Mechanics Statistical

Course: M.Sc. Code: GH-553 Branch: Physics Year: 2022

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Roll No. ............................

[Total No. of Printed Pages : 8

Total No. of Questions : 11]

M.Sc. IInd Semester (Reg./ATKT)

Examination, 2022

Physics

Paper - II

Mechanics Statistical

Time : 3 Hours]

[Maximum Marks : 85

Note : - Attempt all questions from section A, B and C. Internal choice is given in section B and C.

SECTION - 'A' 1×15=15

Objective Type Questions

1.
Choose the correct answer.

(i) The micro-canonical ensemble is a collection is a collection of essentially independent assemblies having the same :

(a) Temperatrue (T), Volume (V) and number of systems (N)

(b) Energy (E), Volume (V), and number of systems (N)

(c) Temperature (T), volume (V) and chemical potential (μ)

(d) None of the above

(ii) The relation between kinetic energy (E) and linear momentum (p) in a system is given by :

(a) E = p / 2m

(b) E = p2 / 2m

(c) E = √p / 2m

(iii) Total number of coordinates in phase space are :

(a) 1

(b) 3

(c) 6

(d) 2

(iv) The statistics which electron obey is :

(a) M-B statistics

(b) B-E statistics

(c) F-D dirac statistics

(d) All of the above

(v) Pauli's exclusion principle must be followed by particles in:

(a) Fermi-Dirac statistics

(b) Bose-Einstein statistics

(c) Maxwell's-Boltzman statistics

(d) None of the above

(vi) The Bose - Einstein condensation in the matter occures at:

(a) Very low density & high temperature

(b) High density and low temperature

(c) Very low density and very low temperature

(d) High density and high temperature

(vii) The cluster expansion is known as:

(a) High temperature expansion

(b) A power series expansion of partition function

(c) Hopping expansion

(d) All of the above

(viii) The Ising model was invented by the physicist :

(a) Ernst Ising

(b) Lars on sagar

(c) Wilhelm Lenz

(d) Gibbs

(ix) The virial coefficients depend on :

(a) The temperature

(b) The particular gas

(c) The temperature and the particular gas

(d) None of these

(x) The fluctuation is a parameter is measured by:

(a) Mean square value

(b) Mean value

(c) Mean square deviation

(d) None of the above

(xi) The reciprocity relation of irreversible process was given by:

(a) Yang and Lee

(b) Onsagar

(c) Landau

(d) Fokker and Plank

(xii) Fluctuation dissipation theorem is related with:

(a) Bose-Einstein condensation

(b) Brownian-motion of particles

(c) Fermi-Dirac statistics

(xiii) Gibb's paradox arises due to:

(a) Omittance of quantum nature of the particles

(b) Indistinguishability of classical particles

(c) Distinguishability of classical particles

(d) Absence of inter-particle interaction

(xiv) The classical partition function z gives the:

(a) Sum of states of the system

(b) Sum of energy of the system

(c) Sum of momentum of the system

(d) None of these

(xv) If Z1, Z2 and Z3 are independent partition functions of system, the total partition function of the combined system is:

(a) z = z1 + z2 + z3

(b) z = 1/z1 + 1/z2 + 1/z3

(c) z = z1.z2.z3

(d) None of these

SECTION - 'B' 5×5=25

Short Answer Type Questions

2.
What do you mean by phase space? How will you divide the phase space into cell?

OR

Define entropy and derive an expression s = k log w, where k is a Boltzmann constant.
3.
Distinguish between Bose-Einstein and fermi-Dirac statistic.

OR

Explain the properties of ideal fermi gases.
4.
Write the virial equation of state for gases and explain it.

OR

What is the mean field theory Ising model.
5.
State fluctuation dissipation theorem.

OR

What is a Brownian motion? Derive an expression due to the thermal fluctuation of pressure on the particle for Brownian motion.
6.
What is an ensemble? Explain canonical, micro canonical and grand canonical ensembles.

OR

Explain density matrix.

SECTION - 'C' 9×5=45

Long Answer Type Questions

7.
What is Gibb's paradox? How it has been solved.
8.
Discuss the phenomenon of Bose-Einstein condensation.

OR

Derive the Fermi-Dirac distribution formula of statistics.
9.
Discuss cluster expansion for a classical gas.

OR

Discuss one dimensional Ising model.
10.
Discuss Onsagar reciprocity relation.

OR

Explain the Fokker - Plank equation in detail.
11.
Write short notes on any two of the following :-

(a) Liouville theorem.

(b) Ising mdoel in two dimension.

(c) Boltzmann transport equation.

(d) Ising model in three dimension.

GH-553 (1) P.T.O.

GH-553 (2)

GH-553 (3) P.T.O.

GH-553 (4)

GH-553 (5) P.T.O.

GH-553 (6)

GH-553 (7) P.T.O.

GH-553 (8) Copies 1000