Statistical Thermodynamics

0351.3209
Undergraduate course, Semester A, 2013/2014
Monday, 16:00-19:00, Ornstein 110

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Program

• Lecture 1 (14/10/13)
  • 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 (21/10/13)
  • Reminder of statistics: continuous probability distributions
  • Basic assumptions: ergodicity, Gibbs' entropy, the fundamental postulate
  • Ensembles
  • Microcanonical ensemble
  • Tutoring: system of two-state particles
  Proof of the H-Theorem
   
• Lecture 3 (28/10/13)
  • System of two-state particles (cont.)
  • Negative temperature
  • Tutoring: system of independent harmonic oscillators
  Exercise #1  Solution #1
  
  
• Lecture 4 (11/11/13)
  • Systems in thermal contact
  • Canonical ensemble: Boltzmann distribution, canonical partition function, Helmholtz free energy
  • Tutoring in the canonical ensemble: system of two-state particles; system of independent harmonic oscillators.
  Exercise #2  Solution #2 (courtesy of Mr. Tal Levy)
  
  
• Lecture 5 (18/11/13)
  • Fluctuations and ensemble equivalence
  • Non-degenerate monoatomic ideal gas
  Exercise #3  Solution #3
  
  
• Lecture 6 (25/11/13)
  • Non-degenerate monoatomic ideal gas (cont.)
  • Non-degenerate molecular ideal gas
  • Tutoring: rotational degrees of freedom in a diatomic ideal gas
  Exercise #4  Solution #4  Article addressing Ex4/Q4
   
• Lecture 7 (2/12/13)
  • Classical statistical thermodynamics
  • Classical ideal gas
  • Equipartition principle
  
  
• Lecture 8 (9/12/13)
  • Maxwell-Bolzmann distribution
  • Tutoring: equipartition principle
  • Nonideal gas: second virial coefficient
  Exercise #5  Solution #5
  
  
• Lecture 9 (16/12/13)
  • Nonideal gas: van der Waals equation of state
  • Systems in thermal and diffusive contact
  • Grand-canonical ensemble: Gibbs distribution, grand-canonical partition function, grand-canonical potential
  
  
• Lecture 10 (23/12/13)
  • Tutoring: non-degenerate ideal gas in the grand-canonical ensemble
  • Tutoring: distribution of particle number in a sub-volume of an ideal gas
  • Degenerate ideal gases: Fermi-Dirac distribution
  Exercise #6  Solution #6
  
  
• Lecture 11 (30/12/13)
  • Bose-Einstein distribution
  • Fermionic gas: density of states, Fermi energy, internal energy at T=0
  
  
• Lecture 12 (6/1/14)
  • Fermionic gas: thermodynamic properties
  • Bosonic gas: Bose-Einstein condensation
  Exercise #7  Solution #7
   
• Lecture 13 (13/1/14)
  • Tutoring
  
  

Past exams