LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – PHYSICS
SUPPLEMENTARY EXAMINATION – JUNE 2007
PH 1806 / 1801- STATISTICAL MECHANICS
Date & Time: 27/06/2007 / 9:00 - 12:00
Dept. No.
Max. : 100 Marks
PART A
ANSWER ALL QUESTIONS
10 X 2 = 20
1. State the postulate of equal-a-priori probability.
2. Define the ensemble average of R(q,p) using the distribution function D(q,p,t).
3. State the condition for thermal equilibrium between two parts of a composite
system.
4. State two features of the Gibb’s canonical ensemble.
5. Why is the transition of He I to He II known as the lambda transition ?
6. What pressure does a fermion gas exert at absolute zero ?
7. State Einstein’s result for the particle diffusion constant.
8. Define Markoff processes.
9. Define (i) Co-relation function and (ii) spectral density for a randomly fluctuating
quantity.
10. Write down the Boltzmann transport equation.
PART B
ANSWER ANY FOUR QUESTIONS
4 X 7.5 = 30
11. State and explain the basic postulates of statistical mechanics.
12. Obtain the distribution function for an ideal Fermi gas.
13. Calculate the entropy of an ideal classical gas.
14. Derive the Richardson-Dushman equation for thermionic emission.
15. Prove that the fractional fluctuation in concentration is smaller than the MB case
for FD statistics and larger for BE statistics.
PART C
ANSWER ANY FOUR QUESTIONS
4 X 12.5 = 50
16.(a) Explain Gibbs paradox. How is it resolved ?
(b) Prove Liouville theorem.
17.(a) Derive the grand canonical distribution.
(b) Consider the ideal gas in the grand canonical ensemble and show that the fugacity
is directly proportional to concentration.
18. Discuss the thermodynamic properties of an ideal Bose-Einstein gas.
19.(a) Outline the Fourier analysis of a random function. Obtain the relations which state
the Wiener – Khintchine theorem.
(b) Discuss the application to electrical noise and hence state the Nyquist theorem.
20. Obtain the Boltzmann transport equation. Use it to find the distribution function in the
absence of collisions.
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