Final
Physics 101: Lecture 22
Temperature and Ideal Gas
Physics 101: Lecture 22, Pg 1
Internal Energy and Temperature

All objects have “internal energy” (measured in Joules)
random motion of molecules
» kinetic energy
collisions of molecules gives rise to pressure

Amount of internal energy depends on
temperature
» related to average kinetic energy per molecule
how many molecules
» mass
“specific heat”
» related to how many different ways a molecule can move



translation
rotation
vibration
» the more ways it can move, the higher the specific heat
Physics 101: Lecture 22, Pg 2
10
Temperature Scales
Celcius
Farenheit
Kelvin
212
100
373.15
32
0
273.15
9
F  C  32
5
K  C  273
Water boils
Water freezes
5
C  F - 32
9
C  K - 273
NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule
Physics 101: Lecture 22, Pg 3
14
Temp Scales Question

Two cups of coffee are heated to 100 degrees
Fahrenheit. Cup 1 is then heated an additional
20 degrees Centigrade, cup 2 is heated an
additional 20 Kelvin. Which cup of coffee is
hotter?
A) One
B) Two
C) Same
Physics 101: Lecture 22, Pg 4
20
Thermal Expansion
 When
temperature rises
molecules have more kinetic energy
» they are moving faster, on the average
consequently, things tend to expand
 amount
of expansion depends on…
change in temperature
original length
Temp: T
L0
Temp: T+T
coefficient of thermal expansion
» L0 + L = L0 +  L0 T
» L =  L0 T (linear expansion)
» V =  V0 T (volume expansion)
L
Physics 101: Lecture 22, Pg 5
23
Density Question
As you heat a block of aluminum from 0 C to 100 C
its density
A. Increases
B. Decreases
T = 100 C
C. Stays the same
T=0C
M, V0
r0 = M / V0
M, V100
r100 = M / V100
< r0
Physics 101: Lecture 22, Pg 6
26
Example: concrete sidewalk

A concrete (=12x10-6 /K) sidewalk is 10m long when
poured on a cold day (0o C) How much will the length
of the sidewalk increase on a hot day (35o C)?
Physics 101: Lecture 22, Pg 7
Example: gas tamk

A steel (β=36x10-6 /K) gas tank has a volume of 75 lit.
You fill it up with gasoline (β=950x10-6 /K) early in
the morning when it is cool During the day the
temperature increases by 20o C. How much gas will
spill out?
Physics 101: Lecture 22, Pg 8
Differential Expansion ACT
 A bimetallic
strip is made with
aluminum =16x10-6 /K on the left, and
iron =12x10-6 /K on the right. At room
temperature, the lengths of metal are
equal. If you heat the strips up, what will
it look like?
A
B
C
Aluminum gets longer, forces curve so its on outside
Physics 101: Lecture 22, Pg 9
29
Amazing Water
 Water
is very unusual in that it has a
maximum density at 4 degrees C. That is
why ice floats, and we exist!
1000.00
999.95
999.90
999.85
999.80
999.75
999.70
999.65
999.60
999.55
Density
0
2
4
6
8
10
Physics 101: Lecture 22, Pg 10
30
Tight Fit
An aluminum plate has a circular hole cut in it. An aluminum ball (solid
sphere) has exactly the same diameter as the hole when both are at room
temperature, and hence can just barely be pushed through it. If both the
plate and the ball are now heated up to a few hundred degrees Celsius, how
will the ball and the hole fit ?
A. The ball wont fit through the hole any more
B. The ball will fit more easily through the hole
C. Same as at room temperature
Physics 101: Lecture 22, Pg 11
35
Why does the hole get bigger when the plate
expands ???
Imagine a plate made from 9 smaller pieces.
Each piece expands.
If you remove one piece, it will leave an “expanded hole”
Object at temp T
Same object at higer T:
Plate and hole both get larger
Physics 101: Lecture 22, Pg 12
36
Stuck Lid Question
A glass jar ( = 3x10-6 K-1) has a metal lid ( =
16x10-6 K-1) which is stuck. If you heat them by
placing them in hot water, the lid will be
A. Easier to open
B. Harder to open
C. Same
Copper lid expands more,
making a looser fit, and easier
to open!
Physics 101: Lecture 22, Pg 13
38
Jar Question
A cylindrical glass container ( = 28x10-6
k-1) is filled to the brim with water (
= 208x10-6 k-1) . If the cup and water
are heated 50C what will happen
A)
B)
C)
Some water overflows
Same
Water below rim
Gasoline:  = 950x10-6 k-1, Steel:  = 36x10-6 k-1
Physics 101: Lecture 22, Pg 14
41
Molecular Picture of Gas
 Gas
is made up of many individual
molecules
 Number density is number of
molecules/volume N/V = r/m
r is the mass density
m is the mass for one molecule
 Number
of moles n=N / NA
NA = Avogadro’s number 6.022x1023 mole-1
Physics 101: Lecture 22, Pg 15
43
Balloon Question 1
 What
happens to the pressure of the air
inside a hot-air balloon when the air is
heated? (Assume V is constant)
1) Increases 2) Same
3) Decreases
Balloon is still open to atmospheric pressure,
so it stays at 1 atm
Physics 101: Lecture 22, Pg 16
30
Balloon Question 2
 What
happens to the buoyant force on
the balloon when the air is heated?
(Assume V remains constant)
1) Increases 2) Same
3) Decreases
FB = r V g
r is density of outside air!
Physics 101: Lecture 22, Pg 17
32
Balloon Question 3
 What
happens to the number of air
molecules inside the balloon when the air
is heated? (Assume V remains constant)
1) Increases 2) Same
3) Decreases
PV = NkT
P and V are constant. If T increases N decreases.
Physics 101: Lecture 22, Pg 18
34
Kinetic Theory:
The relationship between energy and temperature
(for monatomic ideal gas)
px  2mvx
L
t  2
vx
pxx mvx2
Favg 

t
L
L
For N molecules, multiply by N
Using PV = NkT
F Nmvx2
P 
A
V
Note KE = ½ m
v2
= 3/2 m vx
2N
P
Ktr
3V
2
Ktr
3
 kT
2
Physics 101: Lecture 22, Pg 19
40
Example
 What
is the rms speed of a nitrogen N2
molecule in this classroom? (T=20o C)
Physics 101: Lecture 22, Pg 20
Summary
Temperature measure of average Kinetic
Energy of molecules
 Thermal Expansion

L =  L0 T (linear expansion)
V =  L0 T (volume expansion)

Ideal Gas Law PV = n R T
P = pressure in N/m2 (or Pascals)
V = volume in m3
n = # moles
R = 8.31 J/ (K mole)
T = Temperature (K)

Kinetic Theory of Monatomic Ideal Gas
<Ktr> = 3/2 kB T
Physics 101: Lecture 22, Pg 21
50