Calicut University 2006 M.Sc Physics Phy203 -STATISTICAL AND THERMAL - Question Paper
SECOND SEMESTER M.Sc. DEGREE EXAMINATION, AUGUST 2006
Physics
Phy. 203 -STATISTICAL AND THERMAL PHYSICS
(2003 admissions)
C 17063 (Pages : 2) Name.....................................
Reg. No.................................SECOND SEMESTER M.Sc. DEGREE EXAMINATION, AUGUST 2006
Physics
Phy. 203STATISTICAL AND THERMAL PHYSICS (2003 admissions)
Time : Three Hours Maximum : 80 Marks
Section A
Answer any five questions.
Each question carries 4 marks.
1. Show that the number of states in unit volume of phase space is l//i3.
2. Show that in the canonical ensemble formulation, the internal energy of a system can be expressed as TJ = CAB') where A is the Helmholtz free energy.
3. Prove that in the canonical ensemble theory S/ft = - Pr InPr. Discuss the physical importance of this result.
4. The average energy of a harmonic oscillator is given by E = (n. + 1/2) hio where n = 0, 1, 2, 3,.. Fiad. the partition function of this oscillator. Z/
5. State and prove equipartition theorem, j
6. Explain quantum Hall effect.
7. What is fountain effect ? How is it explained ?
8. Briefly outline the one-dimensional Ising model.
(5 x 4 = 20 marks)
Section B
Answer any two questions.
Each question carries 20 marks.
9.(6) (i) Bring out the concept of ensembles in statistical mechanics. How are ensembles
classified ?
(ii) What is meant by Gibbs paradox ? How is it explained ?
Or
(b) Obtain the thermodynamic relations in canonical ensemble. Discuss energy fluctuations in the canonical ensemble.
10. (&) Derive a relation for Bose-Einstein distribution. Discuss thermodynamic behaviour of an ideal Bose gas and explain Bose-Einstein condensation. ,
Or
(b) Discuss the theory of white dwarfs and arrive at the Chandrasekhar limit.
(2 x 20 = 40 marks) Turn over
C 17063
Section C
2
Answer any two questions.
Each question carries 10 marks.
11. (a) Show that for an ideal gas composed of N identical molecules confined to a space of volume V and being in equilibrium at temperature T, the partition function QN (V, T) = [Qj (V, T)]n/N! where Qj (V, T) is the partition function of a single molecule in the system.
(b) Using this partition function show that the average energy U = 3/2 NfeT. fluctuation in the particle density is given by
< (An)2 > / < n >2 = xr
where XT is the isothermal compressibility of the system.
13. (a) Show that <G> = Tr (Gp) where G is an operator and p is the density operator.
(b) A Maxwell-Boltzmann system of N particles exists in one of the three non-degenerate levels of energy -E, 0, +E. Calculate the entropy of the system of OK and the maximum possible entropy of the system.
14. (a) Consider a system consisting of two particles each ofwhich can be in any one of three quantum
states of respective energies 0, E and 3E. The system is in contact with a heat reservoir at temperature T. Find out the partition functions if the particles obey BE statistics and FD Statistics.
(b) Fermi energy EF = 3.14 eV for an electron gas. Calculate Fermi temperature and Cy for T = 100 K.
(2 x 10 = 20 marks)
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