Statistical Thermodynamics

0351.3209
Undergraduate course, Semester A, 2014/2015
Monday, 16:00-19:00, Ornstein 111

---

Program

• Lecture 1 (27/10/14)
  • 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 motion of gas molecules (requires either a Java plugin or downloading a free package of simulations; follow the link)
   
• Lecture 2 (3/11/14)
  • Reminder of statistics: continuous probability distributions
  • Basic assumptions: ergodicity, Gibbs' entropy, the fundamental postulate
  • Ensembles
  Proof of the H-Theorem
   
• Lecture 3 (10/11/14)
  • Microcanonical ensemble
  • Tutoring: system of two-state particles
  • Negative temperature
  • Tutoring: system of independent harmonic oscillators
  Simulation of a small elastic body in the microcanonical ensemble
  Exercise #1  Solution #1
  
  
• Lecture 4 (17/11/14)
  • Systems in thermal contact
  • Canonical ensemble: Boltzmann distribution, canonical partition function, Helmholtz free energy
  
  
• Lecture 5 (24/11/14)
  • Tutoring in the canonical ensemble: system of two-state particles; system of independent harmonic oscillators.
  • Fluctuations and ensemble equivalence
  Exercise #2  Solution #2
  
  
• Lecture 6 (1/12/14)
  • Non-degenerate monoatomic ideal gas
  Exercise #3  Solution #3
   
• Lecture 7 (8/12/14)
  • Non-degenerate molecular ideal gas
  • Tutoring: rotational degrees of freedom in a diatomic ideal gas
  • Classical statistical thermodynamics
  Exercise #4  Solution #4  Article addressing Ex4/Q3
  
  
• Lecture 8 (15/12/14)
  • Classical ideal gas
  • Equipartition principle
  • Maxwell-Bolzmann distribution
  
  
• Lecture 9 (22/12/14)
  • Nonideal gas: second virial coefficient
  • Van der Waals equation of state
  Exercise #5  Solution #5
   
• Lecture 10 (29/12/14)
  • Systems in thermal and diffusive contact
  • Grand-canonical ensemble: Gibbs distribution, grand-canonical partition function, grand-canonical potential
  
  
• Lecture 11 (5/1/15)
  • Tutoring: non-degenerate ideal gas in the grand-canonical ensemble
  • Tutoring: distribution of particle number in a sub-volume of an ideal gas
  • Further tutoring
  Exercise #6  Solution #6
  
  
• Lecture 12 (12/1/15)
  • Degenerate ideal gases: Fermi-Dirac distribution
  • Bose-Einstein distribution
  • Fermionic gas: density of states
  
   
• Lecture 13 (19/1/15)
  • Fermionic gas: Fermi energy, internal energy at T=0
  • Fermionic gas: thermodynamic properties, Fermi energy
  • Bosonic gas: Bose-Einstein condensation
  Exercise #7  Solution #7
  

Past exams