7. Plan for Today (AP Physics 2)
Lecture/Notes on Temperature and Thermal Expansion

8. Thermometer
A thermometer is any device which, through marked scales, can give an indication of its own temperature.
T = kX
X is thermometric property: Expansion, electric resistance, light wavelength, etc.

9. Zeroth Law of Thermodynamics
The Zeroth Law of Thermodynamics: If two objects A and B are separately in equilibrium with a third object C, then objects A and B are in thermal equilibrium with each other.
That quantity that is equal for two things that have been in contact forever A
Object C A B
Thermal Equilibrium
Same Temperature B
Object C

10. Temperature Scales The lower fixed point is the freezing point:
00C or 320F
The upper fixed point is the boiling point:
1000C or F

11. Comparison of Temperature Intervals
100 C0 = 180 F0
5 C0 = 9 F0 tC tF
If the temperature changes from 790F to 700F, it means a decrease of 5 C0.

12. Temperature Labels t = 600C
If an object has a specific temperature, we place the degree symbol 0 before the scale (0C or 0F).
t = 600C
We say: “The temperature is sixty degrees Celsius.”

13. Temperature Labels (Cont.)
If an object undergoes a change of temperature, we place the degree symbol 0 after the scale (C0 or F0) to indicate the interval of temperature.
ti = 600C
tf = 200C
Dt = 600C – 200C
Dt = 40 C0
We say: “The temperature decreases by forty Celsius degrees.”

14. Specific TemperaturestC tF

15. Convert 1600F to 0C from formula:
Example 1: A plate of food cools from 1600F to 650F. What was the initial temperature in degrees Celsius? What is the change in temperature in Celsius degrees?
Convert 1600F to 0C from formula:
tC = 71.10C
9 F0 = 5 C0
Dt = 52.8 C0

16. Limitations of Relative Scales
The most serious problem with the Celsius and Fahrenheit scales is the existence of negative temperatures.
-250C ?
Clearly, if temperature is a measure of the energy per molecule, then the energy is NOT zero at either 00C or 00F!
T = kX = 0 ?

17. Constant Volume Thermometer

18. Constant Volume Thermometer
Valve
Constant volume of a gas. (Air, for example)
Absolute pressure
Work done by Amontons
Plotted pressure vs. temperature differences for different gases
The pressure varies with temperature.

19. Absolute Zero of Temperature
1000C
00C P1 P2 T1 T2
Absolute Zero P T
-2730C
00C
1000C
Plot points (P1, 00C) and (P2, 1000C); then extrapolate to zero.
Absolute Zero = -2730C

20. Absolute Zero & the Kelvin Scale
The Kelvin scale is setup so that its zero point is the coldest possible temperature--absolute zero, at which point a substance would have zero internal energy. This is °C, or °F. Absolute zero can never be reached, but there is no limit to how close we can get to it. Scientists have cooled substances to within 10-5 kelvins of absolute zero. How do we know how cold absolute zero is, if nothing has ever been at that temperature? The answer is by graphing Pressure vs. Temperature for a variety of gases and extrapolating. P
gas A
A gas exerts no pressure when at absolute zero.
gas B
gas C
T (°C) °C
0 °C

21. Comparison of Scales 1 C0 = 1 K C K F ice steam 5 C0 = 9 F
Celsius C
273 K
373 K
Kelvin
0 K K
Fahrenheit
320F
-4600F
2120F F
ice
steam
5 C0 = 9 F
Absolute zero
TK = tC

22. Linear Expansion Things get bigger when they get hotter
How much bigger?

23. Linear Expansion This change in length would depend on
Change in temperature
What if we had twice as much metal to start with?
It makes sense it would expand twice as far
So change in length also depends on original length

24. Linear Expansion

25. Linear Expansion

26. Linear Expansion

27. Units for Coefficient of Linear Expansion

28. Linear Expansion to t Copper:  = 1.7 x 10-5/C0Lo L to t
Copper:  = 1.7 x 10-5/C0
Concrete:  = 0.9 x 10-5/C0
Iron:  = 1.2 x 10-5/C0
Aluminum:  = 2.4 x 10-5/C0

29. Common Coefficients of Linear Expansion

30. DL = aLoDt = (1.7 x 10-5/C0)(90 m)(80 C0)
Example 2: A copper pipe is 90 m long at 200C. What is its new length when steam passes through the pipe at 1000C?
Lo = 90 m, t0= 200C
Dt = 1000C - 200C = 80 C0
DL = aLoDt = (1.7 x 10-5/C0)(90 m)(80 C0)
DL = m
L = Lo + DL
L = 90 m m
L = m

31. Applications of Expansion
Expansion Joints
Bimetallic Strip
Brass
Iron
Expansion joints are necessary to allow concrete to expand, and bimetallic strips can be used for thermostats or to open and close circuits.

