COURSE CODE: PHY 311

COURSE TITLE: KINETIC THEORY AND STATISTICAL MECHANICS

TIME ALLOWED (3 HRS)

INSTRUCTION: Answer any 5 questions

QUESTION 1

a)

i. Differentiate between microstate and macro-state (2 Marks)

ii. What is Entropy?(2 Marks)

b)

i. State mathematically the Stefan-Boltzmann law (2 Marks)

ii. A wire of length 1m and radius 1mm is heated via an electric current to produce 1 kW of radiant power. Treating the wire as a perfect blackbody and ignoring any end effects, calculate the temperature of the wire. (8 Marks)

N:B Electric power = power radiated

QUESTION 2

a) State the Equi-partition theorem (2 Marks)

b) Consider a system A0 consisting of interacting subsystems A1

andA2 for which 1= 1020 and 2= 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 the Boltzmann’s constant?(12 Marks)

QUESTION 3

a) What is Statistical mechanics(4 Marks)

b) Consider systems of 100 molecules in otherwise empty rooms.What is the average number of molecules in the front third of the rooms, thestandard deviation about this value, and the relative fluctuation?(10 Marks)

QUESTION 4

a) State the mathematical expression of Dulong--Petit law. (2 Marks)

b) By what factor does the number of states increase if 1 joule ofheat is added to a system at room temperature (295 K)? (4 Marks)

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. (8 Marks)

QUESTION 5

a) State the second law of thermodynamics?(2 Marks)

b) Find the number of ways in which two particles can be distributed in six statesif :

i. the particles are distinguishable (3Marks)

ii. the particles are indistinguishable and obey Bose-Einstein statistics (3Marks)

iii. the particles are indistinguishable and only one particle can occupy any

one state.(3Marks)

QUESTION 6

a) What do you understand by Ensemble?(2 Marks)

b) Calculate:

i. The average kinetic energy per gas molecule. (3 Marks)

ii. The speed of the molecules at room temperature. (3 Marks)

Take the Boltzmann’s constant and room temperature as 1.38 x 10 -23 JK-1 and 300 K in that order.

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.(6 Marks)

QUESTION 7

a. How many microstates correspond to the same macrostsate?(1 Marks)

b. The equation that aptly describes the Helmholtz free energy of a system for large systems is?(2 Marks)

c.

i. Explain Wien’s Law (2 Marks)

ii. Deduce Wien’s Law from Plank’s radiation Law (5 Marks)

d. Two independent systems have entropies S1 and S2 and probabilities 1 and 2. Find the entropy and the probability of combined systems ?(4 Marks).

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## NOUN Past Questions: PHY311 - Kinetic Theory And Statistical Mechanics

### Re: NOUN Past Questions: PHY311 - Kinetic Theory And Statistical Mechanics

COURSE CODE: PHY 311

COURSE TITLE: KINETIC THEORY AND STAT MECHANICS

Time: 2hrs

Instructions: Answer any five questions

(a) An unbiased die is rolled write down the sample space for the experiment (ii) n coins are tossed, what is the sample space? (b) Two coins are tossed. What is the probability that (i) two head appears (ii) at least one tail appears.

(a) Four coins are flipped in succession. Find the total number of possible outcomes. (b) Seven physicists assembled for a meeting shake hands with one another. How many handshakes take place?

(a) State the Fermi temperature, TF (b) Calculate Fermi heat capacity, CFfor copper, given density= 9g/cm3 , atomic weight = 63.5 and valency equal to one

Prove that (i) K.E. = (3/2)KT (ii) U = 1/2KT using equipartition theorem.

The partition function of an ideal monoatomic gas is given by Z_N=V^N/h^3N 〖(2πmK_B T)〗^(3N⁄2). Calculate (i) the free energy (iii) entropy (iv) Cv and Cp.

Shows that sacker-Tetrode equation is free from Gibbs paradox.

Given that the Helmholtz free energy is F=-((8π^5 K_B^4)/(45h^3 C^3 ))V, Calculate (a) radiation pressure (b) entropy of an assembly of photons and (c) show from the result that CV =3S.

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COURSE TITLE: KINETIC THEORY AND STAT MECHANICS

Time: 2hrs

Instructions: Answer any five questions

(a) An unbiased die is rolled write down the sample space for the experiment (ii) n coins are tossed, what is the sample space? (b) Two coins are tossed. What is the probability that (i) two head appears (ii) at least one tail appears.

(a) Four coins are flipped in succession. Find the total number of possible outcomes. (b) Seven physicists assembled for a meeting shake hands with one another. How many handshakes take place?

(a) State the Fermi temperature, TF (b) Calculate Fermi heat capacity, CFfor copper, given density= 9g/cm3 , atomic weight = 63.5 and valency equal to one

Prove that (i) K.E. = (3/2)KT (ii) U = 1/2KT using equipartition theorem.

The partition function of an ideal monoatomic gas is given by Z_N=V^N/h^3N 〖(2πmK_B T)〗^(3N⁄2). Calculate (i) the free energy (iii) entropy (iv) Cv and Cp.

Shows that sacker-Tetrode equation is free from Gibbs paradox.

Given that the Helmholtz free energy is F=-((8π^5 K_B^4)/(45h^3 C^3 ))V, Calculate (a) radiation pressure (b) entropy of an assembly of photons and (c) show from the result that CV =3S.

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