M.Sc.(Semester II) (CBCS) Examination Oct/Nov-2017
Physics (Materials Science)
STATISTICAL MECHANICS
Day Date: Wednesday, 22-11-2017 Max. Marks: 70
Time: 10:30 AM to 01.00 PM
Instructions: Q. No. and Q. No are compulsory.
Attempt any three from Q. No. to Q. No.
Use of Non programmable calculator is allowed.
All questions carry equal marks.
Q.1 Choose correct alternative: 06
The statement of First law of thermodynamics in case of ideal gas is

−
2 Which of the following are not fermions?
He3 Nucleons
He4 Electrons
3 Two ends of the rod are kept at 100°C and 200°C. when 1000 cal of
heat flows in this rod, then the change in entropy is
0.1 Cal K 50 Cal K
10 Cal K 5 Cal K
4 The classical statistics reduces to quantum statistics under the
following condition
1
1
1
0
Where is the number density of the particles and is
the thermal de-Broglie wavelength
5 Mean number of particles in case of BE statistics is given by
6 In canonical ensemble, the system exchange
Only matter Only energy
Both energy and matter Neither energy not matter
State True or False: 08
Conversion of a metal to superconductor in absence of a magnetic field
is an example of first order phase transition.
The Fermi energy of a free electron gas at absolute zero is of the order
of eV.
In quantum statistics, the normalization condition for canonical
ensemble is given by 1.
The first order phase transitions are accompanied by a discontinuous
change in Gibb's molar free energy function.
In grand canonical ensemble, the relative r.m.s. fluctuations in N is
negligible.
If the entropy of a closed system does not have its maximum value at
any time, then the entropy will increase or at least remain constant at a
late time.
The entropy of the universe in a reversibly process is not constant.
Electrons obey Fermi-Dirac statistic.
Q.2 Write short notes on:
Fokker-Planck equation. 05
Critical indices 04
Law of corresponding states? 05
Q.3 Explain the concept of microcanonical ensemble. Obtain the expression for
Gibb's microcanonical distribution.
10
Write Einstein's approach upon Brownian motion. 04
Q.4 State and explain the second law of thermodynamics. Give its applications. 08
Explain Tisza two fluid model to explain He I to He II transition. 06
Q.5 Derive expression for critical temperature in case of ideal Bose gas. Based
on this explain the phenomenon of Bose-Einstein condensation.
10
Differentiate between macroscopic and microscopic states. 04
Q.6 Develop Langevin theory of Brownian motion of particles. Derive Einstein's
relation for diffusion coefficient in this case.
08
Write note a fluctuation-dissipation theorem, 06
Q.7 State and explain conditions for phase equilibrium. Derive Clasius
Clayperon equation.
10
State and explain Nernst's Theorem. 04