KEELE UNIVERSITY

DEGREE EXAMINATIONS 2008

Level 2 (PRINCIPAL COURSE)

Friday 16th May 2008, 09:30 – 11:30

PHYSICS

PHY-20026

STATISTICAL MECHANICS AND SOLID STATE PHYSICS

Candidates should attempt to answer FOUR questions,

TWO from section A and TWO from section B of the paper.

Tables of physical and mathematical data may be obtained from the

invigilator.

/Cont’d

1

SECTION A: STATISTICAL MECHANICS (Answer TWO questions)

1. (a) Explain the meaning of microstate and macrostate. As an example, give one

macrostate of the “tossing a coin three times” system, and write down all

corresponding microstates. [10]

(b) Explain why the expression

Ω = N!

Qni!

gives the number of microstates for a given macrostate with niparticles in the

non-degenerate energy level Ei. [10]

(c) Which macrostate will be observed in a real system? [5]

(d) Starting with the above expression for Ω, derive the expression

ni=Aexp (−βEi)

for the number of particles in the energy level Ei. [30]

(e) For the following assume β=1

kBT. Show that the normalization constant is

A=N

ZSP

where ZSP is the single particle partition function, and N the number of parti-

cles. [10]

(f) Hence, show that the internal energy is given by

U=NkBT2∂ln ZSP

∂T

where T is the temperature, and kBis the Boltzmann constant. [35]

/Cont’d

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