Section/Objectives Standards Lab and Demo Planning · 2006-03-13 · Quick Demo,p. 315: two...

312A

See page 14T for a key to thestandards.

Differentiated Instruction

Level 1 activities should beappropriate for studentswith learning difficulties.

Level 2 activities shouldbe within the ability rangeof all students.

Level 3 activities aredesigned for above-average students.

Section/Objectives Standards Lab and Demo Planning

State/LocalNational

Chapter Opener

1. Describe thermal energy and compare it to poten-tial and kinetic energies.

2. Distinguish temperature from thermal energy.3. Define specific heat.4. Calculate heat transfer.

5. Define heats of fusion and vaporization.6. State the first and second laws of thermodynamics.7. Distinguish between heat and work.8. Define entropy.

Section 12.2

Section 12.1 Student Lab:Launch Lab, p. 313: 250-mL ovenproof glassbeaker, 150-mL water

Teacher Demonstration:Quick Demo, p. 315: two beakers, ice water,cold tap water, large alcohol thermometerQuick Demo, p. 319: thermometer, 250-mLbeaker, water, calcium chloride, measuring spoon

Student Lab:Mini Lab, p. 324: two foam cups, water, icewater, ice cube, two thermometersAdditional Mini Lab, p. 330: two 250-mLbeakers (one filled with hot water and one withvery cold water), dropper, food coloringPhysics Lab, p. 332–333: hot plate (or Bunsenburner), 250-mL ovenproof glass beaker, 50-200 gof water, two thermometers (non-mercury), stop-watch or timer

UPC.1, UPC.2,UPC.3, A.1, A.2,B.5, B.6

UPC.1, UPC.2,UPC.3, A.1, A.2,B.5, B.6, E.1, E.2,G.3

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312B

FAST FILE Chapters 11–15 Resources, Chapter 12Transparency 12-1 Master, p. 53Study Guide, pp. 41–46Enrichment, pp. 51–52Section 12-1 Quiz, p. 47Teaching Transparency 12-1

Connecting Math to Physics

FAST FILE Chapters 11–15 Resources, Chapter 12Transparency 12-2 Master, p. 55Transparency 12-3 Master, p. 57Transparency 12-4 Master, p. 59Study Guide, pp. 41–46Reinforcement, p. 49Section 12-2 Quiz, p. 48Mini Lab Worksheet, p. 35Physics Lab Worksheet, pp. 37–40Teaching Transparency 12-2

Teaching Transparency 12-3

Teaching Transparency 12-4Connecting Math to PhysicsLaboratory Manual, pp. 57–60Probeware Laboratory Manual, pp. 25–28Forensics Laboratory Manual, pp. 31–34

Interactive Chalkboard CD-ROM: Section 12.1 PresentationTeacherWorks™ CD-ROM

Interactive Chalkboard CD-ROM: Section 12.2 PresentationTeacherWorks™ CD-ROMProblem of the Week at physicspp.com

™ includes: Interactive Teacher Edition ■ Lesson Plannerwith Calendar ■ Access to all Blacklines ■ Correlation to Standards ■ Web links

Reproducible Resources and Transparencies Technology

Legend — Transparency CD-ROM MP3 Videocassette DVD WEB

Assessment ResourcesFAST FILE Chapters 11–15 Resources,Chapter 12

Chapter Assessment, pp. 61–66

Additional Challenge Problems, p. 12Physics Test Prep, pp. 23–24Pre-AP/Critical Thinking, pp. 23–24Supplemental Problems, pp. 23–24

Technology

Interactive Chalkboard CD-ROM:Chapter 12 Assessment

ExamView® Pro Testmaker CD-ROM

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physicspp.com

312A-312B PhyTWEC12-845814 7/12/04 10:43 PM Page 313

http://www.physicspp.com

http://www.physicspp.com/vocabulary_puzzlemaker


What You’ll Learn• You will learn how

temperature relates to the potential and kineticenergies of atoms andmolecules.

• You will distinguish heatfrom work.

• You will calculate heattransfer and the absorptionof thermal energy.

Why It’s ImportantThermal energy is vital forliving creatures, chemicalreactions, and the workingof engines.

Solar Energy A strategyused to produce electricpower from sunlightconcentrates the light withmany mirrors onto onecollector that becomes veryhot. The energy collected ata high temperature is thenused to drive an engine,which turns an electricgenerator.

Think About This �What forms of energy doeslight from the Sun take inthe process of convertingsolar energy into useful workthrough an engine?

312

physicspp.com

CORBIS

312

Chapter OverviewStudents have learned howenergy can be transformed, aswell as how it can be transferredbetween objects. This chapter willinvestigate the transfer of energybetween the particles of a solid,liquid, or gas. The kinetic energyin the motion of the particles thatmake up matter is called thermalenergy, and this energy can betransferred as heat. These con-cepts are useful in explaininghow engines and refrigeratorswork, leading to the second lawof thermodynamics, one of themost fundamental laws of nature.

Think About ThisThe energy from the Sun radiatesthrough space and Earth’s atmos-phere in the form of electromag-netic waves. Light, which is a typeof electromagnetic wave, isfocused by the mirrors andabsorbed by the collector. Theenergy is transferred as heat to awater reservoir to turn water tosteam. The steam is the high-tem-perature heat source for a turbinethat turns an electric generator.See Section 12.2 for a discussionof heat engines.

� Key Termsconduction, p. 315

thermal equilibrium, p. 315

heat, p. 317

convection, p. 317

radiation, p. 317

specific heat, p. 318

heat of fusion, p. 324

heat of vaporization, p. 324

first law of thermodynamics, p. 326

heat engine, p. 326

entropy, p. 328

second law of thermodynamics,p. 330

Purpose Students should learn that heat is trans-ferred spontaneously from an object with a highertemperature to one with a lower temperature.

Materials one 250-mL ovenproof glass beaker,150 mL of water

Teaching StrategiesCAUTION: Students should wear closed-toeshoes (no sandals).

• While discussing what happened, be sure toremind the students that body temperature isroughly 37°C.

• Ask the students how they think the tempera-ture of the school is different on a teacher-only workday than when all the students areat school.

312-339 PhyTWEC12-845814 7/12/04 2:42 AM 12


Section 12.1

1 FOCUS

Bellringer ActivityA Rubber-Band ThermometerAs a demonstration or a studentinvestigation, make a simple ther-mometer using a ruler, a rubberband, a round wooden pencil,and a pin (see diagram). Place thepencil across the ruler and stretchthe rubber band across the endsof the ruler to hold the pencil inplace. The pin is stuck into theside of the pencil to indicate howthe pencil rotates. Hold a desklamp near one part of the rubberband. Because rubber shrinkswhen heated (unlike most sub-stances), the pencil will rotate thepin to point toward the heatedside of the band. When the heatsource is removed, the pin should rotate back to its originalposition. Visual-Spatial

What happens when you provide thermalenergy by holding a glass of water?

QuestionWhat happens to the temperature of water when you hold a glass of water in your hand?

Procedure

1. You will need to use a 250-mL beaker and150 mL of water.

2. Fill the beaker with the 150 mL of water. 3. Record the initial temperature of the water

by holding a thermometer in the water in the beaker. Note that the bulb end of thethermometer must not touch the bottom orsides of the beaker, nor should it touch atable or your hands.

4. Remove the thermometer and hold the beakerof water for 2 min by cupping it with bothhands, as shown in the figure.

5. Have your lab partner record the finaltemperature of the water by placing thethermometer in the beaker. Be sure that thebulb end of the thermometer is not touchingthe bottom or sides of the beaker.

Analysis

Calculate the change in temperature of thewater. If you had more water in the beaker,would it affect the change in temperature? Critical Thinking Explain what caused thewater temperature to change.

12.1 Temperature and Thermal Energy

The study of heat transformations into other forms of energy, calledthermodynamics, began with the eighteenth-century engineers who

built the first steam engines. These steam engines were used to powertrains, factories, and water pumps for coal mines, and thus they contributedgreatly to the Industrial Revolution in Europe and in the United States. Inlearning to design more efficient engines, the engineers developed newconcepts about how heat is related to useful work. Although the study ofthermodynamics began in the eighteenth century, it was not until around1900 that the concepts of thermodynamics were linked to the motions ofatoms and molecules in solids, liquids, and gases.

Today, the concepts of thermodynamics are widely used in variousapplications that involve heat and temperature. Engineers use the laws ofthermodynamics to continually develop higher performance refrigerators,automobile engines, aircraft engines, and numerous other machines.

Section 12.1 Temperature and Thermal Energy 313

� Objectives• Describe thermal energy

and compare it to potentialand kinetic energies.

• Distinguish temperaturefrom thermal energy.

• Define specific heat andcalculate heat transfer.

� Vocabularyconductionthermal equilibriumheatconvection radiationspecific heat

Horizons Companies

313

Expected Results The water should heat up byat least one full degree Celsius.

Analysis The temperature change equals Tf � Ti,approximately one degree Celsius. If there weremore water in the glass, the temperature increasewould be less.

Critical Thinking Heat is transferred because ofa difference in temperatures. The water is initiallyat room temperature (approximately 20°C). A per-son’s body temperature, including hands, isapproximately 37°C. When hands contact thebeaker, heat is transferred from the hands to thebeaker and then to the water, raising the water’stemperature.

ruler

rubber band

pin rotates this way

desk lamp

pencil

pin

This CD-ROM is an editableMicrosoft® PowerPoint®

presentation that includes:

■ Section presentations ■ Interactive graphics■ Image bank■ All transparencies■ Audio reinforcement■ All new Section and Chapter

Assessment questions■ Links to physicspp.com

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314

TechnologyTeacherWorks™ CD-ROMInteractive Chalkboard CD-ROMExamView ® Pro Testmaker CD-ROMphysicspp.comphysicspp.com/vocabulary_puzzlemaker

12.1 Resource MANAGERFAST FILE Chapters 11–15 Resources

Transparency 12–1 Master, p. 53Study Guide, pp. 41–46Enrichment, pp. 51–52Section 12–1 Quiz, p. 47

Teaching Transparency 12-1Connecting Math to Physics

Thermal EnergyYou already have studied how objects collide and trade kinetic energies.

For example, the many molecules present in a gas have linear and rota-tional kinetic energies. The molecules also may have potential energy intheir vibrations and bending. The gas molecules collide with each otherand with the walls of their container, transferring energy among each otherin the process. There are numerous molecules moving freely in a gas,resulting in many collisions. Therefore, it is convenient to discuss the totalenergy of the molecules and the average energy per molecule. The totalenergy of the molecules is called thermal energy, and the average energyper molecule is related to the temperature of the gas.

Hot objects What makes an object hot? When you fill up a balloon withhelium, the rubber in the balloon is stretched by the repeated poundingfrom helium atoms. Each of the billions of helium atoms in the ballooncollides with the rubber wall, bounces back, and hits the other side of theballoon, as shown in Figure 12-1. If you put a balloon in sunlight, youmight notice that the balloon gets slightly larger. The energy from the Sunmakes each of the gas atoms move faster and bounce off the rubber wallsof the balloon more often. Each atomic collision with the balloon wallputs a greater force on the balloon and stretches the rubber. Thus, the bal-loon expands.

