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Physics 172 – Fall 2011
Recitation 14 – Entropy and Temperature
Problem 1
a)
List explicitly all of the different ways that 2 quanta of vibrational energy can be
arranged in 4 onedimensional oscillators, that is, list all of the microstates of a 4
oscillator system in the macrostate with total vibrational energy
2
ω
h
.
b)
Verify that the total number of microstates,
!
(
q
,
N
)
, is equal to
(
q
+
N
!
1)!
q
!(
N
!
1)!
, the
general formula for this number derived in the text.
c)
If you make a sequence of 10,000 independent observations of the microstate of this
system, about how many times do you expect to find it in the 0020 microstate?
About
how many times do you expect to find it in a microstate with 2 quanta in the same
oscillator?
About how many times do you expect to find it in a state in which no
oscillator has more than one quantum of vibrational energy?
[Checkpoint 1]
Problem 2
Consider a nanoparticle consisting of 27 copper atoms.
Recall that the molar mass of
copper is about 63 grams and that the Young’s modulus of copper implies an interatomic
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This note was uploaded on 12/07/2011 for the course PHYS 172 taught by Professor ? during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 ?
 Energy, Entropy

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