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.



V

 

V

0 

T T V T +



T V +



V

Coefficient of Volume Expansion

 For small volume changes the relationship between volume and temperature is linear.

 The coefficient of volume expansion is  .



V

 

V

0 

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 35 x 10 -6 -6 75 x 10 -6 180 x 10 -6  C -1  C -1 210 x 10 -6  C -1  C -1  C -1 950 x 10 -6 1100 x 10 -6  C -1  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.

  The gasoline expands with temperature.

Solve for 

V

 ( 950 x 10 -6 = 

V

0 

T.

 C -1 )(72 L)(14  C)  

V

= 0.95 L  How much gasoline overflows from the tank?

  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.

 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

Stretching Solids

T L T +



T L +



L

 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

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  .

V

0 

V

 

L

0

H

0

W

0 

LH

0

W

0 

L

0 

HW

0 

L

0

H

0 

W



V

 ( 

T



L

0 ( 

T

 3 3 

L

0 )

H

0

W

0

H

0 )

W

0 

L

0

H

0 ( 

T

 3

W

0 ) 

L

a    

T

a

L

0 / 3

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

= a

L

0 

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.

 Temperature change causes a change in length.

 If the stress is due to temperature, it’s a thermal stress.

F A



Y



L L

0 

L

 

T

a

L

0

F A

 

T

a

YL

0

L

0  a

Y



T

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