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. Atoms are in constant motion. Vibration increases with temperature
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A) It gets larger.
B) It gets smaller.
C) It stays the same.
Vibration increases with temperature
Spacing increases with temperatureMicroscopic Spacing
T + DT
V + DV
For small volume changes the relationship between volume and temperature is linear.
The coefficient of volume expansion is b.
Quartz 1 x 10-6C-1
Pyrex glass 9 x 10-6C-1
Glass 27 x 10-6C-1
Steel 35 x 10-6C-1
Aluminum 75 x 10-6C-1
Mercury 180 x 10-6C-1
Water 210 x 10-6C-1
Gasoline 950 x 10-6C-1
Ethyl alcohol 1100 x 10-6C-1
Air (1 atm) 3400 x 10-6C-1Coefficient of Volume Expansion
A 72 L steel gas tank is open and filled to the top with gasoline, b = 950 x 10-6C-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 DV = bV0DT.
(950 x 10-6C-1)(72 L)(14 C)
DV = 0.95 L
The tank expansion was small in comparison.
You get more gas if you fill it when it’s cool!Gas Tank
Water does not follow the pattern.
Below 4 C water expands as it cools
Very cold water stays on top
Ice is even less denseCold Water
The long dimension may matter most.
Focus on one dimension
Other changes are still present, less magnitudeStretching Solids
T + DT
L + DL
If the change is equal in all directions b is split in thirds.
The coefficient of linear expansion in solids (a) is usually one third of b.Linear Expansion
The steel bed of a suspension bridge is 200 m long at 20 gasoline, C.
If the temperature goes from -30 C to +40 C, what contraction and expansion is possible?
Use linear expansion.
Solve for DL = aL0DT.
First in winter,
(12 x 10-6C-1)(200 m)(-50 C)
DL = -0.12 m
Then in summer,
(12 x 10-6C-1)(200 m)(20 C)
DL = 0.048 mSeasonal Changes