Announcements 9/12/11
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Prayer
I’ve got extra copies of the class directory
On Wednesday I will go back and regrade all of the old
clicker quizzes. As long as your clicker is registered by
then, all of your quizzes will count.
Unregistered clickers:
1151FBBB
11A3D26
13C413C4
1416FEFC
14710762
1473197E
160B0B16
16B89D33
190E8D9A
1A3B1E3F
1AEE0CF8
1B495507
1DAE9D2E
26395C43
D68FB9E
Make sure
your clicker
number is
not on this
list!
(If it is, register it
on the class
website ASAP!)
Characterizing velocities
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Recall bouncing balls in jar. Focus on one type of
molecule. Lots of questions, such as :
a. What’s the average velocity?
b. What’s the most popular velocity?
c. What’s the velocity that corresponds to the
average kinetic energy?
d. How many molecules have velocities within a
given range?
How to answer: use statistical distributions,
aka histograms
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) 
1 mv 2 k T with some constants out
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2
B
v e 2
in front to normalize it
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
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
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At 600K, how many
molecules with speeds
between 400 and 600
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
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 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, you must first raise its
temperature to 0C, and then you must
melt it. Which part takes the most
energy?
a. Raising the temperature
b. Melting
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