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. and Q. No.
Use of Non programmable calculator is allowed.
All questions carry equal marks.
Q.1 Choose correct alternative: 06
The entropy of an ideal gas at absolute zero is
∞ 0
Cannot be calculated
The wave functions of two identical particles in states and are given
by and respectively. The particles obey Maxwell-
Boltzmann statistics. The state of the combined two particle system is
expressed as


1
2


1
2
−

Consider a two level quantum system with energies 0 and
The Helmholtz free energy of the system is given by
ln(1 ln(1
ln(1 − ln(1 −
Identify which one is a first order phase transition?
A liquid to gas transition at its critical temperature
A liquid to gas transition close to its triple point
A paramagnetic to ferromagnetic transition in the absence of
magnetic field.
A metal to superconductor transition in the absence of a magnetic
field.
The volume of a perfect gas is doubled, the number of atoms and
energy being held constant. The change in entropy will be:
ln ln
ln 2
1
2

Page 2 of 2
SLR-MO-521
Thermodynamic variables of the system can be volume pressure
temperature number of particles internal energy and chemical
potential etc. For a system to be specified by Microcanonical
Canonical and Grand canonical ensembles, the parameters
required for the respective ensembles are:
MC: CE: GC:
MC: CE: GC:
MC: CE: GC:
MC: CE: GC:
State True or False: 08
The Fermi energy of a free electron gas at absolute zero is of the order
of MeV.
In a process, a thermally isolated system goes over to one microstate
to another, then the entropy tends to increase or remain constant.
The entropy of the universe in a reversible process is increasing.
In grand canonical ensemble, the system exchange both energy and
matter.
The energy density of photon gas maintained at a temperature is
proportional to
During transition of a matter from one phase to another, entropy
remains constant.
The free energy of a photon gas enclosed in a volume is given by
where is a constant and is the temperature of the
gas. The chemical potential of the photon gas is zero.
are not bosons.
Q.2 Write short notes on:
Fluctuation-Dissipation theorem 05
Classical and Quantum statistics 05
Microanonical Ensemble 04
Q.3 What are the energy fluctuations in Canonical Ensemble? Explain. 10
What do you mean by 'critical indices'? 04
Q.4 State and explain conditions for phase equilibrium. Derive Clasius
Clayperon equation.
08
Derive Fokker-Planck equation. 06
Q.5 Obtain the 'equation of state' for an ideal Bose gas. 10
Explain P-T diagram of one component system. 04
Q.6 Explain the concept of Grandcanonical Ensemble. Obtain the expression
for Gibb's Grandcanonical distribution.
08
What is law of corresponding states? 06
Q.7 State and explain the Second law of thermodynamic. Give its applications. 10
Distinguish between First and Second order phase transitions. 04