Chapter 16. Temperature and Chapter 16. Temperature and ExpansionExpansion

A PowerPoint Presentation byA PowerPoint Presentation by

Paul E. Tippens, Professor of PhysicsPaul E. Tippens, Professor of Physics

Southern Polytechnic State UniversitySouthern Polytechnic State University

© 2007

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

Photo by Blake Tippens

Objectives: After finishing this Objectives: After finishing this unit, you should be able to: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.

Thermal EnergyThermal EnergyThermal energy is the total internal energy of an object: the sum of its molecular kinetic and potential energies. Thermal energyThermal energy is the total internal energy of an object: is the total internal energy of an object: the sum of its molecular kinetic and potential energies.the sum of its molecular kinetic and potential energies.

Thermal energy = U + KThermal energy = U + K

U = ½kx2

K = ½mv2

Internal energy -- spring analogies are helpful:

TemperatureTemperatureTemperature is related to the kinetic activity of the molecules, whereas expansion and phase changes of substances are more related to potential energy.

2½mvT

N

Although not true in all cases, a good beginning is to define temperature as the average kinetic energy per molecule.

Temperature vs. Internal EnergyTemperature 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.

Temperature EquilibriumTemperature EquilibriumHeat is defined as the transfer of thermal energy that is due to a difference in temperature.

Hot Coals

Cool Water Same Temperature

Thermal Equilibrium

Insulated Container

Two objects are in thermal equilibrium if and only if they have the same temperature.

ThermometerThermometerA thermometer is any device which, through marked scales, can give an indication of its own temperature.

T = kXT = kX

X is thermometric property: Expansion, electric resistance, light wavelength, etc.

ZerothZeroth Law of ThermodynamicsLaw of Thermodynamics

The The ZerothZeroth Law of Thermodynamics:Law of Thermodynamics: If two objects If two objects AA and and BB are are separatelyseparately in equilibrium with a third object in equilibrium with a third object CC, then , then objects objects A A and and BB are in thermal equilibrium with each other.are in thermal equilibrium with each other.

AObject C

A B

Thermal Equilibrium

Same TemperatureBObject C

1000C 2120F

00C 320F

Temperature ScalesTemperature Scales

The lower fixed point is the ice point, the temperature at which ice and water coexist at 1 atm of pressure:

00C or 320F00C 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 2120F1000C or 2120F

Comparison of Temperature IntervalsComparison of Temperature Intervals

2120F

320F

180 F0

1000C

00C

100 C0

tC tF

Temperature Intervals:

100 C0 = 180 F0

5 C0 = 9 F0

If the temperature changes from 790F to 700F, it means a decrease of 5 C0.

Temperature LabelsTemperature Labels

If an object has a specific temperature, we place the If an object has a specific temperature, we place the degree symboldegree symbol 00 beforebefore the scalethe scale ((00CC or or 00FF).).

t = 60t = 6000CC

We say: “The temperature is sixty degrees Celsius.”

We say: “The temperature is sixty degrees Celsius.”

Temperature Labels (Cont.)Temperature Labels (Cont.)If an object undergoes a If an object undergoes a change of temperaturechange of temperature, we , we place the degree symbolplace the degree symbol 00 afterafter the scalethe scale ((CC00 or or FF00) to ) to indicate the interval of temperature.indicate the interval of temperature.

We say: “The temperature decreases by forty Celsius degrees.”

We say: “The temperature decreases by forty Celsius degrees.”

t = 600C – 200C t = 40 C0

ttii = 60= 6000CC

ttff = 20= 2000CC

Specific TemperaturesSpecific Temperatures

2120F

320F

1000C

00C

180 F0100 C0

tC tF

Same temperatures have different

numbers: 0C 0F

0 00 32100 div 180 div

C Ft t

095 32C Ft t

095 32F Ct t 05

9 32C Ft t

Example 1:Example 1: A plate of food cools from A plate of food cools from 16016000FF to to 656500FF. What was the initial temperature in . What was the initial temperature in degrees Celsius? What is the change in degrees Celsius? What is the change in temperature in Celsius degrees?temperature in Celsius degrees?

Convert 1600F to 0C from formula: 05

9 32C Ft t

00 05 5(128 )(160 32 )

9 9Ct tC = 71.10CtC = 71.10C

0 0 0160 F 65 F 95 Ft 9 F0 = 5 C09 F0 = 5 C0

00

0

5 C95 F9 F

t

t = 52.8 C0t = 52.8 C0

Limitations of Relative ScalesLimitations of Relative ScalesThe 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 00C or 00F!

-250C ?

T = kX = 0 ?T = kX = 0 ?

Constant Volume ThermometerConstant 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.

Absolute Zero of TemperatureAbsolute Zero of Temperature

1000C00C

P1 P2

T1 T2

-2730C 00C 1000C

P

T

Plot points (P1 , 00C) and (P2 , 1000C); then

extrapolate to zero.

