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CHEM_ENG 406: Intro to Statistical Thermodynamics


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Prerequisites

Multivariable Calculus

Description

Selected topic: Introduction to Statistical Thermodynamics.

Thermodynamics holds a special place among physical sciences.  To quote Albert Einstein:  "A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Hence the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that ... it will never be overthrown." 

This course will discuss thermodynamics from a statistical viewpoint, emphasizing the fundamental concepts and the logical structure of the subject.  Statistical thermodynamics is unusual among physical sciences in that the entire theory is built logically starting from two fundamental postulates.  Applications of statistical thermodynamics are extremely wide and diverse.  

The applications discussed in this course have been chosen for their intrinsic interest. Most go beyond a typical engineering curriculum — e.g., thermodynamics of electromagnetic radiation, the phonon gas model, Bose-Einstein condensation, Fermi pressure, white dwarfs and neutron stars, etc.

Course outline:

1.The basic postulates

  1. The Boltzmann factor
  2. Partition function
    4. Canonical distribution
  3. Ideal gas
  4. The van der Waals fluid
  5. Thermodynamics of electromagnetic radiation
  6. Equilibrium (black-body) spectrum 
  7. The ultraviolet catastrophe 
  8. Grand canonical distribution
  9. Bose-Einstein and Fermi-Dirac distributions
  10. Photons
  11. Why the chemical potential of photon is zero
  12. Planck distribution for radiation
  13. Phonon gas model for thermodynamics of solids
  14. Bose-Einstein condensation
  15. Fermions
  16. Fermi pressure 
  17. Why white dwarfs and neutron stars exist
  18. Brownian motion (if time permits)

This graduate-level course is open to undergraduates, multivariable calculus being the only prerequisite.  

The ABET designation for this course is "Mathematics & Basic Science Topics 100%".

There will be no exams. The final grade will be primarily determined by the term paper – a review of published research articles on a topic related to the material of the course. The topic of the term paper will be chosen by each student in accordance with their interests.

No textbook is required or recommended; the class notes will suffice.