1. 12.4 Linear Thermal Expansion

2. Normal Solids Ex. Glass jar too tight, hot water over lid.
Linear expansion – increase in any one dimension of a solid, linear is the expansion occurring along a line.
L – length
T – temp.
Length and temp. is directly proportional.

3. Thermal Expansion
Change in length is proportional to both (initial) L and change in Temp.
Proportionality constant _____, is called the coefficient of linear expansion.
Linear Thermal Expansion of a Solid

4. Thermal Expansion
Coefficient of linear expansion ___ has the unit of _____.
Value of the ____ depends on the nature of the material.

5. Coefficients of Thermal Expansion for Solids and Liquids

6. Example 3: Buckling of a Sidewalk

8. Expansion Joint

9. Usefulness
Anti-scalding device: shuts off the flow of water when it becomes too hot,
Higher temp expands the actuator spring and pushes the plunger forward, shutting off the flow.

10. Practice Problem 9.
A steel section of the Alaskan pipeline had a length of 65 m and a temperature of 18 C when it was installed. What is its change in length when the temperature drops to a frigid -45 C?

12. Thermal Stress Change in temp. causes a force, stress on the material.
Can cause structural damage.
Stress

13. Example 4: The Stress on a Steel Beam

18. Practice Problem 90.
A cylindrical brass rod (cross sectional area = 1.3 x 10^-5 m2) hangs vertically straight down from a ceiling. When an 860N block is hung from the lower end of the rod, the rod stretches. The rod is then cooled such that it contracts to its original length. By how many degrees must the temperature be lowered?

20. The Bimetallic Strip
Made from two thin strips of metal that have different coefficients of linear expansion.
Brass
Steel
When the strip is heated, the brass, having the larger value of ____, expands more than the steel.
The strip bends into an arc, with the longer brass piece having a larger radius than the steel piece.
When the strip is cooled, the bimetallic strip bends in the opposite direction.

22. Video of bimetallic strip

23. Bimetallic strips used in appliances
Automatic coffee maker turns off when the coffee is brewed to the selected strength.
Brewing cycle is on: electricity passes through the heating coil that heats the water.
Flows because the contact mounted on the bimetallic strip touches the contact mounted on the “strength” adjustment knob.
Strip gets hot enough to bend away, electricity stops because it no longer has a continuous path along which to flow.
Brewing cycle is shut off. Pg. 368

25. Conceptual example 5: Do Holes Expand or contract when the temperature increases?

26. Example 6: A Heated Engagement Ring

27. 12.5 Volume Thermal Expansion
The volume of a normal material increases as the temperature increases.
Change in V is proportional to the change in T. Volume Thermal Expansion

28. ____ like _____ is _______.
Values for ____ depend on the nature of the material.
Values are larger for liquids than solids.

29. Example 8: An Automobile Radiator

30. Some substances do not expand when heated.
When water is heated its volume decreases until the temperature reaches 4 C. Above 4 C water behaves normally, and its volume increases as the temp. increases.
The density (mass per unit volume) of water is greatest at 4 C.

31. Freezing pond
When the temp drops the top layer of water becomes 4 C and denser than the warmer water below.
The denser water sinks and pushes up the deeper and warmer water, which in turn is chilled at the surface.
The process continues until the temp. of the entire pond reaches 4 C.

32. Further cooling of the surface water below 4 C makes it less dense than the deeper layers then the surface layer does not sink but stays on top.

33. Homework
Problems: