Chapter 12

Thermal Energy

Heat and TemperatureLight

Law of Conservation of Energy?

When rub your hands together

• What is the Net KE?– Zero, the motion is in opposite directions.

• What is the change is PE? – Zero, your hands are at the same height.

• You did work against friction, where did the energy go?

• You did work against friction, where did the energy go?

Thermal Energy

• Thermal Energy: The total internal Energy

• Internal Energy: The sum of the kinetic and potential energies of the internal motion of particles that make up an object.

Kinetic-molecular Theory• All matter is made up of molecules and

atoms

• Molecules are in constant motion

• Objects in motion have Kinetic Energy.

Kinetic-molecular Theory• Molecules are in constant motion• Objects in motion have Kinetic Energy.

• When particles get hotter, they move faster (e.g. higher Kinetic Energy)

Heat

Heat Applet

The Nature of Matter• Molecules in liquids and gases move freely.• Molecules in solids simply vibrate.

• This means that all molecules possess their own kinetic energy (KE), the energy of motion.

Solid Liquid/Gas

Temperature• Molecules move at different speeds.• Now let’s add some heat?

– Now they are all moving faster!• Temperature relates to the average kinetic

energy of the molecules in a substance.

The higher the temperature, the faster the molecules move.

Temperature Scales

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100

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• Celsius– Water boils at 100oC– Water at Freezes 0oC

• Fahrenheit – Water boils at 212oF– Water Freezes at 32oF

• Kelvin– Absolute Zero 0ºK– Water boils at 373oK– Water Freezes at 273oK

Temperature Scales conversions

Fahrenheit scale freezes 32o above Celsius

180 18 9

10 5 100

Fahrenheit Range

Celsius Range

932

5F CT T

Temperature Scales conversions

532

9C FT T

100 10 5

18 9 180

Celsius Range

Fahrenheit Range

Celsius scale freezes 32o below Fahrenheit

Temperature Scales• There are three major temperature scales that we will

deal with.– The Fahrenheit Scale (°F)– The Celsius Scale (°C)– The Kelvin Scale (°K)

• Conversion formulas are shown below. 325

9CF TT

3295

FC TT

273.15K CT T

273.15C KT T

95 32F CT T 9

5 21 32FT 69.8FT F

273.15K CT T 21 273.15KT 294.15KT K

Sample Temperature Conversion• A beaker of water at room temperature is

measured to be at 21°C.

• What is the Fahrenheit and Kelvin temperature?

Temperature Scales conversions Example 1

• Convert 45ºF to Celsius

532

9C FT T

545 32

9o

CT

513

9CT

7.2oCT C

Temperature Scales conversions Example 1

• Convert 32ºC to Fahrenheit

9(32 ) 32

5FT

932

5F CT T

57.6 32FT

89.6FT

Homework

• WS1 1-5

• WS 1a 1-3

Absolute Zero• The final temperature to note is absolute zero, 0K.• This is the lowest possible temperature.• Here molecules are in a complete state of rest, which

means that there is no kinetic energy.• Absolute zero has never been reached.• However, scientists have come within 0.1K

• Pressure versus Temp graphs 0K

Thermal Contact• KE transfer through thermal contact

Thermal Equilibrium: – Both objects have the same average Kinetic

Energy

HOTCOLD

KEKEKE

KEWarmWARM

What is Heat?• Heat is energy in transfer from an object of

higher temperature to one of lower temperature.

• The quantity of energy transfer from one object to another because of a difference in temperature.

Cold Hot

Heat Flow

Warm Warm

Thermal Energy• The sum of all the kinetic energies within a material is

known as thermal energy.• Both full cups of coffee are at the same temperature.

– Which cup contains greater thermal energy?– Which cup contains a higher average kinetic energy within the

molecules?

AB

B

Both are the same!

Heat & Kinetic Energy• Both Brass blocks are at 115oC.

• Which block has the higher KE?

• Which block has the higher average KE?

