N A L A N D A O P E N U N I V E R S I T Y
M.Sc. Physics, Part-I
PAPER-IV
(Statistical Mechanics)
Annual Examination, 2016
Time 3 Hours. Full Marks 80
Answer any Five Questions.
All questions carry equal marks.
1. What is entropy Show that,
T
U
S K lnz U


where U mean energy
of the gas, S entropy, k Boltzmann constant, z partition function and absolute
temperature of the gas.
2. Explain partition function. Deduce expression for partition function of a monoatomic gas.
3. Prove that the one dimensional Ising model does not explain the spontaneous magnetization.
How does the solution of the two dimensional Ising model overcome these difficulties
4. State and prove Liouvill theorem. How is it analogous to the equation of continuity of an
incompressible fluid
5. Explain ensembles, microcanonical and the grand canonical ensembles. Derive Sackur-Tetrode
equation for a perfect gas.
6. Explain cluster expansion. Discuss the classical approach towards the theory of cluster
expansion.
7. Explain the first and the second order phase transitions. Give the Landau theory of phase
transition.
8. Derive the Virial equation of state and evaluate the Virial coefficients.
9. Derive Fermi-Dirac distribution law or Bose-Einstein distribution law.
10. What are critical indices Explain the different kinds of critical indices.