Absolute Zero = -2730CAbsolute Zero = -2730C

Absolute Zero

Comparison of Four ScalesComparison of Four Scales

1 C0 = 1 K1 C0 = 1 K

5 C0 = 9 F5 C0 = 9 F

095 32F Ct t

059 32C Ft t

TK = tC + 2730TK = tC + 2730

ice

steam

Absolute zero

1000C

00C

-2730C

CelsiusC

Fahrenheit

320F

-4600F

2120F

F

273 K

373 K

Kelvin

0 K

KRankine

0 R

460 R

672 R

R

Linear ExpansionLinear Expansion

L

Lo Lto

t

0L L t

0

LL t

Copper:

= 1.7 x 10-5/C0Copper:

= 1.7 x 10-5/C0

Aluminum:

= 2.4 x 10-5/C0Aluminum:

= 2.4 x 10-5/C0Iron:

= 1.2 x 10-5/C0Iron:

= 1.2 x 10-5/C0

Concrete:

= 0.9 x 10-5/C0Concrete:

= 0.9 x 10-5/C0

Example 2:Example 2: A copper pipe is A copper pipe is 90 m90 m long at long at 202000CC. What is its new length when steam . What is its new length when steam passes through the pipe at passes through the pipe at 10010000CC??

Lo = 90 m, t0 = 200Ct = 1000C - 200C = 80 C0

L = Lo t = (1.7 x 10-5/C0)(90 m)(80 C0)

L = 0.122 m L = Lo + L

L = 90 m + 0.122 m

L = 90.12 mL = 90.12 m

Applications of ExpansionApplications of Expansion

Expansion Joints

Bimetallic Strip

BrassBrassIron

Iron

Expansion joints are necessary to allow concrete to expand, and bimetallic strips can be used for

thermostats or to open and close circuits.

Area ExpansionArea 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.

A0 A

Calculating Area ExpansionCalculating Area Expansion

W

L

LLo

WoW

A0 = L0 W0 A = LW

L = L0 + L0 t W = W0 + W0 t

L = L0 (1 + t ) W = W0 (1 + t

A = LW = L0 W0 (1 + t)2 A = A0 (1 + 2t)

Area Expansion: A = 2

tArea Expansion: A = 2

t

Volume ExpansionVolume Expansion

Expansion is the same in all directions (L,

W, and H), thus:

V = V0 tV = V0 t

The constant is the coefficient of volume expansion. 0

VV t

Example 3.Example 3. A A 200200--cmcm33 Pyrex beaker is filled Pyrex beaker is filled to the top with glycerine. The system is to the top with glycerine. The system is then heated from then heated from 202000CC to to 808000CC. How much . How much glycerine overflows the container?glycerine overflows the container?

Vovr = ?

V0 V

200C800C

200 cm3

Glycerine: 5.1 x 10-4/C0

Pyrex:

= 3 0.3 x 10-5/C0)

= 0.9 x 10-5/C0

Vover = VG - VP

Vovr = G V0 t - P V0 t = (G - P )V0 t

Vovr = (5.1 x 10-4/C0- 0.9 x 10-5/C0)(200 cm3)(800C - 200C)

Example 3.Example 3. (CONTINUED)(CONTINUED)

Vovr = ?

V0 V

200C800C

200 cm3

Glycerine: 5.1 x 10-4/C0

Pyrex:

= 3 0.3 x 10-5/C0)

= 0.9 x 10-5/C0

Vover = VG - VP

Vovr = G V0 t - P V0 t = (G - P )V0 t

Vovr = (5.1 x 10-4/C0- 0.9 x 10-5/C0)(200 cm3)(800C - 200C)

Volume Overflow = 6.01 cm3Volume Overflow = 6.01 cm3

SummarySummaryThermal energy is the total internal energy of an object: the sum of its molecular kinetic and potential energies. Thermal energyThermal energy is the total internal energy of an object: is the total internal energy of an object: the sum of its molecular kinetic and potential energies.the sum of its molecular kinetic and potential energies.

Thermal energy = U + KThermal energy = U + K

The The ZerothZeroth Law of Thermodynamics:Law of Thermodynamics: If two objects If two objects AA and and BB are are separatelyseparately in equilibrium with a third object in equilibrium with a third object CC, then , then objects objects A A and and BB are in thermal equilibrium with each other.are in thermal equilibrium with each other.

A B

Thermal EquilibriumAObject C

B

Summary of Temperature ScalesSummary of Temperature Scales

1 C0 = 1 K1 C0 = 1 K

5 C0 = 9 F5 C0 = 9 F

095 32F Ct t

059 32C Ft t

TK = tC + 2730TK = tC + 2730

ice

steam

Absolute zero

1000C

00C

-2730C

CelsiusC

Fahrenheit

320F

-4600F

2120F

F

273 K

373 K

Kelvin

0 K

KRankine

0 R

460 R

672 R

R

Summary: ExpansionSummary: Expansion

LLo Lto

t

0L L t

0

LL t

Linear Expansion:

A = 2

tA = 2

t

Area Expansion:Expansion

A0 A

Volume ExpansionVolume Expansion

Expansion is the same in all directions (L,

W, and H), thus:

V = V0 tV = V0 t

The constant is the coefficient of volume expansion. 0

VV t

CONCLUSION: Chapter 16CONCLUSION: Chapter 16 Temperature and ExpansionTemperature and Expansion