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PHYS 258  Thermal Physics:
Assignment 4
Due February 7
Student ID:
Last Name:
1.
[4]. TwoState Paramagnet
.
The following questions deal with a two state paramagnetic system comprising
N
magnetic dipoles in an external magnetic field, such that for each magnetic dipole the
energy of its ground state (aligned,
↑
) is 0 and the energy of its excited state
(antialigned,
↓
) is
ε
. Thus, if
n
quanta of energy are in the system, its total energy is
U
=
n
.
(a)
[0.5] Suppose that
N
= 5. How many macrostates are there, and what are their
corresponding values of
U
? For each macrostate, explicitly write down all
possible microstates (e.g.
↑↑↓↑↓
) and so define its multiplicity.
What is
Ω
(all), the total number of microstates?
(b)
[0.5] Suppose that the system exchanges energy with its environment in such a
way that each of these microstates is equally likely to occur, like flipping five fair
coins. What is the probability, at any instant of time, of finding the system in the
microstate:
↑↑↓↑↓
?
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[0.5] What are the probabilities, P(n), at any instant of time, of finding the system
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This note was uploaded on 06/11/2011 for the course PHYS 258 taught by Professor Yurileonenko during the Winter '11 term at Waterloo.
 Winter '11
 YuriLeonenko
 Physics

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