How tightly can I pack wiggling
students into a classroom?
Thermal expansion:
Lengths all change by the same
factor (percentage) per degree.
L  Lo T
Why linear in temperature change?
A concrete slab is measured with a steel measuring
tape in a room where the temperature is at 20o C
and found to measure exactly 10 feet wide. The
slab is measured again on a day when the
temperature is 27o C. The measurement will be
a) Greater than 10 feet
b) Less than 10 feet
c) Exactly 10 feet
αsteel=11 x 10-6/oC αconcrete=12 x 10-6/oC
You heat a disc with a hole in it. Will the
hole expand or shrink, or stay the same?
A.
B.
C.
Expand
Shrink
Stay the same
Area Change . . .

What will it be proportional to?
A  2Ao T
V  Vo T  3Vo T
Ideal gases:
Molecules collide like billiard balls
Molecules don’t occupy space
Never condense into liquids or solids
Don’t exist
Model a lot of things really well!
Ideal Gases
Constant
N
P
T
V
Increase
Decreases
Ideal Gases
Constant
N
P
T
V
Increase
Decreases
Ideal Gases
Constant
N
P
T
V
Increase
Decreases
Ideal Gases
Constant
N
P
T
V
Increase
Decreases
Ideal Gases
Constant
N
P
T
V
Increase
Decreases
In an ideal gas, if you double the volume of
the container, while keeping the
temperature and the number of molecules
the same, the pressure in the gas
Decreases
B. Stays the same
C. Increases
A.
Ideal gas law
PV
 constant  k B
NT
kB = 1.38 x 10-23 J/ºK
PV
 constant  R
nT
R = 8.31 J/moleºK
= 0.0831 liter-atm/moleºK
n = # of moles
N is number of atoms or molecules
1 mole =6.02x1023 particles
Watch Units! T must be in Kelvin
2 NEPHI 2:26
And the Messiah cometh in the fulness of time,
that he may redeem the children of men from the
fall. And because that they are redeemed from the
fall they have become free forever, knowing good
from evil; to act for themselves and not to be
acted upon, save it be by the punishment of
the law at the great and last day, according to the
commandments which God hath given.
How big is a mole?

If the earth was made out of baseballs .
rEarth  6.4  10 6 m
rBaseball  3.7  10  2 m
 rEarth
VEarth
N  0.74
 0.74
VBaseball
 rBaseball

3

  5.2  10 24  8.6 moles

Pennies to the moon
3
d10
d penny  1N
.55

moon m

 2.5  1011  4  10 13 moles
d8
d moon  3.8  10penny
m

In a liter of water . . .
– 55.5 moles
What if I turned that 55 moles
of water into steam at 1 atm?
Suppose we have two jars of gas, one of helium
and one of oxygen. If both jars have the same
volume, and the two gases are at the same
pressure and temperature, which jar contains the
greatest number of molecules?
Jar of helium
B. Jar of oxygen
C. Both jars contain the same number.
A.
Consider both gases to obey the ideal gas law. Also note that the mass of an
oxygen atom is greater than the mass of a helium atom.
A half-liter spray can is “empty” (you can’t
get more out), at 20 C, room temperature.

What is the initial P (in absolute pressure)?

How many molecules are still in the can?
A half-liter spray can is “empty” (you
can’t get more out), at 20 C, room
temperature.

You throw it into the fire at 600 C. What is the
final P in the can (if it doesn’t burst)
A half-liter spray can is “empty” (you
can’t get more out), at 20 C, room
temperature. You throw it into the fire
at 600 C.
Suppose instead you have .6 moles of water in the
can, which becomes an ideal gas at 600 C.
What is the final pressure (in atm) assuming the
can does not break.
What is the mass of air in this room,
assuming it is all O2. Take V= 1800 m3
and T= 20 C. Moxygen=32 g/mole