LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

FG 28

M.Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – APRIL 2008

    PH 1810 / 1801 – STATISTICAL MECHANICS

 

 

 

Date : 05/05/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART A ( 20 MARKS )

ANSWER ALL QUESTIONS. Each question carries 2 marks.

 

1. State the ergodic hypothesis. Is it true ?
2. Distinguish between the micro-canonical ensemble and the canonical ensemble.

3. State the postulate of equal-a-priori probability.

1. Sketch the Maxwell velocity distribution
2. How does the vibrational contribution to the specific heat vary with temperature ?
3. What are quasi-particles ? Give an example.
4. What is the pressure exerted by an ideal Fermi gas at absolute zero ?
5. What is the importance of the Chandrasekhar limit ?
6. What is the implication of Einstein’s result for the energy fluctuations of blackbody radiation ?
7. State Nyquist theorem.

 

    PART B ( 30 MARKS )

ANSWER ANY FOUR QUESTIONS. Each question carries 7.5 marks.

 

1. State and explain the basic postulates of statistical mechanics.
2.  Obtain the distribution for an ideal Maxwell –Boltzmann gas.
3.  Explain Bose-Einstein condensation. Discuss the super-fluidity of Helium by considering it as a form of Bose-Einstein condensation.
4. Derive the Richardson-Dushman equation, which describes thermionic emission.
5.  Obtain the relations, which state the Wiener-Khintchine theorem.

 

PART C ( 50 MARKS )

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 12.5 MARKS.

 

1. (a)  Explain Gibb’s paradox. How is it resolved ?

(b) Prove Liouiville theorem.

1. Calculate the entropy of an ideal  Boltzmann gas  using the micro canonical ensemble. Explain the corrections to be made to obtain the Sackur-Tetrode equation.

 

1.   Discuss the thermodynamic properties of an ideal Bose-Einstein gas.

 

1.  Calculate the pressure exerted by a Fermi-Dirac gas of relativistic electrons in the ground state. Use the result to explain the existence of the Chandrasekhar limit on the mass for a white dwarf.
2.  (a) Calculate the concentration fluctuations for a grand canonical ensemble. Show that for an ideal classical gas it increases as the volume of the gas increases.

(b)   Prove the Nyquist theorem.

 

 

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