Physics (Materials Science) (Semester II)
(CBCS) Examination, 2017
STATISTICAL MECHANICS
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Day Date: Monday, 24-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. Questions NO.1 and 2 are Compulsory.
Answer any three from Q.NO.3 to Q.NO.7.
Figures to the right indicate full marks
All question carry equal marks.
Q.1 Choose the correct alternative: 06
A first order phase transition is characterized by
c A divergence of the specific heat at Tc, the critical
temperature.
A cusp in the average energy at Tc.
The constancy of entropy in the transition.
The latent heat is involved in the transition process.
2 For a system in thermodynamic equilibrium the following must
be necessarily constant throughout the system:
Temperature and pressure.
Temperature and not pressure.
Pressure and chemical potential.
Temperature, pressure and chemical potential.
3 Which of the following atoms cannot exhibit Bose-Einstein
condensation, even in principle?
1H1 4He2
23Na11 40K19
4 A photon gas is at thermal equilibrium at temperature T. The
mean number of photons in an energy state is
5 For the Fermi-Dirac distribution, probability of occupation of a
single particle energy level is equal to:
The average occupancy of that level.
One
½ the average occupancy of that level
Zero
6 Which of the following thermodynamic relation is incorrect?
Here are the pressure, volume and temperature, and
are the Helmholtz Free energy, Gibbs' Free energy,
entropy and average energy respectively.
State True or False/ Fill in the blanks: 08
Entropy of the ice chips in the glass is equal to the entropy of
the water in the glass.
In canonical ensemble, the relative r.m.s. fluctuations in E are
negligible.
At absolute zero, all fermions may be in ground state.
Saturation curve terminates at critical point.
Sound wave travels in the air is an example of isothermal
change.
In classical statistics, the normalization condition for canonical
ensemble is given by
Bose Einstein condensation occurs in case o ideal gas.
He4 particles have spin ½ .
Q.2 Write a short note on following:
Macroscopic and microscopic states. 05
Canonical Ensemble 04
Bose -Einstein condensation 05
Q.3 Explain the concept of Canonical Ensemble. Obtain the expression
for Gibb's Canonical distribution.
10
Give three statements of Second law of thermodynamics. 04
Q.4 State and explain the First law of thermodynamics. Give its
applications.
08
State and explain the third law of thermodynamics. 06
Q.5 Explain Liouville's theorem in classical presentation. 10
What is principle of conservation of density in Liouville's theorem? 04
Q.6 Give the expressions for thermodynamic functions for Gibb's
Canonical Ensemble.
08
State the types of ensembles, with their definitions, in the
application statistical mechanics.
06
Q.7 Develop Langevin theory of Brownian motion of particles. Derive
Einstein's relation for diffusion in this case.
10
Develop the theory for Cluster expansion for classical gas. 04