On the other hand, if you refrigerate a balloon, you will find that itshrinks slightly. Lowering the temperature slows the movement of thehelium atoms. Hence, their collisions do not transfer enough momentumto stretch the balloon quite as much. Even though the balloon contains thesame number of atoms, the balloon shrinks.

Solids The atoms in solids also have kinetic energy, but they are unable tomove freely as gas atoms do. One way to illustrate the molecular structureof a solid is to picture a number of atoms that are connected to each otherby springs. Because of the springs, the atoms bounce back and forth, withsome bouncing more than others. Each atom has some kinetic energy andsome potential energy from the springs that are attached to it. If a solid hasN number of atoms, then the total thermal energy in the solid is equal tothe average kinetic and potential energy per atom times N.

Thermal Energy and TemperatureAccording to the previous discussion of gases and solids, a hot object has

more thermal energy than a similar cold object, as shown in Figure 12-2.This means that, as a whole, the particles in a hot object have greater thermal energy than the particles in a cold object. This does not mean thatall the particles in an object have exactly the same amount of energy; theyhave a wide range of energies. However, the average energy of the particlesin a hot object is higher than the average energy of the particles in a cold object. To understand this, consider the heights of students in a twelfth-grade class. Although the students’ heights vary, you can calculatethe average height of the students in the class. This average is likely to be greater than the average height of students in a ninth-grade class, eventhough some ninth-grade students may be taller than some twelfth-gradestudents.

■ Figure 12-1 Helium atoms in a balloon collide with the rubberwall and cause the balloon toexpand.

Helium balloon

■ Figure 12-2 Particles in a hotobject have greater kinetic andpotential energies than particlesin a cold object do.

Hot object

Cold object

KEhot � KEcold

314 Chapter 12 Thermal Energy

Tie to Prior KnowledgeEnergy We have already investi-gated energy in several forms: lin-ear kinetic energy, rotationalkinetic energy, and elastic poten-tial energy. Each atom or mole-cule in a material can have energyin one or more of these forms.These particles transfer energyamong themselves through elasticand inelastic collisions. This trans-fer of energy is the basis for theflow of heat.

2 TEACH

Concept DevelopmentThermal Energy andTemperature If the classroomarrangement permits, make alarge open area in the center ofthe room. Ask the students togather in the center of the spacewith their arms straight down attheir sides so that their shouldersare touching (crowd them inthere, but do not arrange them allfacing any particular direction).Inform them they are now mole-cules of a solid at a low tempera-ture. Tell them to vibrate, moveup and down on their toes andbend their knees a bit, but not tolift their feet or arms. They arenow molecules of a solid at ahigher temperature (vibrating in afixed position). It’s now time tomelt! Tell them they may nowvibrate as before but also shouldmove their feet slowly while theheel of one foot maintains contactwith the toes of another student.Additionally, they may now raisetheir arms as much as needed butmust maintain hand-to-hand con-tact with at least two other stu-dents at all times (a good placefor molecular “high-fives”). Thesolid has now melted and they area liquid. Kinesthetic

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Temperature Temperature depends only on the average kinetic energy ofthe particles in the object. Because temperature depends on average kineticenergy, it does not depend on the number of atoms in an object. To under-stand this, consider two blocks of steel. The first block has a mass of 1 kg,and the second block has a mass of 2 kg. If the 1-kg block is at the sametemperature as the 2-kg block, the average kinetic energy of the particles ineach block is the same. However, the 2-kg block has twice the mass of the1-kg block. Hence, the 2-kg block has twice the amount of particles as the 1-kg block. Thus, the total amount of kinetic energy of the particles in the 2-kg block is twice that of the 1-kg mass. Total kinetic energy is divided bythe total number of particles in an object to calculate its average kineticenergy. Therefore, the thermal energy in an object is proportional to thenumber of particles in it. Temperature, however, is not dependent on thenumber of particles in an object.

Equilibrium and ThermometryHow do you measure your body temperature? For example, if you sus-

pect that you have a fever, you might place a thermometer in your mouthand wait for a few minutes before checking the thermometer for your temperature reading. The microscopic process involved in measuring temperature involves collisions and energy transfers between the ther-mometer and your body. Your body is hot compared to the thermometer,which means that the particles in your body have greater thermal energyand are moving faster than the particles in the thermometer. When thecold glass tube of the thermometer touches your skin, which is warmerthan the glass, the faster-moving particles in your skin collide with theslower-moving particles in the glass. Energy is then transferred from yourskin to the glass particles by the process of conduction, which is the transfer of kinetic energy when particles collide. The thermal energy of the particles that make up the thermometer increases, while at the sametime, the thermal energy of the particles in your skin decreases.

Thermal equilibrium As the particles in the glass gain more energy, theybegin to give some of their energy back to the particles in your body. Atsome point, the rate of transfer of energy between the glass and your bodybecomes equal, and your body and the thermometer are then at the sametemperature. At this point, your body and the thermometer are said to havereached thermal equilibrium, the state in which the rate of energy flowbetween two objects is equal and the objects are at the same temperature,as shown in Figure 12-3.

The operation of a thermometer depends on some property, such as vol-ume, which changes with temperature. Many household thermometerscontain colored alcohol that expands when heated and rises in a narrowtube. The hotter the thermometer, the more the alcohol expands and thehigher it rises in the tube. In liquid-crystal thermometers, such as the oneshown in Figure 12-4, a set of different kinds of liquid crystals is used. Eachcrystal’s molecules rearrange at a specific temperature, which causes thecolor of the crystal to change and indicates the temperature by color.Medical thermometers and the thermometers that monitor automobileengines use very small, temperature-sensitive electronic circuits to takerapid measurements.

■ Figure 12-3 Thermal energy is transferred from a hot object to a cold object. When thermalequilibrium is reached, the transferof energy between objects is equal.

Before Thermal Equilibrium

After Thermal Equilibrium

Hot object (A) Cold object (B)

KEA � KEB

KEA � KEB


■ Figure 12-4 Thermometers usea change in physical properties to measure temperature. A liquid-crystal thermometer changes color with a temperature change.

Tom Pantages

■ Using Figure 12-3

In order for the molecules in hotobject (A) and cold object (B) tocome to thermal equilibrium, thethermal energies of the moleculesmust be exchanged through molec-ular collisions. Ask students howthe two bodies reach equilibrium.Because thermal energy is trans-ferred from a hot body to a coldbody, there would be a gradual flowof heat from left to right as the colli-sions occur. The rate of this heatflow is affected by both the initialtemperatures of the two bodies andby their area of contact.

315

Thermal ExpansionEstimated Time 10 minutes

Materials two beakers, icewater, cold tap water, large alco-hol thermometer, goggles

Procedure Put the thermometercontaining visible, colored alcoholin a beaker of ice water. After thethermometer has adjusted to thelow temperature, remove it andput it in a beaker of hot tapwater. Ask students what causesthe alcohol to rise in the ther-mometer. The alcohol absorbsthermal energy from the hotwater, causing the liquid toexpand and rise up the fixed-volume capillary tube inside thethermometer. Then ask studentsto explain the liquid’s thermalexpansion on the molecular level.According to the kinetic molecu-lar theory, as the temperature ofthe liquid increases, its moleculeshave higher kinetic energies.Because the molecules movefaster, they collide with eachother more often and more vio-lently, which causes them tooccupy more space.

Calibrate a Thermometer Explain to students that a simple gas thermometer can be made with asmall straw or plastic tube, a piece of modeling clay, and some colored water. Have students putone end of the straw into the colored water and, while holding it there, press a small ball of clayover the other end of the straw. Then have them remove the straw from the water. As the tempera-ture changes, the trapped air will expand or contract in the tube, and the water will move. Ask stu-dents how they can calibrate and mark the tube so that it is a useful thermometer. They can markthe water level once the thermometer has reached thermal equilibrium in a place of known temperature.Then they should repeat the procedure in several other areas with known temperatures. Kinesthetic

312-339 PhyTWEC12-845814 7/12/04 2:45 AM Page 315

Human body Surface of the Sun Nuclear bomb

Flames Center of the Sun Supernova explosions

Interstellar space

Heliumliquefies

Lifeexists

Superconductivitybelow this

temperature

Temperature (K)

Nuclei existbelow this

temperature

Uncharged atomsexist below this

temperature

Lowest temperaturein laboratory

100 10310110�210�410�610�8 104 105 106 107 108 109 1010

■ Figure 12-6 The three most-common temperature scales areKelvin, Celsius, and Fahrenheit.

373.15 100.00 212.00

273.15 0.00 32.00

0.00 �273.15 �459.67

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Temperature Scales: Celsius and KelvinOver the years, scientists developed temperature scales so that they could

compare their measurements with those of other scientists. A scale basedon the properties of water was devised in 1741 by Swedish astronomer andphysicist Anders Celsius. On this scale, now called the Celsius scale, thefreezing point of pure water is defined to be 0°C. The boiling point of purewater at sea level is defined to be 100°C.

Temperature limits The wide range of temperatures present in the uni-verse is shown in Figure 12-5. Temperatures do not appear to have anupper limit. The interior of the Sun is at least 1.5�107°C. Temperatures do,however, have a lower limit. Generally, materials contract as they cool. Ifan ideal gas, such as the helium in a balloon is cooled, it contracts in such a way that it occupies a volume that is only the size of the heliumatoms at �273.15°C. At this temperature, all the thermal energy that canbe removed has been removed from the gas. It is impossible to reduce thetemperature any further. Therefore, there can be no temperature lower than�273.15°C, which is called absolute zero.

The Celsius scale is useful for day-to-day measurements of temperature.It is not conducive for working on science and engineering problems, how-ever, because it has negative temperatures. Negative temperatures suggest a molecule could have negative kinetic energy, which is not possiblebecause kinetic energy is always positive. The solution to this issue is to use a temperature scale based on absolute zero.

The zero point of the Kelvin scale is defined to be absolute zero. On theKelvin scale, the freezing point of water (0°C) is about 273 K and the boilingpoint of water is about 373 K. Each interval on this scale, called a kelvin, isequal to 1°C. Thus, TC � 273 � TK. Figure 12-6 shows representative tem-peratures on the three most-common scales: Fahrenheit, Celsius, and Kelvin.

Very cold temperatures are reached by liquefying gases. Helium liquefiesat 4.2 K, or �269°C. Even colder temperatures can be reached by makinguse of special properties of solids, helium isotopes, and atoms and lasers.

■ Figure 12-5 There is anextremely wide range oftemperatures throughout theuniverse. Note that the scale has been expanded in areas of particular interest.

(cl)Getty Images, (r)FPG/Getty Images, (others)CORBIS

IdentifyingMisconceptionsTemperature Scales Studentsmay often be uncertain aboutwhich temperature scale to use incalculations. The Kelvin scale isthe only thermodynamically cor-rect temperature scale, and it canbe used in every calculation.Because the temperature intervalfor the Celsius scale is the same asthe temperature interval for theKelvin scale, it is permissible touse the Celsius scale if only differ-ences in temperatures are impor-tant. The Fahrenheit scale is neverused in problems. Fahrenheit tem-peratures must be converted toCelsius temperatures or kelvinsbefore doing the calculations.

