1. Chapter 16. Temperature and Expansion
A PowerPoint Presentation by
Paul E. Tippens, Professor of Physics
Southern Polytechnic State University
© 2007

2. Photo by Blake Tippens
TEMPERATURE is a measure of the average kinetic energy per molecule. The infrared radiation coming from the air canal in the ear passes through the optical system of the thermometer and is converted to an electrical signal that gives a digital reading of body temperature.

3. Objectives: After finishing this unit, you should be able to:
Work with Celsius, Kelvin, and Fahrenheit temperature scales for both specific temperatures and temperature intervals.
Write and apply formulas for linear, area, and volume expansion.

4. Internal energy -- spring analogies are helpful:
Thermal Energy
Thermal energy is the total internal energy of an object: the sum of its molecular kinetic and potential energies.
Thermal energy = U + K
Internal energy -- spring analogies are helpful:
U = ½kx2
K = ½mv2

5. Temperature
Temperature is related to the kinetic activity of the molecules, whereas expansion and phase changes of substances are more related to potential energy.
Although not true in all cases, a good beginning is to define temperature as the average kinetic energy per molecule.

6. Temperature vs. Internal Energy
The large pitcher and the small one have the same temperature, but they do not have the same thermal energy. A larger quantity of hot water melts more of the ice.

7. Temperature Equilibrium
Heat is defined as the transfer of thermal energy that is due to a difference in temperature.
Thermal Equilibrium
Hot Coals
Insulated Container
Two objects are in thermal equilibrium if and only if they have the same temperature.
Cool Water
Same Temperature

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. A
Object C A B
Thermal Equilibrium
Same Temperature B
Object C

10. Temperature Scales
1000C
2120F
00C
320F
The lower fixed point is the ice point, the temperature at which ice and water coexist at 1 atm of pressure:
00C or 320F
The upper fixed point is the steam point, the temperature at which steam and water coexist at 1 atm of pressure:
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 Temperatures
Same temperatures have different numbers: 0C 0F
2120F
320F
1000C
00C
180 F0
100 C0 tC 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, the average kinetic energy per molecule is NOT zero at either 00C or 00F!
T = kX = 0 ?

17. Constant Volume Thermometer
Valve
Constant volume of a gas. (Air, for example)
Absolute pressure
A search for a true zero of temperature can be done with a constant-volume thermometer.
For constant volume:
T = kP
The pressure varies with temperature.

18. 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

19. Comparison of Four Scales
1 C0 = 1 K
1000C
00C
-2730C
Celsius C
273 K
373 K
Kelvin
0 K K
Fahrenheit
320F
-4600F
2120F F
Rankine
0 R
460 R
672 R R
ice
steam
5 C0 = 9 F
Absolute zero
TK = tC

20. 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

21. 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

22. 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.

23. 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.

24. 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

25. 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.

26. 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)

27. 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

28. Summary
Thermal energy is the total internal energy of an object: the sum of its molecular kinetic and potential energies.
Thermal energy = U + K
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. A B
Thermal Equilibrium A
Object C B

29. 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
Rankine
0 R
460 R
672 R R
ice
steam
5 C0 = 9 F
Absolute zero
TK = tC

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

31. 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.

32. CONCLUSION: Chapter 16 Temperature and Expansion