Statistical Mechanics

King's College London

Course Description

  • Course Name

    Statistical Mechanics

  • Host University

    King's College London

  • Location

    London, England

  • Area of Study

    Mathematics, Physics, Statistics

  • Language Level

    Taught In English

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • UK Credits

    15
  • Recommended U.S. Semester Credits
    4
  • Recommended U.S. Quarter Units
    6
  • Overview

    Module description:

    Syllabus Outline:

    Microstates, statistical postulate for microstates, macrostate, permutations and combinations, elementary
    probability theory, observed macrostate, Stirling's theorem, distributions in coin tossing, distinguishable
    statistics, Lagrange's methods of undetermined multipliers, microcanonical ensemble and Boltzmann distribution
    for distinguishable particles, the emergence of temperature from conditions for equilibrium, postulate for
    entropy, partition function for a single particle, thermodynamic potentials and variables in terms of partition
    function, energy degeneracy and partition functions, many (weakly interacting) particle partition function,
    derivation of thermodynamics of a paramagnet, derivation of thermodynamics of a simple harmonic oscillator,
    distinguishable and indistinguishable particles, counting states of a gas of indistinguishable particles,
    density of states, partition function of an ideal gas, derivation of the equation state of an ideal gas, the
    Gibbs paradox and indistinguishability, excitation of rotational and vibrational degrees of freedom, rotational
    specific heat of gases, Maxwell-Boltzmann distribution of velocities, quantum statistics (Bose-Einstein and
    Femi-Dirac) for indistinguishable particles, photon gas, density of states for photons, black body radiation,
    Debye frequency and specific heat of phonons, electrons in metals, heat capacity of a Fermi gas, transition
    between quantum and classical statistics, canonical ensemble, grand canonical ensemble, degeneracy in
    astrophysics.

    Aims and Objectives:
    This course introduces the fundamentals of the microscopic origins of thermodynamics for both classical and
    quantum systems. The statistical basis for treating distinguishable and indistinguishable particles is
    established in an elementary way using combinations and permutations. It assumes a competence in calculus and
    some previous knowledge of probability theory would be an advantage. On finishing the course, students should be
    able to work out equations of state and thermodynamic potentials for elementary systems of particles, which, to a
    good approximation, are non-interacting.

Course Disclaimer

Courses and course hours of instruction are subject to change.

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Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.