NATIONAL OPEN UNIVERSITY OF NIGERIA
14/16 AHMADU BELLO WAY, VICTORIA ISLAND, LAGOS
SCHOOL OF SCIENCE AND TECHNOLOGY
MARCH/APRIL 2014 EXAMINATION
COURSE CODE: PHY 311
COURSE TITLE: KINETIC THEORY AND STATISTICAL MECHANICS
TIME ALLOWED: 2 ½ HOURS
INSTRUCTION: ANSWER QUESTION ANY FOUR QUESTIONS
QUESTION 1
a) State the Equi-partition theorem
b) Consider a system A0 consisting of interacting subsystems A1 and A2 for which W1 = 1020 and W2 = 2 × 1020. What is the number of states available to the combined system A0? Also, what are the entropies S1, S2, and S0 in terms of Boltzmann’s constant?
QUESTION 2
a) What is Statistical mechanics
b) How many handshakes take place? Consider systems of 100 molecules in otherwise empty rooms. What is the average number of molecules in the front third of the rooms, the standard deviation about this value, and the relative fluctuation?
QUESTION 3
a) State the mathematical expression of Dulong–Petit law
b) Seven physicists assembled for a meeting shake hands with one another.
c) The number of molecule/m3 of a gas is 2.689 x1025 m-3 at N.T.P . Calculate the number of molecules/m3 of the gas at 2730K and 10-9 m of mercury pressure.
QUESTION 4
a) What is Entropy?
b) Differentiate between microstate and macrostsate .
c) The surface of the Sun acts like a blackbody of temperature
5800 K. What is the rate at which energy leaves each square meter of the Sun’s surface?
QUESTION 5
a) What is degree of freedom?
b) Calculate Cv for copper, given density= 9 g/cm3, atomic weight = 63.5 and valence equal to one.
c) The 3He atom is a fermion with spin 1/2 (why?). The density of liquid 3He is 0.081 g/cm3 near T = 0. Calculate the Fermi energy EF and the Fermi temperature TF.
QUESTION 6
a) What do you understand by Ensemble?
b) Consider 6 molecules and 3 cell of equal energy. All molecules are equally distributed among the cells. Calculate the thermodynamic probability.
c) A coin is so tossed that the probability of getting ‘head’ in a toss is 0.7. Deduce the probability that in 5 tosses , we will get 2 heads 3 tails.
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