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
A) It gets larger.
B) It gets smaller.
C) It stays the same.
Atoms are in constant motion.
Vibration increases with temperature
Spacing increases with temperature
T + DT
V + DV
For small volume changes the relationship between volume and temperature is linear.
The coefficient of volume expansion is b.
Quartz1 x 10-6C-1
Pyrex glass9 x 10-6C-1
Glass27 x 10-6C-1
Steel35 x 10-6C-1
Aluminum75 x 10-6C-1
Mercury180 x 10-6C-1
Water210 x 10-6C-1
Gasoline950 x 10-6C-1
Ethyl alcohol1100 x 10-6C-1
Air (1 atm)3400 x 10-6C-1
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!
Most substances expand uniformly with temperature.
Water does not follow the pattern.
Below 4 C water expands as it cools
Very cold water stays on top
Ice is even less dense
Solids can have dimensions that are quite different.
The long dimension may matter most.
Focus on one dimension
Other changes are still present, less magnitude
T + DT
L + DL
The change in volume applies to the three dimensions.
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.
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 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 m