Critical ThinkingColors of Clothing andAutomobiles Ask students if thefashion trend from lighter-colored clothes in the summer todarker ones in the winter mighthave any scientific basis. Similarly,ask them if you should own ablack car if you live in a warm,sunny region. The darker clothesabsorb more radiant energy, thustransferring more thermal energy tothe wearer during the colderweather. A black car absorbs radiantenergy and requires more air condi-tioning to be comfortable in thesummer.

316

Other Common Thermometers Glass thermometers containing liquids are fragile and are use-ful only over a limited range of temperatures. In many furnaces, temperatures are measured by athermocouple. A thermocouple is a very simple and rugged device made by twisting together theends of two wires made of different metals, such as a copper wire and an iron wire. This twistedconnection is called a thermocouple junction. If the free ends of the wires are connected to avoltmeter, one can measure a small voltage that changes with the temperature of the copper-iron junction.

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CHAPTER

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Transparency 12-1

Page 55, FAST FILE Chapters 11–15 Resources

312-339 PhyTWEC12-845814 7/12/04 2:46 AM Page 316

1. Convert the following Kelvin temperatures to Celsius temperatures.

a. 115 K c. 125 K e. 425 K

b. 172 K d. 402 K f. 212 K

2. Find the Celsius and Kelvin temperatures for the following.

a. room temperature c. a hot summer day in North Carolina

b. a typical refrigerator d. a winter night in Minnesota

� Steam Heating In a steamheating system of a building,water is turned into steam in aboiler located in a maintenancearea or the basement. The steamthen flows through insulated pipesto each room in the building. In the radiator, the steam iscondensed as liquid water andthen flows back through pipes to the boiler to be revaporized.The hot steam physically carriesthe heat from the boiler, and thatenergy is released when thesteam condenses in the radiator.Some disadvantages of steamheating are that it requiresexpensive boilers and pipes mustcontain steam under pressure. �


Heat and the Flow of Thermal EnergyWhen two objects come in contact with each other, they transfer energy.

This energy that is transferred between the objects is called heat. Heat isdescribed as the energy that always flows from the hotter object to thecooler object. Left to itself heat never flows from a colder object to a hotter object. The symbol Q is used to represent an amount of heat, which,like other forms of energy, is measured in joules. If Q has a negative value,heat has left the object; if Q has a positive value, heat has been absorbedby the object.

Conduction If you place one end of a metal rod in a flame, the hot gasparticles in the flame conduct heat to the rod. The other end of the rod alsobecomes warm within a short period of time. Heat is conducted becausethe particles in the rod are in direct contact with each other.

Convection Thermal energy transfer can occur even if the particles in anobject are not in direct contact with each other. Have you ever looked intoa pot of water just about to boil? The water at the bottom of the pot isheated by conduction and rises to the top, while the colder water at the topsinks to the bottom. Heat flows between the rising hot water and thedescending cold water. This motion of fluid in a liquid or gas caused by temperature differences is called convection. Atmospheric turbulence iscaused by convection of gases in the atmosphere. Thunderstorms are excel-lent examples of large-scale atmospheric convection. Ocean currents thatcause changes in weather patterns also result from convection.

Radiation The third method of thermal transfer, unlike the first two, doesnot depend on the presence of matter. The Sun warms Earth from over 150 million km away via radiation, which is the transfer of energy by electromagnetic waves. These waves carry the energy from the hot Sunthrough the vacuum of space to the much cooler Earth.

Specific HeatSome objects are easier to heat than others. On a bright summer day, the

Sun warms the sand on a beach and the ocean water. However, the sandon the beach gets quite hot, while the ocean water stays relatively cool.When heat flows into an object, its thermal energy and temperatureincrease. The amount of the increase in temperature depends on the sizeof the object and on the material from which the object is made.

Meteorology ConnectionMeteorology Connection

317

1. a. �158°C

b. �101°C

c. �148°C

d. 129°C

e. 152°C

f. �61°C

2. a. Room temperature isabout 72°F, 22°C, or 295 K.

b. A refrigerator is kept atabout 4°C, or 277 K.

c. A hot summer day isabout 95°F, 35°C, or 308 K.

d. A typical winter night inMinnesota is about 14°F,�10°C, or 263 K.

Balloons and the Conduction of Heat EnergyMaterials two rubber balloons, a candle, matches, water, goggles, lab glovesProcedure Fill one balloon with water and the other with air. CAUTION: Some students maybe allergic to latex. Hold the air-filled balloon in the flame. The balloon will pop. Now hold thewater-filled balloon in the flame. This balloon will not pop for a long time. Ask the students why.Water has more mass and a higher heat capacity than air. The water absorbs most of the thermalenergy, which greatly reduces the rate at which the rubber heats to its melting point.

— Jeff Radloff • Milford High School • Milford, Ohio

� Students may have directexperience with one of the disad-vantages of steam heat. In olderbuildings especially, the pipes canemit sudden, loud noises, whichcan be difficult to live with. Givenwhat students now know aboutthe role of condensation in steamheat, have them discuss and inferwhat causes this problem, andthen what the solution might be.Interested students may wish to model the problem with adrawing. �

312-339 PhyTWEC12-845814 7/12/04 2:47 AM Page 317


Heat Transfer A 5.10-kg cast-iron skillet is heated on the stove from

295 K to 450 K. How much heat had to be transferred to the iron?

Analyze and Sketch the Problem• Sketch the flow of heat into the skillet from the stove top.

Known: Unknown:

m = 5.10 kg C = 450 J/kg�K Q = ?Ti = 295 K Tf = 450 K

Solve for the UnknownQ � mC(Tf � Ti)

� (5.10 kg)(450 J/kg�K)(450 K � 295 K) Substitute m � 5.10 kg, C � 450 J/kg�K, Tf � 450 K, Ti � 295 K

� 3.6�105 J

Evaluate the Answer• Are the units correct? Heat is measured in J. • Does the sign make sense? Temperature increased, so Q is positive.

3

2

1

Ti � 295 K

m � 5.10 kg

Tf � 450 K

Q

Math Handbook

Order of Operations page 843

The specific heat of a materialis the amount of energy that mustbe added to the material to raisethe temperature of a unit mass byone temperature unit. In SI units,specific heat, represented by C, ismeasured in J/kg�K. Table 12-1provides values of specific heat for some common substances. Forexample, 897 J must be added to 1 kg of aluminum to raise its temperature by 1 K. The specificheat of aluminum is therefore 897 J/kg�K.

The heat gained or lost by an object as its temperature changes dependson the mass, the change in temperature, and the specific heat of the sub-stance. By using the following equation, you can calculate the amount ofheat, Q, that must be transferred to change the temperature of an object.

Liquid water has a high specific heat compared to the other substance inTable 12-1. When the temperature of 10.0 kg of water is increased by 5.0 K, the heat absorbed is Q � (10.0 kg)(4180 J/kg�K)(5.0 K) = 2.1�105 J.Remember that the temperature interval for kelvins is the same as that forCelsius degrees. For this reason, you can calculate �T in kelvins or indegrees Celsius.

Heat Transfer Q � mC�T � mC(Tf � Ti)

Heat transfer is equal to the mass of an object times the specific heat of theobject times the difference between the final and initial temperatures.

Table 12-1Specific Heat of Common Substances

MaterialSpecific Heat

(J/kg�K) MaterialSpecific Heat

(J/kg�K)

Aluminum

Brass

Carbon

CopperGlassIceIron

897

376

710

3858402060450

Lead

Methanol

Silver

SteamWaterZinc

130

2450

235

20204180388

ReinforcementHeat, Thermal Energy, andTemperature Have students, ingroups of two, draw a conceptmap that relates the following keyconcepts or quantities: thermalenergy, temperature, molecularmotion, heat, mass, and specificheat. Students should use shortexplanatory phrases to explain thelinks on the concept map.

Visual-Spatial

318

Question Some-times a short cir-cuit in an electricalwiring system canproduce enough heat to melt awire. How much heat must betransferred to a 20.0-g piece ofcopper wire in order to raise itfrom room temperature (25.0°C)to its melting temperature(1082.0°C)?

Answer

Q � mC(Tf � Ti)� (0.0200 kg)(385 J/kg�°C)(1082.0°C � 25.0°C)� 8140 J

Specific Heat The specific heat values listed in Table 12-1 are valid for temperatures that arenear room temperature. For most practical purposes, specific heat can be considered to be con-stant over a reasonably wide range of temperatures. It is a property of all materials that theirspecific heat decreases at very low temperatures. The specific heat of all materials must go tozero as the temperature is decreased to absolute zero.

312-339 PhyTWEC12-845814 7/21/04 3:15 PM Page 318

3. When you turn on the hot water to wash dishes, the water pipes have to heat up. How much heat is absorbed by a copper water pipe with a mass of 2.3 kg when its temperature is raised from 20.0°C to 80.0°C?

4. The cooling system of a car engine contains 20.0 L of water (1 L of water has a mass of 1 kg).

a. What is the change in the temperature of the water if the engine operates until 836.0 kJ of heat is added?

b. Suppose that it is winter, and the car’s cooling system is filled with methanol. The density of methanol is 0.80 g/cm3. What would be the increase in temperature of the methanol if it absorbed 836.0 kJ of heat?

c. Which is the better coolant, water or methanol? Explain.

5. Electric power companies sell electricity by the kWh, where 1 kWh � 3.6�106 J. Suppose that it costs $0.15 per kWh to run an electric water heater in your neighborhood. How much does it cost to heat 75 kg of water from 15°C to 43°C to fill a bathtub?


Calorimetry: Measuring Specific Heat

A simple calorimeter, such as the one shown inFigure 12-7, is a device used to measure changes inthermal energy. A calorimeter is carefully insulatedso that heat transfer to the external world is kept to a minimum. A measured mass of a substancethat has been heated to a high temperature isplaced in the calorimeter. The calorimeter also contains a known mass of cold water at a measuredtemperature. The heat released by the substance is transferred to the cooler water. The change inthermal energy of the substance is calculated usingthe resulting increase in the water temperature.More sophisticated types of calorimeters are used tomeasure chemical reactions and the energy contentof various foods.

The operation of a calorimeter depends on theconservation of energy in an isolated, closed system.Energy can neither enter nor leave this system. As aresult, if the energy of one part of the systemincreases, the energy of another part of the system must decrease by thesame amount. Consider a system composed of two blocks of metal, blockA and block B, shown in Figure 12-8a on the next page. The total energyof the system is constant, as represented by the following equation.

Conservation of Energy EA � EB � constant

In an isolated, closed system, the thermal energy of object A plus the thermalenergy of object B is constant.

ThermometerStirrer

Lid

Innercontainer

Insulated outercontainer

Test substance

Water

■ Figure 12-7 A calorimeterprovides an isolated, closed systemin which to measure energytransfer.

319

3. 5.3�104 J

4. a. 10.0 K

b. 21 K

c. For temperatures above0°C, water is the bettercoolant because it canabsorb heat withoutchanging its temperatureas much as methanoldoes.

