Thermal Expansion

```Thermal Expansion
Hole Size

A rectangular sheet of metal has a circular hole. What
happens to the size of the hole when the metal is
heated?
A) It gets larger.
B) It gets smaller.
C) It stays the same.
Microscopic Spacing

Atoms are in constant
motion.
• Vibration increases with
temperature
• Spacing increases with
temperature
Change in Volume

The volume of matter
expands when the atomic
spacing increases.
• Increase temperature →
increase volume.

A volume increase is the
same as a density decrease.
T
V
T + T
V + V
V  V0 T
Coefficient of Volume Expansion

For small volume changes
the relationship between
volume and temperature is
linear.

The coefficient of volume
expansion is .
V  V0 T
Material
Quartz
Pyrex glass
Glass
Steel
Aluminum
Mercury
Water
Gasoline
Ethyl alcohol
Air (1 atm)
Coefficient 
1 x 10-6 C-1
9 x 10-6 C-1
27 x 10-6 C-1
35 x 10-6 C-1
75 x 10-6 C-1
180 x 10-6 C-1
210 x 10-6 C-1
950 x 10-6 C-1
1100 x 10-6 C-1
3400 x 10-6 C-1
Gas Tank


A 72 L steel gas tank is open
and filled to the top with
gasoline,  = 950 x 10-6 C-1,
at 18 C. The car sits in the
sun and reaches a
temperature of 32 C.
How much gasoline
overflows from the tank?


The gasoline expands with
temperature.
Solve for V = V0 T.
 (950 x 10-6 C-1)(72 L)(14 C)
 V = 0.95 L


The tank expansion was
small in comparison.
You get more gas if you fill it
when it’s cool!
Cold Water

Most substances expand
uniformly with temperature.

pattern.
• Below 4 C water expands
as it cools
• Very cold water stays on top
• Ice is even less dense
Stretching Solids

Solids can have dimensions
that are quite different.

The long dimension may
matter most.
T
L
T + T
L + L
• Focus on one dimension
• Other changes are still
present, less magnitude
Linear Expansion



The change in volume
applies to the three
dimensions.
If the change is equal in all
directions  is split in thirds.
The coefficient of linear
expansion in solids (a) is
usually one third of .
V0  L0 H 0W0
V  LH 0W0  L0 HW0  L0 H 0 W
V  (T
 L0 (T

3

3
 L0 H 0 (T
H 0 )W0

L  TaL0
a   /3
L0 ) H 0W0
3
W0 )
Seasonal Changes


The steel bed of a
suspension bridge is 200 m
long at 20 C.
If the temperature goes from
-30 C to +40 C, what
contraction and expansion is
possible?



Use linear expansion.
Solve for L = aL0 T.
First in winter,
 (12 x 10-6 C-1)(200 m)(-50 C)
 L = -0.12 m

Then in summer,
 (12 x 10-6 C-1)(200 m)(20 C)
 L = 0.048 m
Thermal Stress

A change in length is
associated with a stress.
F
L
Y
A
L0

Temperature change causes
a change in length.
L  TaL0

If the stress is due to
temperature, it’s a thermal
stress.
F TaYL0

 aYT
A
L0
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