BrassBrass

Homework

• WS #1 4-9

• WS #1 4-13

Specific Heat Video Clip

Specific HeatHeat: The energy that flows as a result of a difference in temperature

Q: The symbol for heat. Measured in Joules

Specific Heat (C): The amount of energy needed to raise a unit of mass one temperature unit.

(J/kg K)

Heat gained

Q: Heat

m: mass

ΔT: Change in Temperature

Q mC T

Sample Heat Problem• How much heat is required to raise the temperature of a

2.4kg gold ingot (c = 129J/kgK) from 23°C to 45°C?

2.4kgQ mc T

2.4 129 22JkgKQ kg C

6811.2Q J

F IT T T 45 23T C C 22T C

Light

Heat TransferExample 1

A 0.40kg block of iron is heated from 295K to 325K. How much heat is absorbed by the iron?

Q mC T (.4 )(450 )(325 295 )J

Kg KQ kg K K

5400Q J

450 JKg KC

Heat TransferWS3 #1

How much heat is absorbed by 60.0g of copper when it is heated from 20ºC to 80ºC

Q mC T (.06 )(385 )(353 293 )J

Kh KQ kg K K

1386Q J

60 .06g kg

80 353oC K385 J

Kg KC

Practice Problems

• WS 3a– #’s 1-3 Specific heat

Calorimerty

Calorimeter: A device used to measure changes in thermal energy.

Calorimerty Utilizes on the conservation of energy.

Qgained + Qlost = Zero

Calorimerty ExampleA .4kg block of zinc @115°C is placed in .5kg of water @15°C. Find the final temperature.

( ) ( ) 0a a f ai b b f bim C T T m C T T

.4 (388 )( 115 ) .5 (4180 )( 15 ) 0o oJ Jf fkgK kgKkg t C kg t C

21.9ofT C

0a a a b b bm C T m C T

0gained lostQ Q

388 Jkg KC

Calorimerty ExampleA .1kg block of brass @90°C is placed in .2kg of water @20°C. Find the final temperature.

.1 (376 )( 90 ) .2 (4180 )( 20 ) 0o o

o oJ Jf fkg C kg C

kg t C kg t C

23.0ofT C

0a a a b b bm C T m C T

Practice Problems• Book Page 252

– #’s 9-11 Calorimetery

• WS4– # 7-11 Calorimetery

WS #3– Problem # 1 a-d– Problem #2 a-d

• Quiz

Latent Heat (Enthalpy)• Describe what Q=mCΔT means• Is it possible to add heat without changing the

temperature?• A heat transfer is also required to change phase. • Heat must be added to go to a more energetic phase.• Heat must be removed to go to a less energetic phase.

Solid Vapor

Vapor

Liquid

+Q +Q

-Q -Q

Substances in Phase Transfer

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Heats of Fusion and Vaporization• Heat of fusion (Hf): the amount of heat energy required

change 1kg of substance in the solid state into the liquid state.

• The equation is as follows:

• The heat of vaporization (Hv) is the amount of heat energy required to change 1kg of substance in the liquid state into the vapor state.

• The equation is as follows:

fQ mL

vQ mL

Sample Heating Across Phase• A block of ice (m = 1.2kg) at -10°C being heated

to water at 80°C. How much heat is used?

• These problems have 1-5 steps.

Ice -10°C Ice 0°C Water 0°C

Water 80°C

3 Steps

Heating Melting Heating

Q mc T fQ mH Q mc T

fQ mc T mL mc T 51.2 2060 10 1.2 3.34 10 1.2 4180 80J J J

kg C kg kg CQ kg C kg kg C 826800Q J

The Heating Curve (H2O)• As H2O is heated from ice below freezing to steam

above boiling, the temperature can be plotted with respect to time.

• Where are the flat spots located?

Temperature remains constant during phase changes.

Once each phase change is complete, temperature can rise

again.

Heating Curve of Water

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60

80

100

120

140

0 5 10 15 20

Time (min)

Tem

per

atu

re (

C)

HeatHeatingMeltingBoiling Heat

The Cooling Curve (H2O)• The cooling curve is very similar to the heating curve• What can you conclude about temperatures when cooling

between phases?