5. $0.36

CalorimetryEstimated Time 5 minutes

Materials thermometer, 250-mLbeaker, water, calcium chloride(sold at hardware stores for dry-ing humid basements), measuringspoon, goggles

Procedure Pour 200 mL of waterinto the beaker and measure itstemperature. Add one teaspoonof calcium chloride to the waterand mix briefly. Measure the solu-tion temperature until it stabilizes.Add another teaspoon of calciumchloride and repeat. Measure thetemperature again. Repeat onceor twice more. Graph the meas-ured temperatures versus thenumber of teaspoons added.From the temperature differencesand the specific heat of the water,the students can calculate theenergy released when the cal-cium chloride dissolves in thewater. This technique is one wayto measure the energy releasedor absorbed by a reaction.

Chemical Engineering Understanding the transfer of heat in chemical production processes isan important part of chemical engineering. In the production of industrial chemicals, heat mustbe provided to cause a chemical reaction to occur, or the heat produced by a reaction must beremoved. Adding or removing heat incurs enormous costs in electrical power or in refrigerationequipment. Chemicals are often produced not in batches but in continuous processes in whichmaterials flow through a reaction container, so a chemical engineer must be able to calculate theflow of chemicals, their rate of reaction, and the rate of heat transferred.

312-339 PhyTWEC12-845814 7/12/04 2:49 AM Page 319


Insulation

A

AB

B

EAB � EA � EB

EBEA

■ Figure 12-8 A system iscomposed of two model blocks at different temperatures thatinitially are separated (a). Whenthe blocks are brought together,heat flows from the hotter block tothe colder block (b). Total energyremains constant.

Suppose that the two blocks initially are separated but can be placed incontact with each other. If the thermal energy of block A changes by anamount �EA, then the change in thermal energy of block B, �EB, must berelated by the equation, �EA � �EB � 0. Thus, �EA � ��EB. The change in energy of one block is positive, while the change in energy of the otherblock is negative. For the block whose thermal energy change is positive,the temperature of the block rises. For the block whose thermal energychange is negative, the temperature falls.

Assume that the initial temperatures of the two blocks are different.When the blocks are brought together, heat flows from the hotter block to the colder block, as shown in Figure 12-8b. The heat flow continuesuntil the blocks are in thermal equilibrium, which is when the blocks havethe same temperature.

In an isolated, closed system, the change in thermal energy is equal tothe heat transferred because no work is done. Therefore, the change inenergy for each block can be expressed by the following equation:

�E � Q � mC�T

The increase in thermal energy of block A is equal to the decrease inthermal energy of block B. Thus, the following relationship is true:

mACA�TA � mBCB�TB � 0

The change in temperature is the difference between the final and initialtemperatures; that is, �T � Tf � Ti. If the temperature of a block increases,Tf � Ti, and �T is positive. If the temperature of the block decreases, Tf Ti, and �T is negative. The final temperatures of the two blocks areequal. The following is the equation for the transfer of energy:

mACA(Tf � TA) � mBCB(Tf � TB) � 0

To solve for Tf, expand the equation.

mACATf � mACATA � mBCBTf � mBCBTB � 0

Tf(mACA � mBCB) � mACATA � mBCBTB

Tf �mACATA � mBCBTB��

mACA � mBCB

a

b

DiscussionQuestion Water plays a uniquerole in living things. Our bodiesare made mostly of water. Whatwould be the possible effects onhumans if the specific heat ofwater and the heat of vaporizationdid not have unusually large val-ues and instead were quite low?

Answer Our body temperaturewould be more easily influenced byexternal conditions. The large spe-cific heat of water means that a lotof internal energy must be added orremoved in order to change the tem-perature of the human body. Forexample, when a person drinks acold soda, his or her body tempera-ture does not decrease. Water’s highheat of vaporization also helps coolour bodies when we sweat. With alower heat of vaporization, we mighthave to sweat a great deal more toremove excess heat.

Logical-Mathematical

Using an AnalogyCalorimeters It may help stu-dents to understand how acalorimeter works if they compareits chamber to a vacuum flask thatis used to store hot or cold bever-ages. The vacuum flask does notallow heat to readily enter orleave the system. Similarly, thewalls of a calorimeter must bewell insulated. If heat can enter orleave the system, then the changein water temperature will notaccurately reflect the heatabsorbed or given off by the sam-ple in the chamber.

320

Keeping Track of the Exchange of Heat Students often have problems in calculations of thefinal temperatures in calorimetry because they misuse minus signs or fail to account for all ofthe heat exchanged. Remind them that exchanging heat is like exchanging money: the moneygoes from one person to another and is not lost. Also, they should expect that the final tempera-ture in a calorimeter will be somewhere between the initial temperatures of the coldest andhottest objects. Finally, when calculating the �T in a formula, the correct sign can always beobtained by subtracting the initial temperature from the final temperature.

312-339 PhyTWEC12-845814 7/12/04 2:49 AM Page 320

Transferring Heat in a Calorimeter A calorimeter

contains 0.50 kg of water at 15°C. A 0.040-kg block

of zinc at 115°C is placed in the water. What is the

final temperature of the system?

Analyze and Sketch the Problem• Let zinc be sample A and water be sample B. • Sketch the transfer of heat from the hotter

zinc to the cooler water.

Known: Unknown:

mA � 0.040 kg Tf � ?CA � 388 J/kg�°CTA � 115°CmB � 0.50 kgCB � 4180 J/kg�°CTB � 15.0°C

Solve for the UnknownDetermine the final temperature using the following equation.

Tf �

�

� 16°C

Evaluate the Answer• Are the units correct? Temperature is measured in Celsius.• Is the magnitude realistic? The answer is between the initial temperatures

of the two samples, as is expected when using a calorimeter.

3

Substitute mA � 0.040 kg, CA � 388 J/kg�°C, TA � 115°C, mB � 0.50 kg, CB � 4180 J/kg�°C,TB � 15°C

(0.040 kg)(388 J/kg�°C)(115°C) � (0.50 kg)(4180 J/kg�°C)(15.0°C)��

(0.040 kg)(388 J/kg�°C) � (0.50 kg)(4180 J/kg�°C)

mACATA � mBCBTB��mACA � mBCB

2

1

mB � 0.50 kg TB � 15°C

mA � 0.040 kg TA � 115°C Tf � ?

Before block ofzinc is placed

After block of zinc is placed

Zinc

Water


6. A 2.00�102-g sample of water at 80.0°C is mixed with 2.00�102 g of water at 10.0°C. Assume that there is no heat loss to thesurroundings. What is the final temperature of the mixture?

7. A 4.00�102-g sample of methanol at 16.0°C is mixed with 4.00�102 g of water at 85.0°C. Assume that there is no heat loss tothe surroundings. What is the final temperature of the mixture?

8. Three lead fishing weights, each with a mass of 1.00�102 g and at atemperature of 100.0°C, are placed in 1.00�102 g of water at 35.0°C.The final temperature of the mixture is 45.0°C. What is the specificheat of the lead in the weights?

9. A 1.00�102-g aluminum block at 100.0°C is placed in 1.00�102 g ofwater at 10.0°C. The final temperature of the mixture is 25.0°C. What is the specific heat of the aluminum?

Math Handbook

Operations withSignificant Digitspages 835—836

321

6. 45.0°C

7. 59.5°C

8. 2.53�102 J/kg�°C

9. 8.36�102 J/kg�°C

QuestionA 0.025-kg block ofcopper at a tem-perature of 82°C isadded to a calorimeter contain-ing 0.025 kg of water at a tem-perature of 22°C. What is thetemperature of the copper blockand the water when they reachthermal equilibrium?

AnswerTf � (mACATA � mBCBTB)/(mACA � mBCB)Tf � ((0.025 kg)(4180 J/kg�°C)(22°C) � (0.025 kg)(385 J/kg�°C)(82°C))/((0.025 kg)(4180 J/kg�°C) �

(0.025 kg)(385 J/kg�°C))Tf � 27°C

Specific Heat and Atomic Mass In 1819, Alexis-Thérèse Petit and Pierre-Louis Dulong demon-strated that the product of specific heat and atomic mass is very nearly constant for a broadrange of solid elements. Thus, the specific heats of these elements are inversely proportional totheir atomic masses. Therefore, with the specific heat of a new element determined, one couldquickly approximate its atomic mass. Jöns Jacob Berzelius found this discovery useful in improv-ing his table of atomic mass, a precursor to the periodic table of the elements.

312-339 PhyTWEC12-845814 7/12/04 2:50 AM Page 321


10. Temperature Make the following conversions.

a. 5°C to kelvins

b. 34 K to degrees Celsius

c. 212°C to kelvins

d. 316 K to degrees Celsius

11. Conversions Convert the following Celsius tem-peratures to Kelvin temperatures.

a. 28°Cb. 154°Cc. 568°C

d. �55°C

e. �184°C

12. Thermal Energy Could the thermal energy of abowl of hot water equal that of a bowl of coldwater? Explain your answer.

13. Heat Flow On a dinner plate, a baked potatoalways stays hot longer than any other food. Why?

14. Heat The hard tile floor of a bathroom always feelscold to bare feet even though the rest of the room iswarm. Is the floor colder than the rest of the room?

15. Specific Heat If you take a plastic spoon out of acup of hot cocoa and put it in your mouth, you arenot likely to burn your tongue. However, you couldvery easily burn your tongue if you put the hotcocoa in your mouth. Why?

16. Heat Chefs often use cooking pans made of thickaluminum. Why is thick aluminum better than thinaluminum for cooking?

17. Heat and Food It takes much longer to bake awhole potato than to cook french fries. Why?

18. Critical Thinking As water heats in a pot on astove, the water might produce some mist above itssurface right before the water begins to roll. Whatis happening, and where is the coolest part of thewater in the pot?

12.1 Section Review

physicspp.com/self_check_quiz

Biology ConnectionBiology Connection

■ Figure 12-9 A lizard regulatesits body temperature by hidingunder a rock when the atmosphereis hot (a) and sunbathing whenthe atmosphere gets cold (b).

Animals can be divided into two groups based on their body tempera-tures. Most are cold-blooded animals whose body temperatures dependon the environment. The others are warm-blooded animals whose bodytemperatures are controlled internally. That is, a warm-blooded animal’sbody temperature remains stable regardless of the temperature of the envi-ronment. In contrast, when the temperature of the environment is high,the body temperature of a cold-blooded animal also becomes high. Acold-blooded animal, such as the lizard shown in Figure 12-9, regulatesthis heat flow by hiding under a rock or crevice, thereby reducing its bodytemperature. Humans are warm-blooded and have a body temperature ofabout 37°C. To regulate its body temperature, a warm-blooded animal increases or decreases the level of its metabolic processes. Thus, awarm-blooded animal may hibernate in winter and reduce its body tem-perature to approach the freezing point of water.

a b

(l)John Cancalosi/Peter Arnold, Inc., (r)Jenny Hager/The Image Works

3 ASSESS

Check for UnderstandingFreezing Water on Bridges Askstudents why signs near bridges inthe northern parts of the UnitedStates often say, “CAUTION:Bridge Freezes Before RoadSurface.” The underside of thebridge is exposed to cold air, whichcan cool the bridge very rapidly andcause any water on its upper surfaceto freeze. The ground under a roadinsulates the road’s surface and pro-vides additional mass that must becooled to 0°C before water willfreeze on its surface.

