Announcements 1/19/11





Prayer
Regarding the TA’s comments about ( ) vs [ ] vs
{ } — Those were specifically about how to get
Mathematica to work properly. You don’t have
to use those symbols that way in the
handwritten homework that you turn in. (At
least one student asked Chris about that.)
One HW paper with no CID… anyone claim?
One lab with incorrect CID… wrote down 617…
anyone claim?
Today’s newspaper article
Characterizing velocities

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):







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

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:





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

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)





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”
with some
kBT
2
constants
f (v)  v  e
out in front to
Where does this eqn come from? Wait a few weeks. normalize it
 12 mv2

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
speed (m/s)
1200
1400
1600

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
Thought question

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!

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


Demo: Boiling water with a vacuum
Video: Boiling water in a paper cup
Reading Quiz

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

Q=mcDT
Thought Question

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

Thermal energy that is used to melt or
freeze something is called:
a. latent heat
b. mass heat
c. mass-pacity
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

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




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