Cooling Curve of Water

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0

20

40

60

80

100

120

140

0 5 10 15 20

Time (min)

Tem

per

atu

re (

C)

SolidifyingCoolingCondensingCooling also requires the temperature to be held constant while in the midst of a phase

change.

The temperature can continue to drop after all of the substance is converted into the next

phase.

Cool

Phase Change WS7 #1• Between A-B: The ice is warming to 0oC• Between B-C: Thermal energy melts the ice at 0oC• Between C-D: The water is warm to 100oC• Between D-E: The water boils and changes to vapor at

100oC• After E: The temperature of the vapor increases

Latent Heat

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100

150

Time

Tem

pera

ture

(C

)

A

B

C ED

Practice Problems

• WS #7– # 1 b-g– # 2,3

Heat of fusion WS8 #1If 5,000J is added to ice at 0oC, how much ice is melted?

Q=mLf Q=mLv

Water Hf=3.34x105J/kg

Water Hv=2.26x106J/kg

/ fm Q L55000 / 3.34 10 /m J x J kg

.015m kg

Heat of fusion WS8 #2

How much heat must be transferred to 100g of ice at 00C until the ice melts and the temperature of the resulting water rises to 200C?

Water Hf=3.34x105J/kg

melt ice fQ mH heat waterQ mC T

43.34 10 8360

41760total

total

Q x J J

Q J

5.1 (3.34 10 )JkgQ kg x43.34 10Q x J

0

0.1 (4180 )20Jkg C

Q kg C8360Q J

Homework

WS #8– #’s 3-5

• Book Page 255– # 16 Heat of fusion

• WS #7 (5 heats)

Thermal Energy Transfer• Conduction:

– Transfer of Kinetic Energy by contact

• Convection:– Heat transfer by the motion of a fluid (e.g. air)

• Radiation:– Electromagnetic waves carry energy

Note: Conduction and Convection require matter

Thermal Energy Transfer video Clip

Conduction• Conduction is the transfer of heat through molecular

collisions.• This form of heat transfer best occurs in solids where

molecules are closely packed.• Materials that conduct heat well are called conductors.

(Eg. metals such as copper and iron)• Materials that conduct heat poorly are called insulators.

(Eg. foam, air, and asbestos)Magnification

Convection• Convection is the transfer of heat though moving fluids.• A fluid is any substance that flows, which includes all

liquids and gases.• Examples include convection ovens and cloud formation.

Convection ?

• Have you ever watched a pot of water when it is being heated, especially while boiling? What do you notice?

• You will notice that there are currents within the pot.

The Heating Water Pot

The process of convection transfers heated water from the bottom of the pot to the top, where it is exchanged for cooler water.

Convection

• Gulf stream current

• http://rads.tudelft.nl/gulfstream/#fig2

Convection

It was remarkable how weightlessness affected things: I found that if I stayed perfectly still, my own body heat built up around me like a tenuous blanket, because there was no convection to carry it away. But my slightest motion dispelled this warmth and let me cool.

– Jim Lovell, Apollo 13

Radiation (not radioactivity)

• Radiation is the transfer of heat via electromagnetic waves.

• These waves include visible light, but are mostly infrared.

• No matter is required for this type of heat transfer.

• Examples include the sun’s heat and warmth felt from a flame.

Open Space

?Radiation

More on Radiation• All objects emit heat in the form of radiation (radiant heat).• Hotter objects emit more energetic waves.• Some extremely hot objects can emit visible light, a form

of electromagnetic radiation.• In fact, all forms of radiation travel at the speed of light.

82.998 10 ms

Objects in thermal equilibrium will emit the same amount of radiation that they receive from other

objects.

Heat Transfer Question• Consider a camp fire burning vigorously.

– How is heat normally transferred while warming its viewers?• Radiation

– How is heat transferred when you put a hand in the smoke?• Convection

– How is heat transferred to a stick when it is placed in the hot coals?

• Conduction

• Some situations involve

multiple heat transfer

types like this.

