Description

Yashwantrao Chavan Maharashtra Open University (YCMOU)

Yashwantarao Chavan Maharashtra Open University, Nashik
Dnyangangotri, Near Gangapur Dam, Govardhan Nashik-422222

V153 M.Sc. (PHYSICS) (SEM-III)
PHY601-Statistical Mechanics
Home Assignments (Year 2024-25)

SEMESTER – III
PHY 601: Statistical Mechanics Marks: 20

HOME ASSIGNMENT-1
Q.1. Solve following Long Answer Question. 10 Marks
a) Explain how Maxwell’s relations are derived using thermodynamic potentials such as the internal energy, Helmholtz free energy, Gibbs free energy, and enthalpy. Discuss how Maxwell’s relations simplify calculations of thermodynamic properties and illustrate with examples.
Q.2. Solve following Short Answer Questions. 10 Marks
a) Define the partition function in the context of a canonical ensemble. Why is it a central quantity in statistical mechanics? 5 Marks
b) What is Bose-Einstein (BE) statistics, and how does it differ from Fermi-Dirac statistics? 5 Marks

HOME ASSIGNMENT-2
PHY 601: Statistical Mechanics Marks: 10
Q.1. Solve following Multiple Choice Questions (MCQ). (Each-1 Mark) 10 Marks
1) The probability distribution in a microcanonical ensemble is:
A) Gaussian B) Constant for all accessible states
C) Exponential D) Zero for all states
2) In a canonical ensemble, the temperature of the system is:
A) Fixed and uniform B) Constant but not uniform
C) Variable across the system D) Dependent on the partition function only
3) The partition function Z for a system of N distinguishable, non-interacting particles is given
by:
A) Z = Z1N B) Z = NZ1 C) Z = Z1/N D) Z = N ln(Z1)
4) Which of the following quantities remains constant in a grand canonical ensemble?
A) Energy B) Temperature C) Number of particles D) Volume
5) The Sackur-Tetrode equation is used to calculate the entropy of:
A) A fermionic system B) A classical ideal gas
C) A photon gas D) A Bose-Einstein condensate
6) The chemical potential of photons in an electromagnetic field is:
A) Positive B) Negative C) Zero D) Dependent on temperature
7) In Fermi-Dirac statistics, what is the occupation probability at absolute zero for a state with
energy equal to the Fermi energy?
A) 0 B) 0.5 C) 1 D) It depends on the temperature
8) The phenomenon of Bose-Einstein condensation occurs when:
A) All particles in a Bose gas occupy the highest energy state
B) The temperature is higher than the critical temperature
C) A macroscopic number of particles occupy the lowest energy state
D) The chemical potential becomes negative
9) In classical statistics, the Maxwell-Boltzmann distribution applies to:
A) Distinguishable particles with no restriction on state occupancy
B) Indistinguishable particles with each state occupied by one particle
C) Particles following the Pauli Exclusion Principle
D) Systems at extremely low temperatures
10) The term “ensemble” in statistical mechanics refers to:
A) A single isolated system
B) A collection of all possible states of a system under specified conditions
C) An approximation method for quantum systems
D) Only the microcanonical ensemble