M. Sc. Physics (Materials Science) (Semester II)
(CBCS) Examination, 2017
STATISTICAL MECHANICS
Day Date: Monday, 24-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. Q.1 and Q.2 is compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Q.1 Choose correct alternatives: 08
Which of the following is not example of second order phase
transition?
Iron ferromagnetic to paramagnetic state at Tc
Conductor to superconductor at Tc.
Water into vapour at Tc
Liquid He I to liquid He II at
The statement of First law of thermodynamics in case of liquid
film is


For two assemblies of equal volumes are at same temperature
and pressure, the entropy on removing partition becomes
The factor In 2 arise due to
The indistinguishability of classical particles.
The distinguishability of classical particles
The steady flow of particles
The absence of interpaticle interaction
In isotherms of liquid- gas transition (van der Waals curves) of
real gas.
Maxima and minima points come closer with rise in
temperature.
Maxima and minima points turn away with rise in
temperature.
There are no maxima and minima points in the region
T<Tc.
There are maxima and minima points in the region T>Tc.
In relation to statistical mechanics (Choose incorrect
statement)
All particles of a given kind are treated as mutually
Page 2 of 2
indistinguishable.
The phase space of degrees of freedom will have 2
dimensions its unit cell volume will be
With a system having particles, probability of two
halves of a box having particle density difference of
0.0001% in negligibly small.
Photons may be treated as following Fermi-Dirac statistics.
An ensemble is considered to be in statistical equilibrium if




Q.1 State true or false: 08
He4 are bosons.
40K19 atoms can exhibit Bose-Einstein condensation.
The thermodynamic properties of a system derived for
canonical ensemble and microcanonical ensemble are
identical.
Particles having spin= ½ are known as Bosons.
The complete phase space is the sum of configuration and
momentum spaces.
Bursting of cycle tube is an example of isothermal change.
In canonical and grand canonical ensembles, the relative
r.m.s. fluctuations in E are negligible.
The total wave function of the Bose-Einstein system is
symmetric under exchange of co-ordinate of any particles.
Q.2 Write short answers on the following:
Tisza two find model to explain He I to He II transition. 05
Zeroth law of thermodynamics. 04
Clasius Clayperon equation. 05
Q.3 Give the expression for thermodynamic functions for Gibb's
Canonical Ensemble.
10
Differentiate between Bosons and Fermions. 06
Q.4 Explain Liouville's theorem in classical presentation. 08
Obtain the 'equation of state' for an ideal Bose gas. 06
Q.5 Discuss in detail the case of weakly degenerate ideal Fermi Gas. 08
Differentiate between microscopic and microscopic states. 08
Q.6 Develop Langevin theory of Brownian motion of particles. Derive
Einstein's relation for diffusion coefficient in this case.
08
Explain P-T diagram of one component system. 06
Q.7 Explain Liouville's theorem in classical presentation. 10
Write noteon Gibb's paradox. 04