Announcements 9/13/10
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5 students still haven’t registered their clickers. Be sure to register
them via the course website.
a. Check your scores via the course website!
– Make sure you have scores listed under the “Clicker Quizzes”
category.
Mathematica T-shirt today in honor of the first Mathematica
problem due tonight. Mathematica is available in N212, N337, and
possibly other computer labs.
a. To get into those two rooms, you need the combination from
dept secretary Diann.
b. To use the computers in those rooms, you need a departmental
computer account (form on dept website, under “computer
support”).
I will hold my office hours in N337 today, and will go over the
“Basic commands of Mathematica” handout from course website.
Hopefully several computers will be available.
TA’s office hours still in underground lab.
Quick Writing
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In light of what we discussed last lecture,
how would you describe temperature on the
microscopic level?
Height Histogram (made up data):
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Total students = 49
Round heights to closest
integer, plot histogram
What is the combined area of
all bars?
If I pick a student at random,
what are chances he/she will
be 68 inches tall?
What is the area of the bar at
68 inches divided by the total
area?
How many students will be
exactly 68.000000 inches tall?
If I pick a student at random,
what are chances he/she will
be 61.5-64.5 inches tall?
What is average height of all
students? (At least, how would
you figure that out?)
7
6
Number of students
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5
4
3
2
1
0
60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
Height (inches)
“Normalized” Histogram:
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Total students = 49
Y-axis now divided by total #
of students.
What is combined area of all
bars?
If I pick a student at
random, what are chances
he/she will be 61.5-64.5
inches tall? (At least, how
would you figure that out?)
How many students have
heights between 61.5 and
64.5 inches?
What is average height of all
students?
0.14
0.12
#students / total # students
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0.10
0.08
0.06
0.04
0.02
0.00
60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
Height (inches)
Probability Distribution Function
0.10
#students / total # students
0.08
0.06
0.04
0.02
0.00
50
55
60
65
70
75
80
Height (inches)
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Imagine total # =10 billion. Tiny “bins”. Connect peaks of
curve with line… becomes a function
What is combined area of all bars?
If I pick a person at random, what are chances he/she will be
63.6-67.2 inches tall?
How many people have heights between 63.6 and 67.2 inches?
What is average height of all people? (If a non-symmetric
curve, this is not just the peak of the curve.)
Velocity Distribution: “Maxwell-Boltzmann”
f (v)  v  e
2
 12 mv2
kBT
Where does this eqn come from? Wait a few weeks.
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300 K
# molecules / total # molecules
0.0020
0.0015
600 K
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900 K
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0.0010
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0.0005
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0.0000
0
200
400
600
800
1000
speed (m/s)
1200
1400
1600
with some
constants
out in front to
normalize it
How many molecules with
speeds between 200 and
300 m/s?
What is “vmost probable”?
What is “vaverage”?
What is “vrms”?
How many molecules are
at exactly the “most
probable” velocity?
Calvin and Hobbes, Bill Watterson
Calvin and Hobbes, Bill Watterson
Calvin and Hobbes, Bill Watterson
Calvin and Hobbes, Bill Watterson
Thought question
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An ideal gas has a mixture of heavy and light
monatomic molecules at the same
temperature. Which molecules will have the
most kinetic energy (on average)?
a. heavy
b. light
c. same
Heat = not a fluid!
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Sir Benjamin
Thompson, Count
Rumford, 1753-1814
a. Boiling water with a
cannon
Image credit: Wikipedia
James Joule, 1818-1889
Image credit: Wikipedia
Demo/Video
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Demo: Boiling water with a vacuum
Video: Boiling water in a paper cup
Reading Quiz
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What name do we give to the heat capacity
per unit mass?
a. entropy
b. internal energy
c. mass-pacity
d. normalized heat capacity
e. specific heat
Specific Heat
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Q=mcDT
Thought Question
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If you add 500 J of heat
to a mass of water, and
500 J of heat to the
same mass of copper,
which one increases the
most in temperature?
a. Water
b. Copper
c. Same
Reading Quiz
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Thermal energy that is used to melt or
freeze something is called:
a. latent heat
b. mass heat
c. melty-freezy heat
d. molar heat
e. specific heat
Phase Changes
Water boiling
100o C
Water
boils
T
Ice melting
0o C
Ice
melts
Heat energy added (Q)
Ice warming
Water warming
Steam warming
Latent Heats
Thought Question
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If you want to melt a cube of ice
that’s initially at -40 C, which part
takes the most energy?
a. Raising the temperature
b. Converting from solid to liquid
phase
c. Same
Calorimetry
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Worked problem (class designed):
____ grams of hot iron at _____ C is added
to ____ g of water at _____ C in a
styrofoam insulated container. What is the
final temperature of the mixture? (Neglect
the container.)
ciron = 448 J/kgC
cwater = 4186 J/kgC
Lwater-steam = 2.26  106 J/kg