M.Sc. (Semester II) (CBCS) Examination Mar/Apr-2018
Physics (Materials Science)
STATISTICAL MECHANICS
Time: 2½ Hours
Max. Marks: 70
Instructions: Q. and are compulsory. Answer any three questions from Q.3 to Q.7. Figures to the right indicate full marks. All questions carry equal marks.
Q.1

Select the most correct alternative
06
A phase space is a dimensional space.
2
5
3
6
Which of the following is a Boson?
Electron
Positron
Proton
Photon
On the P-T diagram of phase transition, the state in which three phases coexist is represented by a point, known as
Critical point
Sublimation point
Boiling point
Triple point
If N is the number of particles then the standard relative deviation from mean value in case of energy fluctuation is order of


1
2
In which of the following ensemble, the temperature, chemical potential and volume is same but energy and number of particles are variable?
Canonical ensemble
Microcanonical ensemble
Grand canonical ensemble
None of the above
Which of the following is true for FD statistics

− −1
−1
−

State true or false Fill in the blank
08
For microcanonical ensemble, volume and energy of a system is variable (True/False)
Fermi energy level is the highest occupied energy level by fermions at absolute zero. (True/False)
He4 is a spin half particle. (True/False)
Specific heat at constant volume of an ideal Bose gas is discontinuous at T=T0 (where T0 is degeneracy temperature). (True/False)
In canonical ensemble, the relative r. m. s. energy fluctuations of system is negligible if Number of particles in the system is very large (True/False)
Page 2 of 2
SLR-UN-478
λ transition in liquid helium is an example of phase transition of second kind (True/False)
Photons obey Pauli's exclusion principle. (True/False)
The pressure of Fermi gas at absolute zero temperature is proportional to 5/3 power of the density. (True/False)
Q.2
Write a short note on following:
Maxwell Boltzmann statistics
05
Classical ideal gas
04
Phase transition
05
Q.3
Define and explain the types of ensembles. State their importance in statistical mechanics.
10
Differentiate between Fermi-Dirac statistics and Bose-Einstein statistics.
04
Q.4
Explain the second order phase transition with examples.
08
Derive the Fokker-Plank equation.
06
Q.5
What is an ideal Bose gas? Explain the Chemical Potential and Energy of an ideal BE gas.
08
Explain the law of corresponding states.
06
Q.6
What is mean by thermodynamic fluctuation? Explain fluctuation in enthalpy and volume.
10
Derive an expression for distribution of particles having half-integral spin.
04
Q.7
State the conditions for phase equilibrium and properties of matter near critical point.
10
State and explain third law of thermodynamics.
04