Master of Science I (Physics Material Science) Examination:
Oct Nov 2016 Semester II (New CBCS)
SLR No. Day
Date Time Subject Name Paper
No. Seat No.
SLR SH
541
Thursday
17/11/2016
10.30 AM
to
01.00 PM
Statistical Mechanics
C
V
Instructions: Question No. 1 and 2 is compulsory.
Attempt any three questions from Q.no. 3 to Q. no. 7
Figures to right indicate full marks.
Use of non programmable calculators is allowed.
Total Marks: 70
Q.1 Choose correct alternative. 10
The first law of thermodynamics is conservation of
Momentum Energy
Both a and b None of these.
The change in entropy is
Positive in a reversible
change
Negative in an irreversible
change.
Positive in an irreversible
change
Negative in a reversible
change
Change in entropy depends
Only on the transfer of heat Only on change of
temperature
On transfer of mass On the thermodynamic state
In Gibb's function G in thermodynamics is defined as G H-TS. In an
isothermal, isobaric, reversible process, G
remain constant but not zero varies linearly
varies non linearly is zero
According to Maxwell's law of distribution of velocities of molecules, the
most probable velocity is velocity.
Greater than the mean Equal to the mean
Equal to root mean square Less than the root mean square
In a micro canonical ensemble, a system A of fixed volume is in contact
with a large reservoir B. Then
A can exchange only energy with B
A can exchange only particles with B
A can exchange neither energy nor particles with B
A can exchange both energy and particles with B
In case of Bose Einstein condensation pressures.
Number of particles increase in lower energy levels at low
temperatures and high
Number of particles decreases in lower energy levels at low
temperatures and high
Number of particles increase in lower energy levels at high
temperatures and low
Number of particles decreases in lower energy levels at high
temperatures and low
Page 2 of 3
The quantum statistics reduces to classical statistics under the following
condition
λ3 ≈ 1 λ3 1
λ3 1 0
Fill in the blanks State true/ false 06
Micro-canonical ensemble is related to system in which neither
nor change. (energy, particles)
Plank's radiation law can be derived by using by using
Maxwell-Boltzmann statistic. (True/ False)
B.E. statistic is applicable to photon and symmetric particles.
(True/False).
The entropy of a system approaches a constant value as the temperature
approaches absolute zero. (True/False)
In physics, a function describes the statistical properties of a
system in thermodynamic equilibrium. (partition)
statistics describes a distribution of particles over energy
states in systems consisting of many identical practical particles that obey
the Pauli exclusion principle. (Fermi-Dirac)
Q.2 Attempt the following:
What is grand canonical ensemble? 05
Give the definition of entropy in statistical physics. 04
A one -dimensional quantum harmonic oscillator (whose ground state
energy is is in thermal equilibrium with a heat bath at temperature T.
What is the mean value of the oscillator's energy, as a function of
T
What is the mean value of the ΔE, the root-mean-square fluctuation in
energy about
How do and ΔE behave in the limits kT and kT
05
Q.3 Answer the following:
Explain the 1st and 2nd order phase transitions in detail. 08
Verify Liouville's theorem in the case of the motion of the motion of three
particles in a constant gravitational field.
06
Q.4 Answer the following: 14
Show that the Sackur-Tetrode equation, may be written in the form:
Where p is the pressure of the ideal gas.
Explain Boltzmann statistics, Fermi statistics and Bose statistics, especially
about their difference. How are they related to the indistinguishability of
identical particles?
Give as physical a discussion as you can, on why the distinction between the
above three types of statistics becomes unimportant in the limit of high
temperature (how high is high?)
Page 3 of 3
Q.5 Attempt the following:
What is canonical ensemble? Drive canonical distribution law with partition
function.
10
Write anote on density matrix. 04
Q.6 Answer the following:
Explain Phase equilibrium and derive the Clausius-Clapeyron equation. 10
Explain Langevin's opinion related to Brownian motion of particle. 04
Q.7 Answer the followings:
Solve and explain Fokkr-Planck equation 07
Explain Einstein-Smoluchowski theory of Brownian motion and drive the
Smoluchowski equation