32. Area Expansion Expansion on heating. A0 A
Area expansion is analogous to the enlargement of a photograph.
Example shows heated nut that shrinks to a tight fit after cooling down.

33. Calculating Area Expansion
A0 = L0W0 A = LW DW DL L Lo Wo W
L = L0 + aL0 Dt W = W0 + aW0 Dt
L = L0(1 + aDt ) W = W0(1 + aDt
A = LW = L0W0(1 + aDt)2
A = A0(1 + 2a Dt)
Area Expansion: DA = 2aA0 Dt

34. Calculating Area Expansion
A0 = L0W0 A = LW DW DL L Lo Wo W
L = L0 + aL0 Dt W = W0 + aW0 Dt
L = L0(1 + aDt ) W = W0(1 + aDt
A = LW = L0W0(1 + aDt)2
A = A0(1 + 2a Dt)
Area Expansion: DA = 2aA0 Dt

35. Calculating Area Expansion
A0 = L0W0 A = LW DW DL L Lo Wo W
L = L0 + aL0 Dt W = W0 + aW0 Dt
L = L0(1 + aDt ) W = W0(1 + aDt
A = LW = L0W0(1 + aDt)2
A = A0(1 + 2a Dt)
Area Expansion: DA = 2aA0 Dt

36. Calculating Area Expansion
A0 = L0W0 A = LW DW DL L Lo Wo W
L = L0 + aL0 Dt W = W0 + aW0 Dt
L = L0(1 + aDt ) W = W0(1 + aDt
A = LW = L0W0(1 + aDt)2
A = A0(1 + 2a Dt)
Area Expansion: DA = 2aA0 Dt

37. Expansion is the same in all directions (L, W, and H), thus:
Volume Expansion
Expansion is the same in all directions (L, W, and H), thus:
DV = bV0 Dt
b = 3a
The constant b is the coefficient of volume expansion.

38. Coefficients for Volume Expansion

39. Vovr = bGV0 Dt - bPV0 Dt = (bG - bP )V0 Dt
Example 3. A 200-cm3 Pyrex beaker is filled to the top with glycerine. The system is then heated from 200C to 800C. How much glycerine overflows the container?
Vovr= ? V0 V
200C
800C
200 cm3
Glycerine: b = 5.1 x 10-4/C0
Pyrex: b = 3a b = 3(0.3 x 10-5/C0) b = 0.9 x 10-5/C0
Vover = DVG - DVP
Vovr = bGV0 Dt - bPV0 Dt = (bG - bP )V0 Dt
Vovr = (5.1 x 10-4/C x 10-5/C0)(200 cm3)(800C - 200C)

40. Vovr = bGV0 Dt - bPV0 Dt = (bG - bP )V0 Dt
Example 3. (CONTINUED)
Vovr= ? V0 V
200C
800C
200 cm3
Glycerine: b = 5.1 x 10-4/C0
Pyrex: b = 3a b = 3(0.3 x 10-5/C0) b = 0.9 x 10-5/C0
Vover = DVG - DVP
Vovr = bGV0 Dt - bPV0 Dt = (bG - bP )V0 Dt
Vovr = (5.1 x 10-4/C x 10-5/C0)(200 cm3)(800C - 200C)
Volume Overflow = 6.01 cm3

41. What’s Special About Water
Liquids usually increase in volume with increasing temperature
AKA they decrease in density
Water generally does this except at temperatures just above freezing

42. Chart of Water Density vs. Temperature

43. Why this matters
Lets fish continue to live in ponds (water freezes from the top down and not from the bottom up
Also why your pipes might burst in the water

44. Summary of Temperature Scales
1 C0 = 1 K
1000C
00C
-2730C
Celsius C
273 K
373 K
Kelvin
0 K K
Fahrenheit
320F
-4600F
2120F F
ice
steam
5 C0 = 9 F
Absolute zero
TK = tC

45. Summary: Expansion Linear Expansion: to t Area Expansion: DA = 2aA0 DtLo L to t
DA = 2aA0 Dt
Area Expansion:
Expansion A0 A

46. Expansion is the same in all directions (L, W, and H), thus:
Volume Expansion
Expansion is the same in all directions (L, W, and H), thus:
DV = bV0 Dt
b = 3a
The constant b is the coefficient of volume expansion.