Farwa, Faiza, Humaira, Javeria and Ayesha
Department of Chemistry
Terminal Examination, MPhil Statistical Mechanics
Time Allowed: 3 hours
Attempt all questions
Marks: 50
Date: 06th june, 2021
Q-1(i) In how many ways 6 persons to be seated on a sofa set with three seats?
(ii)
In how many ways the word MURREE can be permuted?
(8 marks)
(iii) In how many ways 9 people can be seated on a bench if only 4 seats are available?
Q-2 (i) What are the vibrational contribution to G o for O2 (g) at 298.15 K? (The vibrational
frequency is 1580.246/cm.)
(ii) Derive the following expression for the vibrational contribution to the internal energy Ev
RTx/(ex-1) where x = hυ/kT
=
(12 marks)
Q-3. (a) Construct a diagram for N=6. U = 6e and gj=3 using M-B statistic., and then construct
similar to it but one particle is removed from the arbitrary level 3, so that U ´= 6ϵ-3ϵ.
(b) How many possible macrostates are there in the new system? (c) Calculate average occupation
number of the levels of the new system. (d) How many microstates? (e) Calculate the change in
entropy upon removing one particle from level 3.
(`10 marks)
Q-4. six distinguishable particles are distributed over 3 non-degenerate energy levels. Level 1 is
at zero energy, level 2 has an energy 1e, level 2 has an energy 2e. (a) Calcul;ate the total numer of
microstates for the system. (b) Calculate the number of microstates such that there are 3 particles
in level 1, 2 inlevel 2 and one in level3. (c) Find the energy of the distribution for which Wk is the
l;argest, (d) Calculate the total number of microstates if the total energy is 5e. (10 marks)
Q-5.
(a) Construct a diagram for M-B statistic having eight energy levels. . show the possible
macrostates of the system if the energy U = 7ε for six distinguishable particles, obeying M-B statistics. (b)
Calculate the thermodynamic probability of each macrostate, and (c) show that the total number of
possible microstates Ω is 5.77 x 105. (d) Find the average occupation number of each level.
Useful constants:
K = 1.38 x 10-23 J/k, h = 6.626 x 10 -34 J.S, c = 2.997 x 10 8 m/s