(4×5=20)

PG – 700

*PG700*

II Semester M.Sc. Examination, June 2016 (2010 Scheme) PHYSICS Paper – 201 : Statistical Mechanics Time : 3 Hours

Max. Marks : 80

Instructions : 1) Answer all questions. 2) Questions 1 to 8 carry 15 marks. 3) Question No. 9 carries 20 marks. 1. a) Explain the terms : i) Statistical ensemble. ii) Quasi-static processes b) Discuss the approach to thermal equilibrium between two macroscopic systems thermally interacting with each other. (6+9) OR 2. a) What is an isolated system ? Discuss. b) With the help of suitable examples, explain how the number of states accessible to an isolated system approach a maximum, with the removal of some constraints on it. (5+10) 3. a) Define partition function and show that the canonical partition function is related to the mean energy of the system. b) Discuss the calculation of thermodynamic quantities for an ideal monoatomic gas using partition function. (6+9) OR 4. a) Explain the concept of entropy. b) What is Gibb’s Paradox ? Discuss, with reference to an ideal monoatomic gas, how the paradox can be resolved. (5+10)

P.T.O.

PG – 700

*PG700*

5. a) What are the symmetry requirements for a quantum mechanical description of fermions and bosons ? b) Arrive at an expression for the quantum distribution function for a system of bosons. (5+10) OR 6. a) Arrive at an expression for the Fermi-Dirac distribution function. b) Estimate the contribution of free electrons to the specific heat in metals.

(10+5)

7. a) What is Brownian motion ? Explain. b) Set up the Langerin equation and solve it to obtain an expression for the mean square displacement of Brownian particle. (5+10) OR 8. a) Obtain the expression for spectral density J(w) in terms of Fourier coefficient C(w). b) Explain the terms : i) Ensemble average and ii) Time average.

(10+5)

9. Answer any four of the following : a) State and explain the basic postulate of equal a priori probability. b) Write a note on equipartition theorem. c) Write a note on Maxwell’s velocity distribution. d) Explain the terms ‘distinguishable’ and ‘indistinguishable’ particles, with reference to a system of identical particles. e) Write a note on Random talk. f) What are Onsager reciprocity relations? Explain their significance. –––––––––––––––

(4×5=20)