ExtensionClothing for the OutdoorsSuppliers have developed sophis-ticated clothing materials for hik-ers, campers, and mountaineers touse in cold weather and at highaltitudes. Ask the students toresearch the useful properties ofitems such as fiberfill insulation,goose down, polymers for under-wear and shirts, fleece and syn-thetic fleece, and reflectiveblankets.

322

10. a. 278 K c. 485 Kb. �239°C d. 43°C

11. a. 301 K d. 218 Kb. 427 K e. 89 Kc. 841 K

12. If the bowls are identical, the bowl ofhot water has more total thermalenergy.

13. A potato has a large specific heatand conducts heat poorly, so it losesits heat energy slowly.

14. The tile conducts heat more effi-ciently than most materials.

15. The plastic spoon has a lower spe-cific heat, so it does not transmitmuch heat to your tongue as it cools.

16. Thick aluminum conducts heat betterand does not have any “hot spots.”

17. Potatoes do not conduct heat well.Increasing surface area by cutting upa potato into small parts increasesheat flow into the potato. Heat flowfrom hot oil to the potato is also moreefficient than from hot air.

18. The heat flows from the burner (thehottest part) to the top surface of thewater (coldest).

12.1 Section Review

312-339 PhyTWEC12-845814 7/12/04 2:51 AM Page 322

http://www.physicspp.com/self_check_quiz

� Objectives• Define heats of fusion and

vaporization.

• State the first and secondlaws of thermodynamics.

• Distinguish between heatand work.

• Define entropy.

� Vocabulary

heat of fusionheat of vaporizationfirst law of thermodynamicsheat engineentropysecond law of

thermodynamics

12.2 Changes of State and the Laws of Thermodynamics

Eighteenth-century steam-engine builders used heat to turn liquidwater into steam. The steam pushed a piston to turn the engine, and

then the steam was cooled and condensed into a liquid again. Adding heatto the liquid water changed not only its temperature, but also its structure.You will learn that changing state means changing form as well as chang-ing the way in which atoms store thermal energy.

Changes of StateThe three most common states of matter are solids, liquids, and gases.

As the temperature of a solid is raised, it usually changes to a liquid. Ateven higher temperatures, it becomes a gas. How can these changes beexplained? Consider a material in a solid state. When the thermal energyof the solid is increased, the motion of the particles also increases, as doesthe temperature.

Figure 12-10 diagrams the changes of state as thermal energy is addedto 1.0 g of water starting at 243 K (ice) and continuing until it reaches 473 K (steam). Between points A and B, the ice is warmed to 273 K. Atsome point, the added thermal energy causes the particles to move rapidlyenough that their motion overcomes the forces holding the particlestogether in a fixed location. The particles are still touching each other, butthey have more freedom of movement. Eventually, the particles becomefree enough to slide past each other.

Melting point At this point, the substance has changed from a solid to aliquid. The temperature at which this change occurs is the melting point ofthe substance. When a substance is melting, all of the added thermalenergy goes to overcome the forces holding the particles together in thesolid state. None of the added thermal energy increases the kinetic energy ofthe particles. This can be observed between points B and C in Figure 12-10,where the added thermal energy melts the ice at a constant 273 K. Becausethe kinetic energy of the particles does not increase, the temperature doesnot increase between points B and C.

Boiling point Once a solid is completely melted,there are no more forces holding the particles inthe solid state. Adding more thermal energy again increases the motion of the particles, andthe temperature of the liquid rises. In the diagram, this process occurs between points Cand D. As the temperature increases further, someparticles in the liquid acquire enough energy to break free from the other particles. At a specifictemperature, known as the boiling point, furtheraddition of energy causes the substance toundergo another change of state. All the addedthermal energy converts the substance from theliquid state to the gaseous state.

273

243

323

373

A

B C

DE

Heat (J)

813.7395.761.7 3073

Steam

Water

Ice � Water

Water�

Steam

Tem

per

atu

re (

K)

Section 12.2 Changes of State and the Laws of Thermodynamics 323

■ Figure 12-10 A plot oftemperature versus heat addedwhen 1.0 g of ice is converted tosteam. Note that the scale isbroken between points D and E.

323

Section 12.2

1 FOCUS

Bellringer ActivityWork and Internal Energy Haveeach student take a clean steelpaper clip and reshape it into a“U.” Tell students to hold thebend in the middle of the clip totheir upper lip. Students shouldnotice that the clip feels slightlycool. Then ask them to bend theirclips vigorously several times andhave them again touch the clip totheir upper lip. They shouldnotice that the clip feels warmer,owing to the work done on themetal. Kinesthetic

Tie to Prior KnowledgeFriction Students have seen thatenergy is lost to friction. This fric-tion increases the temperature ofobjects. Have the students rubtheir hands, creating friction, andnotice that their hands getwarmer. Someone out campingmight rub his or her hands towarm them or hold them near acampfire. The camper is perform-ing work by rubbing his or herhands. The fire warms the handsprimarily though radiant heattransfer. The first law of thermo-dynamics relates work, heat, inter-nal energy, and temperature.

Kinesthetic

Teaching Transparency 12-3Teaching Transparency 12-4Connecting Math to Physics

TechnologyTeacherWorks™ CD-ROMInteractive Chalkboard CD-ROMExamView ® Pro Testmaker CD-ROMphysicspp.comphysicspp.com/vocabulary_puzzlemaker

12.2 Resource MANAGERFAST FILE Chapters 11–15 Resources

Transparency 12–2 Master, p. 55Transparency 12–3 Master, p. 57Transparency 12–4 Master, p. 59Study Guide, pp. 41–46Reinforcement, p. 49Section 12–2 Quiz, p. 48Mini Lab Worksheet, p. 35Physics Lab Worksheet, pp. 37–40

Teaching Transparency 12-2

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Physics: Principles and Problems Teaching Transparencies

373

323

273

243

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3073

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Wat

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CHAPTER

12 Transparency 12-2

Page 57, FAST FILE Chapters 11–15 Resources

312-339 PhyTWEC12-845814 7/12/04 3:24 AM Page 323



As in melting, the temperaturedoes not rise while a liquid boils. InFigure 12-10, this transition is repre-sented between points D and E. Afterthe material is entirely converted togas, any added thermal energy againincreases the motion of the particles,and the temperature rises. Abovepoint E, steam is heated to tempera-tures greater than 373 K.

Heat of fusion The amount of energyneeded to melt 1 kg of a substance iscalled the heat of fusion of that sub-stance. For example, the heat offusion of ice is 3.34�105 J/kg. If 1 kg

of ice at its melting point, 273 K, absorbs 3.34�105 J, the ice becomes 1 kgof water at the same temperature, 273 K. The added energy causes a changein state but not in temperature. The horizontal distance in Figure 12-10from point B to point C represents the heat of fusion.

Heat of vaporization At normal atmospheric pressure, water boils at 373K. The thermal energy needed to vaporize 1 kg of a liquid is called the heatof vaporization. For water, the heat of vaporization is 2.26�106 J/kg. Thedistance from point D to point E in Figure 12-10 represents the heat ofvaporization. Every material has a characteristic heat of vaporization.

Between points A and B, there is a definite slope to the line as the tem-perature is raised. This slope represents the specific heat of the ice. Theslope between points C and D represents the specific heat of water, and theslope above point E represents the specific heat of steam. Note that theslope for water is less than those of both ice and steam. This is becausewater has a greater specific heat than does ice or steam. The heat, Q,required to melt a solid of mass m is given by the following equation.

Similarly, the heat, Q, required to vaporize a mass, m, of liquid is givenby the following equation.

When a liquid freezes, an amount of heat, Q � �mHf, must be removedfrom the liquid to turn it into a solid. The negative sign indicates that theheat is transferred from the sample to the external world. In the same way,when a vapor condenses to a liquid, an amount of heat, Q � �mHv, mustbe removed from the vapor. The values of some heats of fusion, Hf, andheats of vaporization, Hv, are shown in Table 12-2.

Heat Required to Vaporize a Liquid Q � mHv

The heat required to vaporize a liquid is equal to the mass of the liquid timesthe heat of vaporization of the liquid.

Heat Required to Melt a Solid Q � mHf

The heat required to melt a solid is equal to the mass of the solid times theheat of fusion of the solid.

Table 12-2Heats of Fusion and Vaporization of Common Substances

MaterialHeat of Fusion

Hf (J/kg)Heat of Vaporization

Hv (J/kg)

Copper

Mercury

Gold

Methanol

Iron

Silver

Lead

Water (ice)

2.05�105

1.15�104

6.30�104

1.09�105

2.66�105

1.04�105

2.04�104

3.34�105

5.07�106

2.72�105

1.64�106

8.78�105

6.29�106

2.36�106

8.64�105

2.26�106

Melting1. Label two foam cups A and B. 2. Measure and pour 75 mL ofroom-temperature water into eachcup. Wipe up any spilled liquid.3. Add an ice cube to cup A, andadd ice water to cup B until thewater levels are equal. 4. Measure the temperature of the water in each cup at 1-minintervals until the ice has melted.5. Record the temperatures in a data table and plot a graph.

Analyze and Conclude 6. Do the samples reach the same final temperature? Why?


324

2 TEACH

Using ModelsMelting and Vaporization Oneway to demonstrate the energyrequired to change a solid to aliquid and then to a gas would bethe melting of an ice sculpture.Begin with small ice sculptures(colored water frozen in a candymold). Place two in dishes: one atroom temperature and one undera heat lamp. Put a third one in azipper storage bag and ask stu-dents to hold it in their handsand roll it around. The moreenergy applied, the quicker the icewill melt. Under the heat lamp, itwill eventually evaporate.

Melting

See page 37 of FAST FILEChapters 11–15 Resources for theaccompanying Mini Lab Worksheet.

CAUTION: If any water is spilled,wipe up quickly to avoid a slip-pery floor hazard.

Purpose to observe heat transferduring a change of state

Materials two foam cups, water,ice water, ice cube, two thermometers

Expected Results The cup withthe ice will be cooled to a lowertemperature than the cup with theice water.

Analyze and Conclude6. Many students will not believethe results. Even though the icecube and the ice water are both atapproximately 0°C, the ice will coolthe water better than the ice water.The ice cube takes energy tochange from a solid to a liquid.

Boiling Water in a VacuumMaterials warm water, flask, bell jar, vacuum pump with a desiccatorProcedure Fill the flask one-third full of warm water. Place the flask in a bell jar connectedto a vacuum pump. Evacuate the air. Students will see the water boil. Ask students to predictthe temperature of the water. Many will say that it is hot. Allow students to touch the water.The water is cooler than before. The boiling has removed some water and, with it, some heat.

— Perry Mick • Ellis High School • Ellis, KS

312-339 PhyTWEC12-845814 7/21/04 12:59 AM Page 324


Heat Suppose that you are camping in the mountains. You need to melt 1.50 kg of snow

at 0.0°C and heat it to 70.0°C to make hot cocoa. How much heat will be needed?