Homework

• WS #4 1-6– Thermal Energy Transfer

Homework

• WS #2 – Temperature Conversions

Thermal Expansion• The change in length of a material due to

change in temperature.

Thermal Expansion Video Clip

• Expansion and Contraction movie clip.

Linear Expansion• Most objects expand when heated and contract when

cooled

• The change in length of a solid is proportional to ΔT

• The change in length is proportional to the length of the object

( )i i iL L L T T

Linear Expansion animation

• Expansion Joint

Linear Expansion animation• Expansion joint versus NO joint

Linear Expansion animation• Expansion in a U joint

Linear Expansion animation• Expansion in an elbow joint

Linear Expansion WS9 #1A metal bar is 2.6m long at 210C. The bar is heat to 930C and the length increases by 3.4mm. What is the coefficient of linear expansion?

2.6Li m

33.4 10L x m

021Ti C093T C

( )i i iL L L T T

( )i iL L T T 3

0

3.4 10

2.6 (72 )i

L x m

L T m C

5 0 11.8 10 ( )x C Heat

Sample Linear Expansion Problem• A train rail is initially 20m long in the morning when the

temperature outside is 10°C. By how much will the rail expand in the heat of the day when the temperature reaches 35°C?

• The coefficient of linear expansion for steel is:

• Now find L.

• What is the final length?

6 18.0 10 C

iL L T 620 8.0 10 35 10L m C C 0.004L m

f iL L L f iL L L

20 0.004 20.004fL m m m

Linear Expansion WS9 #2• A piece of aluminum siding 3.66m long on a -

28.00C winter day is how long on a hot 390C summer day?

6 0 125 10x C

( )i i iL L L T T 6 0 1 0 03.66 (25 10 )(3.66 )(39 28 )L m x C m C C

3.666L m

Practice Problems

• WS 9 Linear Expansion– #’s 3-5

The Bimetallic Strip• A bimetallic strip consists of two metal strips

pressed together into a single strip.• A common strip consists of steel and brass. • Since different materials expand at different

rates, the strip will bend.

Room TempBrass

Steel

High Temp

Brass

Steel

Low TempBrass

Steel

The Bimetallic Strip (Cont.)• Bimetallic strips are most often used in temperature

sensitive instruments as thermostats.

• The strip is wound into a coil.

• As temperature changes, the coil expands or contracts to activate a switch controlling a heating/cooling system.

Heat

AC

I’m Hot!!!I’m

Cold!!

Expansion of Water• Water initially at 100C that cools to 40C• Water initially at 40C that cools to 00C• Water initially at 00C that freezes to 00C ice• Water initially at 100C that cools to 40C• Water initially at 100C that cools to 40C

Unique Properties of Water (Cont.)• In liquid water, the molecules move freely in no particular

order or array. This is what allows them to flow.

• When water freezes, the molecules form a hexagonal pattern.

• Why may ice possess less density?

O

HH

OHH

OHH

O

H

H

O HH

OH

H

O

H

H

O HH

OHH

O

HH

OH

H

O HH

OHH

OH H

O HH

OHH

OH

H

OHH

Liquid Water

OH

H

OHH

OHH

OHH

OHH

OH

H

Solid Ice

OH

H

OHH

OHH

OHH

OHH

OH

HO

HH

OHH

OHH

OHH

OHH

OH

H

Open Space

Applications of Linear Expansion• Linear expansion must be taken into consideration for

engineers designing something that will experience a range of temperatures.

• Here are just a few select examples:

Railroads Bridges Metal Roofs

Practice Problems

• WS #5 1-16 Thermal Expansion

End Unit on Heat

• E

Latent Heat

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(C

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Change of State

• States of mater– Solid– Liquid– Gas

examples

• Examples– Temperature scales

• Examples– Convert Celsius to Fahrenheit– Convert Fahrenheit to Celsius

• Heat transfer types• Calorimeter and specific heat• Thermal expansion• Examples

– Conservation of energy transfer

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Thermal Energy

COLD HOT