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**Chapter 16. Temperature and Expansion**

A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007

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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.

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**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.

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**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

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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.

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**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.

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**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

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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.

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**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

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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

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**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.

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**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.”

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**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.”

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**Specific Temperatures**

Same temperatures have different numbers: 0C 0F 2120F 320F 1000C 00C 180 F0 100 C0 tC tF

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**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

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**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 ?

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**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.

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**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

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**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

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**Linear Expansion to t Copper: = 1.7 x 10-5/C0**

Lo 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

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**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

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**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.

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**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.

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**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

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**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.

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**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)

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**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

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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

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**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

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**Summary: Expansion Linear Expansion: to t Area Expansion: DA = 2aA0 Dt**

Lo L to t DA = 2aA0 Dt Area Expansion: Expansion A0 A

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**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.

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**CONCLUSION: Chapter 16 Temperature and Expansion**

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A third temperature scale has been developed, which relates the temperature changes to pressure changes for a fixed volume of gas. This scale is not based.

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