Analyze and Sketch the Problem• Sketch the relationship between heat and water in its

solid and liquid states. • Sketch the transfer of heat as the temperature of the

water increases.

Known: Unknown:

m � 1.50 kg Hf � 3.34�105 J/kg Qmelt ice � ?Ti � 0.0°C Tf � 70.0°C Qheat liquid � ?C � 4180 J/kg�°C Qtotal � ?

Solve for the UnknownCalculate the heat needed to melt ice.

Qmelt ice � mHf� (1.50 kg)(3.34�105 J/kg) Substitute m � 1.50 kg, Hf � 3.34�105 J/kg

� 5.01�105 J � 5.01�102 kJ

Calculate the temperature change.�T � Tf � Ti

� 70.0°C � 0.0°C Substitute Tf � 70.0°C, Ti � 0.0°C

� 70.0°C

Calculate the heat needed to raise the water temperature.Qheat liquid � mC�T

� (1.50 kg)(4180 J/kg�°C)(70.0°C) Substitute m � 1.50 kg, C = 4180 J/kg�°C, �T � 70.0°C� 4.39�105 J� 4.39�102 kJ

Calculate the total amount of heat needed.Qtotal � Qmelt ice + Qheat liquid

� 5.01�102 kJ + 4.39�102 kJ Substitute Qmelt ice � 5.01�102 kJ, Qheat liquid � 4.39�102 kJ� 9.40�102 kJ

Evaluate the Answer• Are the units correct? Energy units are in joules. • Does the sign make sense? Q is positive when heat is absorbed.• Is the magnitude realistic? The amount of heat needed to melt the ice is greater

than the amount of heat needed to increase the water temperature by 70.0°C. It takes more energy to overcome the forces holding the particles in the solid state than to raise the temperature of water.

3

2

1

Hf

Ti � 0.0°C

1.5 kgSnow

Tf � 70.0°C

Q

19. How much heat is absorbed by 1.00�102 g of ice at �20.0°C to become water at 0.0°C?

20. A 2.00�102-g sample of water at 60.0°C is heated to steam at 140.0°C. How much heatis absorbed?

21. How much heat is needed to change 3.00�102 g of ice at �30.0°C to steam at 130.0°C?

Math Handbook

Operations withScientific Notationpages 842—843

325

19. 3.75�104 J

20. 502 kJ

21. 9.40�102 kJ

Question 1.0 kg ofwater is heatedfrom room tem-perature (25.0°C) toboiling and is then reduced tohalf of its initial volume. Howmany joules of heat must thestove provide to do this?

Answer Heat is needed to raisethe temperature of 1.0 kg ofwater from 25°C to 100°C and to vaporize 0.5 kg of water.Q � mC�T � (�

12�)mHV � (1.0 kg)

(4180 J/kg�°C)(100.0°C � 25.0°C) �

(�12�)(1.0 kg)(2.26�106 J/kg)

Q � 1.4�106 J

Melting Temperatures in Solutions The addition of a substance, called a solution, to water toform a solution changes the water’s melting and boiling temperatures. For example, salt is sprin-kled on icy sidewalks to melt the ice. Antifreeze added to an automobile cooling system increasesthe boiling temperature of the water. Ask students to answer the following questions and reporttheir findings to the class. How do the melting and boiling temperatures change with the numberof particles dissolved in water? Do all solutes have the same effects on melting and boiling? Howcan these changes in temperature be explained in terms of what students have learned aboutmelting and boiling? Logical-Mathematical

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Cold reservoir at TL

Hot reservoir at TH

Heatengine

QH

QH � W � QLQL

W

The First Law of ThermodynamicsBefore thermal energy was linked to the motion of atoms, the study of

heat and temperature was considered to be a separate science. The first lawdeveloped for this science was a statement about what thermal energy isand where it can go. As you know, you can heat a nail by holding it over aflame or by pounding it with a hammer. That is, you can increase the nail’sthermal energy by adding heat or by doing work on it. We do not normallythink that the nail does work on the hammer. However, the work done bythe nail on the hammer is equal to the negative of the work done by thehammer on the nail. The first law of thermodynamics states that thechange in thermal energy, �U, of an object is equal to the heat, Q, that isadded to the object minus the work, W, done by the object. Note that �U,Q, and W are all measured in joules, the unit of energy.

Thermodynamics also involves the study of the changes in thermalproperties of matter. The first law of thermodynamics is merely a restatementof the law of conservation of energy, which states that energy is neither created nor destroyed, but can be changed into other forms.

Another example of changing the amount of thermal energy in a systemis a hand pump used to inflate a bicycle tire. As a person pumps, the airand the hand pump become warm. The mechanical energy in the movingpiston is converted into thermal energy of the gas. Similarly, other formsof energy, such as light, sound, and electric energy, can be changed intothermal energy. For example, a toaster converts electric energy into heatwhen it toasts bread, and the Sun warms Earth with light from a distanceof over 150 million km away.

Heat engines The warmth that you experience when you rub your handstogether is a result of the conversion of mechanical energy into thermalenergy. The conversion of mechanical energy into thermal energy occurseasily. However, the reverse process, the conversion of thermal energy intomechanical energy, is more difficult. A device that is able to continuouslyconvert thermal energy to mechanical energy is called a heat engine.

A heat engine requires a high-temperature source from which thermalenergy can be removed; a low-temperature receptacle, called a sink, intowhich thermal energy can be delivered; and a way to convert the thermalenergy into work. A diagram of a heat engine is shown in Figure 12-11.An automobile internal-combustion engine, such as the one shown inFigure 12-12, is one example of a heat engine. In the engine, a mixture ofair and gasoline vapor is ignited and produces a high-temperature flame.Input heat, QH, flows from the flame to the air in the cylinder. The hot airexpands and pushes on a piston, thereby changing thermal energy intomechanical energy. To obtain continuous mechanical energy, the enginemust be returned to its starting condition. The heated air is expelled andreplaced by new air, and the piston is returned to the top of the cylinder.

The First Law of Thermodynamics �U � Q � W

The change in thermal energy of an object is equal to the heat added to theobject minus the work done by the object.

■ Figure 12-11 A heat enginetransforms heat at hightemperature into mechanicalenergy and low-temperaturewaste heat.

IdentifyingMisconceptionsEngines and Energy Many stu-dents will think that an engine isa device that takes energy andconverts it directly into work. Forinstance, they may think that a carengine converts all of the chemi-cal energy of gasoline into thework that drives the car. Instead,the engine uses only part of theavailable chemical energy to pro-duce useful work. The rest isexpelled as waste heat. The enginealso requires a lower-temperaturereservoir into which the wasteheat can be expelled. A car enginewould not work on a planetwhere the atmospheric tempera-ture is hotter than the combustiontemperature.

Critical ThinkingHeat Released by CondensationAsk students why exposing theskin to steam can cause a muchmore severe burn than exposingthe skin to boiling water. At thesame pressure, the temperature ofsteam can exceed 100°C, while thetemperature of liquid water cannot.Also, steam that touches the skincan condense as water at 100°C,releasing its large heat of vaporiza-tion in the process.

326

Visually Impaired Put several drops of peppermint oil in one evaporating dish and severaldrops of oil of wintergreen in another. Put the dish with the peppermint oil on a hot plate set onlow, and put the dish with oil of wintergreen in a beaker of crushed ice. Put the two dishes equi-distant from the class. The odor of peppermint oil reaches students first and is much stronger.Ask students to explain their observation. Because the hot plate is constantly adding heat to thepeppermint oil, more of the peppermint oil’s molecules have sufficient kinetic energy to escape theattractive forces of the liquid. Kinesthetic

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■ Figure 12-12 The heatproduced by burning gasolinecauses the gases that areproduced to expand and to exertforce and do work on the piston.

Air andgasolinevapor

Spark plug

Piston

Intake Compression Spark Power Exhaust

Exhaust

The entire cycle is repeated many times each minute. The thermal energyfrom the burning of gasoline is converted into mechanical energy, whicheventually results in the movement of the car.

Not all of the thermal energy from the high-temperature flame in anautomobile engine is converted into mechanical energy. When the auto-mobile engine is functioning, the exhaust gases and the engine partsbecome hot. As the exhaust comes in contact with outside air and transfersheat to it, the temperature of the outside air is raised. In addition, heatfrom the engine is transferred to a radiator. Outside air passes through theradiator and the air temperature is raised.

All of this energy, QL, transferred out of the automobile engine is calledwaste heat, that is, heat that has not been converted into work. When theengine is working continuously, the internal energy of the engine does not change, or �U � 0 � Q � W. The net heat going into the engine is Q � QH � QL. Thus, the work done by the engine is W � QH � QL. In anautomobile engine, the thermal energy in the flame produces the mechan-ical energy and the waste heat that is expelled. All heat engines generatewaste heat, and therefore no engine can ever convert all of the energy intouseful motion or work.

Efficiency Engineers and car salespeople often talk about the fuel efficiencyof automobile engines. They are referring to the amount of the input heat,QH, that is turned into useful work, W. The actual efficiency of an engineis given by the ratio W/QH. The efficiency could equal 100 percent only if allof the input heat were turned into work by the engine. Because there isalways waste heat, even the most efficient engines fall short of 100-percentefficiency.

In solar collectors, heat is collected at high temperatures and used todrive engines. The Sun’s energy is transmitted as electromagnetic wavesand increases the internal energy of the solar collectors. This energy is then transmitted as heat to the engine, where it is turned into useful work andwaste heat.

Refrigerators Heat flows spontaneously from a warm object to a coldobject. However, it is possible to remove thermal energy from a colderobject and add it to a warmer object if work is done. A refrigerator is a com-mon example of a device that accomplishes this transfer with the use ofmechanical work. Electric energy runs a motor that does work on a gas andcompresses it.

■ Using Figure 12-12 andFigure 12-13

These figures diagram the flow ofheat and work in engines andrefrigerators. Show the two figurestogether and ask the students tocompare them. The differences haveto do with the directions of thearrows for W, QH, and QL. Ask stu-dents the following questions:Would it be possible to use a heatengine to provide the work W tooperate a refrigerator? Could thatrefrigerator then be used to providethe heat QH to run another heatengine that could produce morework, W2? This could be done, but itis not useful. Some of the usefulenergy is lost in each of these stepsdue to the inherent waste heat lostin each engine and refrigerator.

Concept DevelopmentWaste Heat Ask the students tocite examples of waste heat pro-duced in our homes and aroundour cities and what effect this heathas on the environment nearcities. Examples might include theheat removed from a building by airconditioning and the heat from auto-mobile engines. This waste heat cancause local temperatures to rise,especially in urban areas.


327

Heating Homes The Chinese were the first to use central heating for their homes. Instead ofbuilding a fire inside the house, they would build one outside. The fire heated air that circulatedby convection currents through hollow spaces under the flooring. The floor tiles heated up, heat-ing each room efficiently. The Inuit reversed the concept in their igloos. By digging the entrywaylower than the inside of the igloo, they create a natural pressure barrier to keep the hot air in.Because cold air is more dense and sinks to the lowest point, the entranceway fills with cold airfrom the outside, stopping the flow of air. The warmer air inside the igloo stays inside because itis less dense than the colder air in the entry.

