Microstate and Macrostate - Statistical Mechanics - Past Exam, Exams for Statistics. Alliance University

Statistics

Description: This is the Past Exam of Statistical Mechanics which includes Reciprocal Lattice Vector, Primitive Translation Vectors, Miller Indices, Cartesian Unit Vectors, Volume of Unit Cell, Equilibrium Distance, Angular Frequency, Optical Vibration etc. Key important points are: Microstate and Macrostate, Corresponding Microstates, Number of Microstates, Non-Degenerate Energy Level, Normalization Constant, Particle Partition Function, Internal Energy, Boltzmann Constant
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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=NkBT2ln ZSP
T
where T is the temperature, and kBis the Boltzmann constant. [35]
/Cont’d
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