Statistical Thermodynamics

0351.3209
Undergraduate course, Semester A, 2011/2012
Monday, 16:00-19:00, Ornstein 110

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Program

• Lecture 1 (31/10/11)
  • The context of statistical thermodynamics: why study large systems separately?
  • Reminder of thermodynamics: thermodynamic laws, thermodynamic potentials, natural variables
  • Reminder of statistics: discrete probability distributions
  Simulation of irreversibility in a gas of hard disks (requires Java)
   
• Lecture 2 (7/11/11)
  • Reminder of statistics (cont.): continuous probability distributions, central value theorem
  • Underlying assumptions: ergodicity, Gibbs' entropy, the fundamental postulate
  • Ensembles
  • Microcanonical ensemble
  • Tutoring: system of two-state particles; entropy of mixing; negative temperature
  Proof of the H-Theorem
  Exercise #1  Solution #1
   
• Lecture 3 (14/11/11)
  • Tutoring: system of independent harmonic oscillators
  • Systems in thermal contact
  • Canonical ensemble: Boltzmann distribution, canonical partition function
  
  
• Lecture 4 (21/11/11)
  • Canonical ensemble (cont.): Helmholtz free energy
  • Tutoring in the canonical ensemble: system of two-state particles; system of independent harmonic oscillators.
  • Fluctuations and ensemble equivalence
  Exercise #2  Solution #2 (courtesy of Mr. Tal Levy)
   
• Lecture 5 (28/11/11)
  • Non-degenerate monoatomic ideal gas
  • Non-degenerate molecular ideal gas
  
  
• Lecture 6 (5/12/11)
  • Non-degenerate molecular ideal gas (cont.)
  • Tutoring: rotational degrees of freedom in a diatomic ideal gas
  • Classical statistical thermodynamics
  • Classical ideal gas
  Exercise #3  Solution #3  Article addressing Ex3/Q4
   
• Lecture 7 (12/12/11)
  • Equipartition principle
  • Maxwell-Bolzmann distribution
  • Nonideal gas: second virial coefficient; van der Waals equation of state
  Exercise #4  Solution #4
   
• Lecture 8 (26/12/11)
  • Mean-field approximation
  • Debye-Huckel theory for a plasma/electrolyte
  
  
• Lecture 9 (2/1/12)
  • Systems in thermal and diffusive contact
  • Grand-canonical ensemble: Gibbs distribution, grand-canonical partition function, grand-canonical potential
  • Tutoring: non-degenerate ideal gas in the grand-canonical ensemble
  Exercise #5  Solution #5
   
• Lecture 10 (9/1/12)
  • Degenerate ideal gases: Fermi-Dirac and Bose-Einstein distributions
  • Fermionic gas: density of states, thermodynamic properties
  
  
• Lecture 11 (16/1/12)
  • Fermionic gas: Fermi energy, internal energy at T=0
  • Bosonic gas: Bose-Einstein condensation
  Exercise #6  Solution #6
   
• Lecture 12 (23/1/12)
  • Thermal radiation
  • Correlations in liquids
  
  
• Lecture 13 (30/1/12)
  • Tutoring

Past exams