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Refrigerator

Cold reservoir at TL

Hot reservoir at TH

QH

QH � W � QLQL

W

■ Figure 12-13 A refrigeratorabsorbs heat, QL, from the coldreservoir and gives off heat, QH, to the hot reservoir. Work, W, is done on the refrigerator.

22. A gas balloon absorbs 75 J of heat. The balloon expands but staysat the same temperature. How much work did the balloon do inexpanding?

23. A drill bores a small hole in a 0.40-kg block of aluminum and heatsthe aluminum by 5.0°C. How much work did the drill do in boringthe hole?

24. How many times would you have to drop a 0.50-kg bag of lead shotfrom a height of 1.5 m to heat the shot by 1.0°C?

25. When you stir a cup of tea, you do about 0.050 J of work each timeyou circle the spoon in the cup. How many times would you have to stir the spoon to heat a 0.15-kg cup of tea by 2.0°C?

26. How can the first law of thermodynamics be used to explain how to reduce the temperature of an object?

The Second Law of ThermodynamicsMany processes that are consistent with the first law of thermodynam-

ics have never been observed to occur spontaneously. Three such processesare presented in Figure 12-14. For example, the first law of thermody-namics does not prohibit heat flowing from a cold object to a hot object.However, when hot objects have been placed in contact with cold objects,the hot objects have never been observed to become hotter. Similarly, thecold objects have never been observed to become colder.

Entropy If heat engines completely converted thermal energy intomechanical energy with no waste heat, then the first law of thermody-namics would be obeyed. However, waste heat is always generated, andrandomly distributed particles of a gas are not observed to spontaneouslyarrange themselves in specific ordered patterns. In the nineteenth century,French engineer Sadi Carnot studied the ability of engines to convert ther-mal energy into mechanical energy. He developed a logical proof that evenan ideal engine would generate some waste heat. Carnot’s result is bestdescribed in terms of a quantity called entropy, which is a measure of thedisorder in a system.

The gas draws heat from the interior of the refrigerator, passes from thecompressor through the condenser coils on the outside of the refrigerator,and cools into a liquid. Thermal energy is transferred into the air in theroom. The liquid reenters the interior, vaporizes, and absorbs thermalenergy from its surroundings. The gas returns to the compressor and theprocess is repeated. The overall change in the thermal energy of the gas iszero. Thus, according to the first law of thermodynamics, the sum of theheat removed from the refrigerator’s contents and the work done by themotor is equal to the heat expelled, as shown in Figure 12-13.

Heat pumps A heat pump is a refrigerator that can be run in two direc-tions. In the summer, the pump removes heat from a house and thus coolsthe house. In the winter, heat is removed from the cold outside air andtransferred into the warmer house. In both cases, mechanical energy isrequired to transfer heat from a cold object to a warmer one.

ReinforcementEngines and Refrigerators Havethe students work in pairs to create a concept map that relatesthe following concepts or quanti-ties: heat engine, refrigerator, heat, work, efficiency, temperaturereservoir. Students should useshort explanatory phrases toexplain the links on the conceptmap. Visual-Spatial

328

22. 75 J

23. 1.8�103 J

24. 9 drops

25. 2.6�104 stirs

26. Because �U � Q � W, itis possible to have a nega-tive �U and therefore coolan object if Q � 0 and theobject does work, forinstance, by expanding.Alternatively, have W � 0and Q negative so theobject transfers heat to itssurroundings. Any combi-nation of these will workas well.

Work on Gases How do you perform work on an object? If an external force F stretches a wirein length by an amount �L, then the amount of work done on the wire is Wexternal � F�L. Thework done by the wire would be Wwire � �F�L. According to the First Law of Thermodynamics itfollows that �Uwire = Q � Wwire � Q � (�F�L) � Q � F�L. Students will learn, in the next chap-ter, that pressure � force/area is the useful formula to use in working with gases. The work doneby an external pressure in compressing a gas is Wexternal � �P�V, where �V is the change involume of the gas. The minus sign applies because the volume decreases as the external pres-sure increases.

312-339 PhyTWEC12-845814 7/12/04 2:55 AM Page 328


TimeTime

Consistent with the First Lawof Thermodynamics but do not

occur spontaneously

Hot Cold

Heat engine QH � W

Q

Hot Cold

Heat engine QH � W � QL

Q

Occur spontaneously

Entropy has some interesting properties. Compare thefollowing situations. Explain how and why these changes in entropy are different.

1. Heating 1.0 kg of water from 273 K to 274 K.

2. Heating 1.0 kg of water from 353 K to 354 K.

3. Completely melting 1.0 kg of ice at 273 K.

4. Heating 1.0 kg of lead from 273 K to 274 K. TfTi

1 kg1 kgQ

■ Figure 12-14 Many processesthat do not violate the first law ofthermodynamics do not occurspontaneously. The spontaneousprocesses obey both the first andsecond law of thermodynamics.

When a baseball is dropped and falls due to gravity, it possesses poten-tial and kinetic energies that can be recovered to do work. However, whenthe baseball falls through the air, it collides with many air molecules thatabsorb some of its energy. This causes air molecules to move in randomdirections and at random speeds. The energy absorbed from the baseballcauses more disorder among the molecules. The greater the range of speedsexhibited by the molecules, the greater the disorder, which in turn increasesthe entropy. It is highly unlikely that the molecules that have been dis-persed in all directions will come back together, give their energies back tothe baseball, and cause it to rise.

Entropy, like thermal energy, is contained in an object. If heat is added to an object, entropy is increased. If heat is removed from an object,entropy is decreased. If an object does work with no change in tempera-ture, the entropy does not change, as long as friction is ignored. The changein entropy, �S, is expressed by the following equation, in which entropyhas units of J/K and the temperature is measured in kelvins.

Change in Entropy �S � �QT

�

The change in entropy of an object is equal to the heat added to the objectdivided by the temperature of the object in kelvins.

329

1.

�S � �

� [(1.0 kg)(4180 J/kg�K)(274 K � 273 K)]/(273 K)

� 15 J/K

2.

�S � �

� [(1.0 kg)(4180 J/kg�K)(354 K � 353 K)]/(353 K)

� 12 J/K3.

�S � �mHf�

TQ�T

(mC�T )�

TQ�T

(mC�T )�

TQ�T

�

� 1.2 � 103 J/K

4.

�S � �

� [(1.0 kg)(130 J/kg�K)(274 K � 273 K)]/(273 K)

� 0.48 J/K

(mC�T )�

TQ�T

(1.0 kg)(3.34 � 105 J/kg)��

(273 K)

DiscussionQuestion If you want to increasethe entropy of a pot of water byan amount �S, is it more timeefficient to use the lowest-temperature flame on a stove or a higher-temperature propanetorch?

Answer In either case, the amountof heat that you must add is Q � T�S. Because less heat isneeded at a lower temperature toincrease the entropy, the lowest-temperature flame would be themost efficient. However, the conduc-tion of heat to the water is slowerwith the low-temperature flamebecause of the smaller temperaturedifference between the flame andthe container. Thus, in terms of time,the high-temperature flame is moreefficient.


Entropy in Other Fields The concept of entropy as a measure of the disorder of a system ofmany particles has become useful in other fields of study. Computer scientists employ mathe-matical recipes that use randomness to seek speedy solutions to complex problems. Theserecipes sometimes include maximizing the entropy of the mathematical system. The entropy con-cept is useful in describing certain types of mathematical codes, including those used by spiesand the genetic codes stored in DNA. Ideas related to entropy have also been employed to pre-dict the behavior of financial markets.

312-339 PhyTWEC12-845814 7/12/04 2:56 AM Page 329

■ Figure 12-15 The spontaneousmixing of the food coloring andwater is an example of the secondlaw of thermodynamics.

■ Figure 12-16 If no work is doneon a system, entropy spontaneouslyreaches a maximum.


The second law of thermodynamics states that natural processes go ina direction that maintains or increases the total entropy of the universe.That is, all things will become more and more disordered unless someaction is taken to keep them ordered. The increase in entropy and the sec-ond law of thermodynamics can be thought of as statements of the prob-ability of events happening. Figure 12-15 illustrates an increase in entropyas food-coloring molecules, originally separate from the clear water, arethoroughly mixed with the water molecules over time. Figure 12-16 showsan example of the second law of thermodynamics that might be familiarto many teenagers.

The second law of thermodynamics predicts that heat flows sponta-neously only from a hot object to a cold object. Consider a hot iron barand a cold cup of water. On the average, the particles in the iron will bemoving very fast, whereas the particles in the water will be moving slowly.When the bar is plunged into the water and thermal equilibrium is even-tually reached, the average kinetic energy of the particles in the iron andthe water will be the same. More particles now have an increased randommotion than was true for the initial state. This final state is less orderedthan the initial state. The fast particles are no longer confined solely to theiron, and the slower particles are no longer confined only to the water; allspeeds are evenly distributed. The entropy of the final state is greater thanthat of the initial state.

Violations of the second law We take for granted many daily events thatoccur spontaneously, or naturally, in one direction. We would be shocked,however, if the reverse of the same events occurred spontaneously. You arenot surprised when a metal spoon, heated at one end, soon becomes uniformly hot. Consider your reaction, however, if a spoon lying on a tablesuddenly, on its own, became red hot at one end and icy cold at the other.If you dive into a swimming pool, you take for granted that you push thewater molecules away as you enter the water. However, you would beamazed if you were swimming in the pool and all the water moleculesspontaneously threw you up onto the diving board. Neither of these imagined reverse processes would violate the first law of thermodynamics.They are simply examples of the countless events that do not occur becausetheir processes would violate the second law of thermodynamics.

(t)Doug Martin, (others)Richard Hutchings/CORBIS

330

■ Entropy and Disorder Entropyis often thought of as the amountof disorder in a system. The rela-tion of entropy to work is illus-trated by relating how much workit takes to reorder a disorderedsystem. Give each of severalgroups of students a pack ofplaying cards. Each of the groupsshould arrange the cards in orderby value and suit. Then a studentin each group should take onesuit of 13 cards, shuffle them ran-domly, and then reorder the suitas quickly as possible. The time ittakes to reorder the suit shouldbe measured. The process shouldbe repeated with two suits (astack of 26 cards) and then withthree- and four-suit stacks. Thetime and work needed to organizefour suits should be much morethan four times the time neededto organize one suit of cards. Theentropy of the disordered systemincreases exponentially with thenumber of particles in the system.

Interpersonal

Solar Collectors The collection of solar energy to produce electrical power was discussed inthe photo that opened this chapter. Ask students to design and to build simple solar-energy col-lectors using materials found around the house, such as cardboard, umbrellas, aluminum foil,plastic cups, and tape. The goal should be to reflect sunlight to a collection point that includes asmall beaker of water. The amount of energy collected can be calculated by measuring theincrease in temperature of the water. Student teams should present their designs with the rea-soning behind their design decisions, their collection devices, and their measurements of thedevices’ performance.

