subject to the same penalties.

Course Evaluation
The Department of Physics requires student assessment of all courses taught by the
Department. These assessments provide essential feedback to faculty on their teaching
by identifying both strengths and possible areas of improvement. In addition, annual
student assessment of teaching provides part of the information used by the
Department’s Tenure and Promotion Committee in evaluating the faculty member's
contribution in the area of teaching.

The Department's teaching evaluation questionnaire invites student response both
through numerically quantifiable data, and written student comments. In conformity with
University of Guelph Faculty Policy, the Department’s Tenure and Promotions

Committee only considers comments signed by students (choosing "I agree" in question
14). Your instructor will see all signed and unsigned comments after final grades are
submitted. Written student comments may also be used in support of a nomination for
internal and external teaching awards.

Note: No information will be passed on to the instructor until after the final grades have
been submitted.

Standard Statements
E-mail Communication
As per university regulations, all students are required to check their University of
Guelph e-mail account regularly: e-mail is the official route of communication between
the University and its students.

When You Cannot Meet a Course Requirement
When you find yourself unable to meet an in-course requirement because of illness or
compassionate reasons, please email the course instructor to make arrangements.

Drop Date
At Guelph, the last date to drop one-semester courses, without academic penalty, is
Friday, November 2nd. For regulations and procedures for Dropping Courses, see the
Undergraduate Calendar.

Copies of out-of-class assignments
Keep paper and/or other reliable back-up copies of all out-of-class assignments: you
may be asked to resubmit work at any time.

Accessibility
The University of Guelph is committed to creating a barrier-free environment. Providing
services for students is a shared responsibility among students, faculty and
administrators. This relationship is based on respect of individual rights, the dignity of
the individual and the University community's shared commitment to an open and
supportive learning environment. Students requiring service or accommodation, whether
due to an identified, ongoing disability or a short-term disability, should contact Student
Accessibility Services (SAS) as soon as possible.

For more information, contact SAS at 519-824-4120 ext. 56208 or visit the SAS website.

Academic Misconduct
The University of Guelph is committed to upholding the highest standards of academic
integrity and it is the responsibility of all members of the University community – faculty,
staff, and students – to be aware of what constitutes academic misconduct and to do as
much as possible to prevent academic offences from occurring. University of Guelph
students have the responsibility of abiding by the University's policy on academic
misconduct regardless of their location of study; faculty, staff and students have the
responsibility of supporting an environment that discourages misconduct. Students need

to remain aware that instructors have access to and the right to use electronic and other
means of detection.

Please note: Whether or not a student intended to commit academic misconduct is not
relevant for a finding of guilt. Hurried or careless submission of assignments does not
excuse students from responsibility for verifying the academic integrity of their work
before submitting it. Students who are in any doubt as to whether an action on their part
could be construed as an academic offence should consult with a faculty member or
faculty advisor.

The Academic Misconduct Policy is detailed in the Undergraduate Calendar.

Recording of Materials
Presentations which are made in relation to course work—including lectures—cannot be
recorded or copied without the permission of the presenter, whether the instructor, a
classmate or guest lecturer. Material recorded with permission is restricted to use for
that course unless further permission is granted.

Resources
The Academic Calendars are the source of information about the University of Guelph’s
procedures, policies and regulations which apply to undergraduate, graduate and
diploma programs.

Course Outline
I. Thermodynamics: Review and unfinished business [Chapters 1 to 3, 5.1, 5.2]
     1. Equation of state, state variables, constraints, equilibrium
     2. van der Waals equation of state, limiting cases, isothermal compressibility,
        phase coexistence, thermal, mechanical and diffusive equilibrium
     3. First law, energy, heat, work, quasi-static processes, adiabatic processes
     4. Isolated systems (U, V, N fixed) and the second law, entropy, example: van
        der Waals model, properties of entropy
     5. Structure of thermodynamics: derivatives of entropy are equations of state,
        second derivatives are response functions, examples: equipartition,
        thermodynamic identity
     6. Equivalent representations of thermodynamics, free energies, geometrical
        interpretation of the Legendre transform, extremum principles [5.1, 5.2]
     7. Derivative relations and thermodynamic identities arising from free energies,
        Maxwell relations
     8. Examples involving Maxwell relations: heat capacities and compressibilities

II. Calculating thermodynamic potentials: ensembles and examples (mainly Ch.
6)

     9. Macrostates and microstates, multiplicity of the two-state paramagnet,
        fundamental assumption

10. Classical entropy of the ideal gas in the microcanonical ensemble [Chapter
        2]
    11. Two-state paramagnet in thermal contact with a reservoir, the Boltzmann
        factor [6.1]
    12. General theory for systems in contact with a reservoir, partition function,
        averages in the canonical ensemble [6.2]
    13. Examples, paramagnet, Einstein solid
    --Thanksgiving--
    14. Partition function and Helmholtz free energy, composite systems
    15. Classical partition function for the ideal gas, and thermodynamics [8.1]

    16.   Equipartition of energy among degrees of freedom [1.3, 6.3]
    17.   Energy fluctuations in the canonical ensemble
    18.   Weakly interacting gases [8.1]
    19.   Identical particles, indistinguishability, and mixing
    20.   Issues with the classical model for ideal gas thermodynamics
    21.   Partition function for a quantum particle in a 1D box, 3D case, N non-
          interacting particles, internal degrees of freedom, heat capacity, rotation of
          diatomic molecules.
    Midterm evening of Monday, October 29th (following lecture 22)
    22. Chemical potential of an ideal gas, diffusive equilibrium in an external field:
        isothermal atmosphere, mobile magnetic particles
    23. The Gibbs factor, grand partition function, averages in the grand canonical
        ensemble [7.1]
    24. Example: adsorption of oxygen in the blood, particle number fluctuations

40th class day Friday, November 2nd

III. Quantum statistical mechanics (Chapter 7)

    25. Fermions and bosons, microstates of N ideal, indistinguishable quantum
        particles, occupation numbers, quantum statistics, quantum volume
    26. Fermi-Dirac and Bose-Einstein distribution functions, classical limit
    27. Degenerate ideal Fermi gas, ground state of a Fermi gas (T=0)
    28. Thermodynamic properties of the ground state of a Fermi gas
    29. Non-zero temperatures, density of states, Sommerfeld expansion
    30. Heat capacity of a degenerate ideal Fermi gas, electrons in metals
    31. Chemical potential of Bose gas, ground and excited state occupancies
    32. Bose-Einstein condensation, examples: liquid 4He, dilute gas
    33. Gas of photons in thermal equilibrium, Planck distribution
    34. Planck spectrum for blackbody radiation, thermodynamics
    35. Debye theory of lattice vibrations in solids: phonons
    36. Phonon thermodynamics, phonon contribution to the heat capacity of a solid