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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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hole size
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

Microscopic Spacing
change in volume
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 + DT

V + DV

coefficient of volume expansion
For small volume changes the relationship between volume and temperature is linear.

The coefficient of volume expansion is b.

MaterialCoefficient b

Quartz 1 x 10-6C-1

Pyrex glass 9 x 10-6C-1

Glass 27 x 10-6C-1

Steel 35 x 10-6C-1

Aluminum 75 x 10-6C-1

Mercury 180 x 10-6C-1

Water 210 x 10-6C-1

Gasoline 950 x 10-6C-1

Ethyl alcohol 1100 x 10-6C-1

Air (1 atm) 3400 x 10-6C-1

Coefficient of Volume Expansion
gas tank
A 72 L steel gas tank is open and filled to the top with gasoline, b = 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 DV = bV0DT.

(950 x 10-6C-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
cold water
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

Cold Water
stretching solids
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

Stretching Solids

T

L

T + DT

L + DL

linear expansion
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.

Linear Expansion
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 DL = aL0DT.

First in winter,

(12 x 10-6C-1)(200 m)(-50 C)

DL = -0.12 m

Then in summer,

(12 x 10-6C-1)(200 m)(20 C)

DL = 0.048 m

Seasonal Changes
thermal stress
Thermal Stress
  • A change in length is associated with a stress.
  • Temperature change causes a change in length.
  • If the stress is due to temperature, it’s a thermal stress.

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