Announcements 9/10/12
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Prayer
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. Check to make sure you have
quiz scores on your grade printout!
Unregistered clickers from Friday: 971463E, 3368A2F9,
C80BC30
Review: equipartition theorem & vrms
Calvin &
Hobbes
Molecular View of Pressure
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Related problem: What is average pressure by
baseballs (m = 145 g) on a wall (A = 9 m2). Speed
= 85 mph (38 m/s). Elastic collisions, each lasting
for 0.05 seconds. (This is the time the ball is in
contact with the wall.) A baseball hits the wall
every 0.5 seconds.
Answer: 2.45 Pa
Actual problem: a cube filled with gas
a. Pressure on right wall from one molecule?
where we
stopped
Answer: 2mvx/(L2 tbetween hits) = mvx2/L3
b. Pressure on right wall from all molecules
Answer: P = Nmvx2/V
Molecular View of Pressure, cont.
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Result for v instead of vx:
P = N m ⅓ v2 / V
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What does PV equal?
Compare to: PV = N kB T
What does v equal? What does T equal?
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What is temperature? (revisited)
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Demo
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Demo: kinetic theory machine
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“Heavy” vs. “light” molecules which ones
move faster?
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Clicker question: Which “molecules” have the
most kinetic energy?
a. The heavy ones
b. The light ones
c. Same
From warmup
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Extra time on?
a. difference between vavg and vrms (many people)
– See HW problem 5.3
b. supercooling demo (3 people)
– “a demonstration of supercooled water would be
"supercool” (ha ha)”
Other comments?
a. Section 21.6. doesn't seem to exist in the Eighth
Edition (several people)
From warmup
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The last homework assignment (due friday) took me 5
hours because I could not figure out how to do 4-5. I
eventually found an equation that worked...but it was
kind of pure luck.
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: Class of 49 students
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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
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.
# molecules / total # molecules
Warmup: What is difference
between vave, vrms, and vmp? Why
is vmp the smallest of the three
velocities?
300 K
0.0020
0.0015
600 K
900 K
0.0010
0.0005
0.0000
0
200
400
600
800
1000
speed (m/s)
1200
1400
1600
v-rms, the root-mean-square, based on
the overall translational kinetic energy
of the gas, while v-avg is the statistical
average of the speed of all the
particles, and v-mp is the "most
probable" or the statistical mode of the
speeds (the highest point on the
distribution graph). v-mp is the smallest
because the graph is skewed to the left
From warmup
300 K
# molecules / total # molecules
0.0020
0.0015
600 K
900 K
0.0010
0.0005
0.0000
0
200
400
600
800
1000
1200
1400
1600
speed (m/s)
Answer: V_ave is just the regular average: add up the speeds
and divide by number of particles. V_rms is "root mean
square": add up the *squares* of the velocities, divide by
the number of particles, then take the square root. It
corresponds to the speed of the average kinetic energy.
V_mp is the "most probable" velocity: the peak of the
speed histogram. V_mp is the smallest because the
distribution of speeds is skewed to the right--the peak in
Fig. 21.11 (7th edition) is decidedly to the left of center.
Velocity Distribution: “Maxwell-Boltzmann”
f (v) 
1 mv 2 k T with some constants out

2
B
v e 2
in front to normalize it
Questions
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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?
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
From warmup
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In terms that a lay person could easily
understand, explain what heat capacity is.
Explain the difference between "heat capacity"
and "specific heat". Why do we need both?
a. Heat capacity is the amount of energy that
you need to increase a sample of whatever
size by one degree Celsius while specific
heat is the amount of energy needed to
raise one kilogram of some substance by
one degree Celsius.
Specific Heat
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Q=mcDT
Clicker 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
Clicker question:
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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
From warmup:
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In regions B and D, energy is being added but the
temperature is constant. How can energy be added to a
system and the temperature not change? Where is the
energy going?
a. As I understand it, the energy is being spent in
breaking apart particles that love each other too
much to part their separate ways. Only after they
have been broken down light enough to fly will they
turn into steam.
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
Demo
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Boiling water with a vacuum
Clicker 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