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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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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. Photo by Blake Tippens

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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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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 U = ½kx 2 K = ½mv 2 Internal energy -- spring analogies are helpful:

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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. Hot Coals Cool WaterSame Temperature Thermal Equilibrium Insulated Container Two objects are in thermal equilibrium if and only if they have the 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. 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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100 0 C212 0 F 00C00C32 0 F Temperature Scales The lower fixed point is the ice point, the temperature at which ice and water coexist at 1 atm of pressure: 0 0 C or 32 0 F The upper fixed point is the steam point, the temperature at which steam and water coexist at 1 atm of pressure: C or F

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Comparison of Temperature Intervals F 32 0 F 180 F C 00C00C 100 C 0 tCtC tFtF Temperature Intervals: 100 C 0 = 180 F 0 5 C 0 = 9 F 0 If the temperature changes from 79 0 F to 70 0 F, it means a decrease of 5 C 0.

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Temperature Labels If an object has a specific temperature, we place the degree symbol 0 beforethe scale( 0 C or 0 F). If an object has a specific temperature, we place the degree symbol 0 before the scale ( 0 C or 0 F). t = 60 0 C 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 afterthe scale(C 0 or F 0 ) to indicate the interval of temperature. If an object undergoes a change of temperature, we place the degree symbol 0 after the scale (C 0 or F 0 ) to indicate the interval of temperature. We say: The temperature decreases by forty Celsius degrees. t = 60 0 C – 20 0 C t = 40 C 0 t i = 60 0 C t f = 20 0 C

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Specific Temperatures F 32 0 F C 00C00C 180 F C 0 tCtC tFtF Same temperatures have different numbers: 0 C 0 F

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Example 1: A plate of food cools from F to 65 0 F. What was the initial temperature in degrees Celsius? What is the change in temperature in Celsius degrees? Convert F to 0 C from formula: t C = C 9 F 0 = 5 C 0 t = 52.8 C 0

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Limitations of Relative Scales The most serious problem with the Celsius and Fahrenheit scales is the existence of negative temperatures. Clearly, the average kinetic energy per molecule is NOT zero at either 0 0 C or 0 0 F! C ? 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 For constant volume: T = kP The pressure varies with temperature.

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Absolute Zero of Temperature C00C00C P1P1 P2P2 T1T1 T2T C 00C00C100 0 C P T Plot points (P 1, 0 0 C) and (P 2, C); then extrapolate to zero. Absolute Zero = C Absolute Zero

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Comparison of Four Scales 1 C 0 = 1 K 5 C 0 = 9 F T K = t C ice steam Absolute zero C 00C00C C Celsius C Fahrenheit 32 0 F F F F 273 K 373 K Kelvin 0 K0 K K Rankine 0 R0 R 460 R 672 R R

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Linear Expansion L LoLo L toto t Copper: = 1.7 x /C 0 Aluminum: = 2.4 x /C 0 Iron: = 1.2 x /C 0 Concrete: = 0.9 x /C 0

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Example 2: A copper pipe is 90 m long at 20 0 C. What is its new length when steam passes through the pipe at C? L o = 90 m, t 0 = 20 0 C t = C C = 80 C 0 L = L o t = (1.7 x /C 0 )(90 m)(80 C 0 ) L = mL = L o + L 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 Area expansion is analogous to the enlargement of a photograph. Example shows heated nut that shrinks to a tight fit after cooling down. Expansion on heating. A0A0 A

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Calculating Area Expansion W L L LoLo WoWo W A 0 = L 0 W 0 A = LW L = L 0 + L 0 t W = W 0 + W 0 t L = L 0 (1 + t ) W = W 0 (1 + t A = LW = L 0 W 0 (1 + t) 2 A = A 0 (1 + 2 t) Area Expansion: A = 2 t

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Volume Expansion Expansion is the same in all directions (L, W, and H), thus: V = V 0 t The constant is the coefficient of volume expansion.

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Example 3. A 200-cm 3 Pyrex beaker is filled to the top with glycerine. The system is then heated from 20 0 C to 80 0 C. How much glycerine overflows the container? V ovr = ? V0V0 V 20 0 C 80 0 C 200 cm 3 Glycerine: 5.1 x /C 0 Pyrex: = x /C 0 ) = 0.9 x /C 0 V over = V G - V P V ovr = G V 0 t - P V 0 t = ( G - P )V 0 t V ovr = (5.1 x /C x /C 0 )(200 cm 3 )(80 0 C C)

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Example 3. (CONTINUED) V ovr = ? V0V0 V 20 0 C 80 0 C 200 cm 3 Glycerine: 5.1 x /C 0 Pyrex: = x /C 0 ) = 0.9 x /C 0 V over = V G - V P V ovr = G V 0 t - P V 0 t = ( G - P )V 0 t V ovr = (5.1 x /C x /C 0 )(200 cm 3 )(80 0 C C) Volume Overflow = 6.01 cm 3

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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. 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. AB Thermal Equilibrium A Object C B

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Summary of Temperature Scales 1 C 0 = 1 K 5 C 0 = 9 F T K = t C ice steam Absolute zero C 00C00C C Celsius C Fahrenheit 32 0 F F F F 273 K 373 K Kelvin 0 K0 K K Rankine 0 R0 R 460 R 672 R R

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Summary: Expansion L LoLo L toto t Linear Expansion: A = 2 t Area Expansion: Expansion A0A0 A

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Volume Expansion Expansion is the same in all directions (L, W, and H), thus: V = V 0 t The constant is the coefficient of volume expansion.

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CONCLUSION: Chapter 16 Temperature and Expansion

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