• Some sample Monte Carlo simulation programs for 2D Ising and Potts models are here.
• The final project presentations will take place during the scheduled exam time slot, Dec.5, 14:00-17:00 in Taro 309, and on Dec.16, 14:00-17:00, location TBA. See the program to find out when you are presenting:
• LaTeX, requires techexplorer plug-in
• PostScript, requires Ghostview or a similar viewer
• PDF, requires Ghostview, Adobe Acrobat, or a similar viewer
• Note that attendance on both days and active participation in the discussions is mandatory. Review the abstracts of the others in advance of the presentations, take notes, and ask questions after the presentations. Your project mark will depend on it.
• In lieu of the in-class Test No.4, the final take-home assignment is due by Nov.30, 16:00. No extensions!
• As announced in class, this assignment includes:
1. EFTS, p.105
2. K&K, Pr. 10-1
3. K&K, Pr. 14-1 and EFTS, p.108
4. EFTS, p.133
5. EFTS, p.135
• In-class Test No.3 is on Nov.16
• In-class Test No.2 is on Oct.19
• Revised pp. 42-45c in the notes are now online; also included in the lecture notes.
• Oct.2. In-class Test No.1 is this Thursday, Oct.5, 8:00-9:50, covers the material of the first two homework assignments, i.e. up to and including the first of the Maxwell relations.
• Sep.25. Weekly tutorials begin Sep.28: every Thu., 9:00-9:50, immediately following the lecture
• Sep.11. The lecture notes are now online.

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Introduction to probability distribution functions, accessible states, entropy, temperature, partition functions and relations to thermodynamic functions.

Thermal physics is the branch of science which deals with collections of large numbers of particles, on the order of 10²³. The properties of almost anything we can measure in our world, be it the temperature of a star or a cup of coffee, are determined by the principles that you will learn in this course.

Fundamentally, statistical mechanics starts from the ground up: from microscopic, quantum mechanical states of the particles, to the bulk properties that arise when a very large number of such particles come together. This "science of large numbers" offers us a powerful way of scaling up from the microscopic so that, for example, we can explain why heat flows from how to cold, and make other accurate predictions about the outside world.

PHYS 2P50

• Thermal Physics, by C.Kittel and H.Kroemer, 2nd Ed., W.H.Freeman & Co., New York, 1995.

• Introduction to Thermal Physics, by D.V.Schroeder, Addison Wesley, New York, 2000.
• Statistical Physics, by F.Reif, McGraw Hill, New York, 1965.
• Heat and Thermodynamics, by M.Zemansky and R.H.Dittman, 6th Ed., McGraw Hill, New York, 1981.

08:00 - 09:00 M W Th, in MC J404

TBA

E. Sternin (MC B206, ext. 3414, e-mail: [email protected])

Component	Weight	Comments
Homework	-	assigned weekly, not marked
Tutorial Tests	65%	4 in-class tests, 15%+15%+15%+20%
Term paper and oral presentation	35%	there is no final exam in the course

1. Introduction
• thermodynamics vs. statistical physics
• states of the system are quantum states
• model spin system; the degeneracy function
• probability distribution; calculating averages
2. Fundamental concepts of thermal physics
• all accessible states of a closed system are equally probable
• systems in thermal contact; entropy and temperature
• the second law of thermodynamics
• Examples
• thermal engines
• the direction of heat flow
• paramagnetism
• magnetic cooling
3. Boltzmann distribution
• Boltzmann factor, partition function, canonical ensemble
• a two-state system in detail; heat capacity
• Helmholtz free energy
• reversible processes
• thermodynamic identity, dU=TdS-pdV
• pressure
• first of Maxwell relations
• Example: N atoms in a box
• energy is a function of temperature only
• ideal gas law
• entropy, Cv, Cp - the hard way
• same, using free energy
• Sackur-Tetrode equation
• Example: a two-level system
• Example: a harmonic oscillator

4. Planck distribution
• QM description of a particle in a box
• density of states
• photons (EM radiation in a cavity)
• density of states
• black-body radiation - Planck radiation law
• Stefan-Boltzmann law
• phonons (elastic waves in solids)
• Debye temperature
• low-temperature limit - Debye T³ law
5. Gibbs distribution
• systems in diffusive contact
• chemical potential
• direction of particle flow
• example: ideal gas
• entropy and chemical potential
• thermodynamic identity, summary of thermodynamic relations
• Gibbs factor and Gibbs sum (the grand partition function)
• example: a two-level system
• other distribution functions: Bose-Einstein and Fermi-Dirac
• classical regime: ideal gas, revisited
• chemical potential, free energy, pressure
• entropy: Sackur-Tetrode equation, Gibbs paradox
• energy: degrees of freedom, heat capacity of diatomic gases
• chemical potential and potential energy
• example: isothermal atmosphere
• chemical potential and work
• example: reversible isothermal expansion
• example: reversible isentropic process
• example: irreversible expansion into vacuum
• experimental tests of Sackur-Tetrode equations
• fluctuations in an ideal gas

6. Fermi and Bose gases
• Summary: Fermi-Dirac, Bose-Einstein, and classical distributions
• degenerate Fermi gas in 3D
• geometry, density of orbitals, Fermi energy
• heat capacity of N fermions
• approximations and heat capacity in real metals
• temperature dependence of chemical potential
• boson gas
• Bose-Einstein condensation, BE condensation temperature
• phase transition to a condensed state; superfluidity of He(4)
• fluctuations in Fermi and Bose gases
• BE condensation temperature and separation of energy levels
7. Thermodynamic potentials
• Helmholtz and Gibbs free energy
• Maxwells' relations through cross-derivatives of G
• intensive and extensive variables
• Enthalpy
• example: derivation of Cp=Cv+R
• example: equilibrium in chemical reactions, law of mass action, Saha equation

8. Imperfect gases
• derivation of the van der Waals equation (approximate)
• law of corresponding states, the critical point
• free energy and phase equilibria; Maxwell's construction
• van der Waals formula is [one possible] interpolation
• proper derivation of the vdW equation (a la Landau)
9. Kinetic theory of gases
• Maxwell distribution of velocities
• Transport processes: predictions of statistical mechanics
• mean free path
• phenomenological transport laws
• derivation of a transport equation: viscosity
• experimental example: from Boyle (1660) to Maxwell (1866)
• transport of energy: heat
• transport of the number of particles: diffusion
• experimental example: pore size determination by NMR
10. Introduction to interacting systems
• statistical mechanics: a quantum mechanical perspective
• stationary states; energy representation; expectation values
• random fluctuations in wave functions; time average
• density matrix formalism
• thermal average is the derivative of free energy
• example: non-interacting spins in an external magnetic field; a review
• the Ising model of a ferromagnet
• mean-field approximation
• self-consistency relation; graphical and numerical solutions
• critical exponents; predictioins of mean-field theory

• Student presentations: TBA