Temperature and MixingPurpose to demonstrate that athigher temperatures particles movefaster

Materials two 250-mL beakers(one filled with hot water and onewith very cold water), dropper, foodcoloring

Procedure Carefully release onedrop of food coloring into eachbeaker. Do not touch or shake thebeakers. Observe how quickly thecolor diffuses in each beaker.

Assessment In which containerdid the color diffuse faster? Why?The color diffused faster in the hotwater because the particles aremoving more quickly (greaterkinetic energy) than those in thecold water.

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27. Heat of Vaporization Old-fashioned heatingsystems sent steam into radiators in each room ofa house. In the radiators, the steam condensedback to water. Analyze this process and explainhow it heated a room.

28. Heat of Vaporization How much heat is neededto change 50.0 g of water at 80.0°C to steam at110.0°C?

29. Heat of Vaporization The specific heat of mer-cury is 140 J/kg�°C. Its heat of vaporization is3.06�105 J/kg. How much energy is needed toheat 1.0 kg of mercury metal from 10.0°C to itsboiling point and vaporize it completely? The boil-ing point of mercury is 357°C.

30. Mechanical Energy and Thermal EnergyJames Joule carefully measured the difference intemperature of water at the top and bottom of awaterfall. Why did he expect a difference?

31. Mechanical Energy and Thermal EnergyA man uses a 320-kg hammer moving at 5.0 m/s to smash a 3.0-kg block of lead against a 450-kgrock. When he measured the temperature he foundthat it had increased by 5.0°C. Explain how thishappened.

32. Mechanical Energy and Thermal Energy Waterflows over a fall that is 125.0 m high, as shown in Figure 12-17. If the potential energy of the wateris all converted to thermal energy, calculate thetemperature difference between the water at thetop and the bottom of the fall.

33. Entropy Evaluate why heating a home with natu-ral gas results in an increased amount of disorder.

34. Critical Thinking A new deck of cards has all thesuits (clubs, diamonds, hearts, and spades) inorder, and the cards are ordered by number withinthe suits. If you shuffle the cards many times, areyou likely to return the cards to their original order?Explain. Of what physical law is this an example?

125.0 m

12.2 Section Review

physicspp.com/self_check_quiz

The second law of thermodynamics and the increase in entropy alsogive new meaning to what has been commonly called the energy crisis.The energy crisis refers to the continued use of limited resources of fossil fuels, such as natural gas and petroleum. When you use a resource,such as natural gas to heat your home, you do not use up the energy in the gas. As the gas ignites, the internal chemical energy contained in the molecules of the gas is converted into thermal energy of the flame. The thermal energy of the flame is then transferred to thermal energy in the air of your home. Even if this warm air leaks to the outside, theenergy is not lost. Energy has not been used up. The entropy, however, has increased.

The chemical structure of natural gas is very ordered. As you havelearned, when a substance becomes warmer, the average kinetic energy ofthe particles in the substance increases. In contrast, the random motion ofwarmed air is very disordered. While it is mathematically possible for theoriginal chemical order to be reestablished, the probability of this occur-ring is essentially zero. For this reason, entropy often is used as a measureof the unavailability of useful energy. The energy in the warmed air in ahome is not as available to do mechanical work or to transfer heat to otherobjects as the original gas molecules were. The lack of usable energy isactually a surplus of entropy.

■ Figure 12-17

3 ASSESS

Check for UnderstandingHeat, Work, and Entropy Askstudents what makes heat differ-ent from work and which of thetwo carries entropy. Ask them todraw arrows that show howentropy increases in the operationof a heat engine. Heat is the spon-taneous flow of energy from awarmer object to a colder object. Theaddition of heat increases theentropy of an object. Work can bedone on an object without increasingits entropy. In a heat engine, theentropy of the hot reservoir isdecreased, and the entropy of thecold reservoir is increased. For theengine to operate continuously, theentropy of the engine must remainconstant.

ExtensionEntropy and Thinking Ask stu-dents to discuss the following: Asa computer performs calculations,it is organizing information.Therefore, the computer’s entropyis decreasing. Discuss whether theprocesses of computation violatethe second law of thermodynam-ics. The computer can be viewed asa closed system in which order isincreased by work done on the system. However, in doing so thecomputer releases heat, therebyincreasing the entropy of the rest ofthe universe. So, in keeping with thesecond law of thermodynamics, theentropy of the universe alwaysincreases.

331

27. The condensing steam released itsheat of vaporization into the room.

28. 1.18�105 J29. 3.5�105 J30. The water at the top has gravitational

potential energy that is dissipatedinto thermal energy when the watersplashes at the bottom.

31. Part of the kinetic energy of the ham-mer is absorbed as thermal energy bythe lead block. The hammer’s energyis 4.0 kJ, and the change in thermalenergy of the block is 2.0 kJ. Abouthalf of the hammer’s energy went tothe lead block.

32. 0.293°C33. The gas releases heat at its combus-

tion temperature. The natural gas

molecules break up and combustwith oxygen. The heat is distributedin many new ways, and the naturalgas molecules cannot be readilyreassembled.

34. No. This is an example of the secondlaw of thermodynamics, in which dis-order increases.

12.2 Section Review

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332

Heating and CoolingWhen a beaker of water is set on a hot plate and the hot plate is turned on, heat istransferred. It first is transferred to the beaker and then to the water at the bottomof the beaker by conduction. The water then transfers heat from the bottom to thetop by moving hot water to the top through convection. Once the heat source isremoved or shut off, the water radiates thermal energy until it reaches room tem-perature. How quickly the water heats up is a function of the amount of heatadded, the mass of the water, and the specific heat of water.

QUESTIONHow does the constant supply of thermal energy affect the temperature of water?

Alternate CBL instructionscan be found on the Web site.

physicspp.com

■ Measure, in SI, temperature and mass.■ Make and use graphs to help describe the

change in temperature of water as it heats upand cools down.

■ Explain any similarities and differences in thesetwo changes.

■ Be careful when using a hot plate. It canburn the skin.

hot plate (or Bunsen burner)250-mL ovenproof glass beaker50–200 g of watertwo thermometers (non-mercury)stopwatch (or timer)

1. Set the hot plate to the highest setting, or asrecommended by your teacher. Allow a fewminutes for the plate to heat up.

2. Measure the mass of the empty beaker.

3. Pour 150 mL of water into the beaker andmeasure the combined mass of the water andthe beaker.

4. Calculate and record the mass of the water inthe beaker.

5. Create a data and observations table.

6. Record the initial temperature of the water andthe air in the classroom. Note that the bulb end of the thermometers must not touch thebottom or sides of the beaker, nor should ittouch a table or your hands.

7. Place the beaker on the hot plate and recordthe temperature every minute for 5 min.

8. Carefully remove the beaker from the hot plateand record the temperature every minute forthe next 10 min.

9. At the end of 10 min, record the temperatureof the air.

10. Turn off the hot plate.

11. When finished, allow the equipment to cooland dispose of the water as instructed by your teacher.

Procedure

Materials

Safety Precautions

Objectives

Horizons Companies

Time Allotmentone lab period

Process Skills organize information(summarize, explain), practice experi-mental skills (measure in SI, hypothe-size), calculate

Safety PrecautionsUse only glassware that is rated foruse with a direct heat source. Also, besure there is enough water in thebeaker so that it does not break whenit is heated. Exercise caution with thehot plate—the surface is very hot. Thecord should be tucked safely behindthe unit so that it cannot be pulled andso that it is not in contact with the sur-face of the hot plate. Use only alcohol-filled thermometers (no mercury).

Alternative Materials Using CBLor handheld computer probes ispreferable to using a thermometerbecause a more constant stream ofdata can be recorded.

Teaching Strategies• It is important to stress precise

measurements to the nearest0.1°C. With small changes intemperature (especially duringcooling), a pattern may be diffi-cult to find if measurements aremade only to the nearest degree.

• Students’ cooling curves will varyif factors such as the surfacearea of the water (the size of thebeaker) vary.

332

Sample DataMass of water: 151.2 g Initial air temp.: 21.4°C Final air temp.: 21.8°C Change in air temp.: 0.4°C

HeatingTime Temp or(min) (°C) Cooling

0 22.5 —1 25.7 H2 32.4 H3 40.8 H4 48.9 H5 58.3 H


6 59.2 C7 57.5 C8 56.3 C9 55 C

10 53.8 C


11 52.9 C12 52 C13 51.1 C14 50.3 C15 49.2 C

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333

1. Calculate the change in air temperature todetermine if air temperature may be an extraneous variable.

2. Make a scatter-plot graph of temperature (vertical axis) versus time (horizontal axis). Use a computer or a calculator to construct thegraph, if possible.

3. Calculate What was the change in water tem-perature as the water heated up?

4. Calculate What was the drop in water temper-ature when the heat source was removed?

5. Calculate the average slope for the temperatureincrease by dividing change in temperature bythe amount of time the water was heating up.

6. Calculate the average slope for the temperaturedecrease by dividing change in temperature by the amount of time the heat source wasremoved.

1. Summarize What was the change in watertemperature when a heat source was applied?

2. Summarize What was the change in watertemperature once the heat source was removed?

3. What would happen to the water temperatureafter the next 10 min? Would it continue cooling down forever?

4. Did the water appear to heat up or cool downquicker? Why do you think this is so? Hint:Examine the slopes you calculated.

5. Hypothesize Where did the thermal energy inthe water go once the water began to cooldown? Support your hypothesis.

1. Does placing your thermometer at the top ofthe water in your beaker result in differentreadings than if it is placed at the bottom of the beaker? Explain.

2. Hypothesize what the temperature changesmight look like if you had the followingamounts of water in the beaker: 50 mL, 250 mL.

3. Suppose you insulated the beaker you wereusing. How would the beaker’s ability to heatup and cool down be affected?

1. Suppose you were to use vegetable oil in thebeaker instead of water. Hypothesize what thetemperature changes might look like if youwere to follow the same steps and perform the experiment.

2. If you were to take soup at room temperatureand cook it in a microwave oven for 3 min,would the soup return to room temperature in 3 min? Explain your answer.

Real-World Physics

Going Further

Conclude and Apply

Analyze

To find out more about thermal energy, visit theWeb site: physicspp.com

Data TableMass of water

Initial air temperature

Final air temperature

Change in air temperature

Time (min) Temperature (°C) Heating or Cooling

Analyze1. 0.4°C, or greater with a large class

and more hot plates

2.

3. 5.8°C

4. 9.1°C

5. 7.1°C/min

6. 0.91°C/min

Conclude and Apply1. After an initial period, the water

heated at a fairly constant rate.

2. It decreased at a fairly constant rate.

3. The water would continue to cooldown until it reached thermal equi-librium with the room.

4. It heated up much more quicklythan it cooled, as evidenced by themuch steeper slope in the begin-ning of the graph. The heatingprocess is faster because heat wasadded by an external source.

5. It escaped into the air. There was noinsulation to keep it in the beaker.This is supported by the measuredincrease in air temperature.

Going Further1. Possibly, because the water at the

bottom is closer to the heat source.

2. With 50 mL, the temperaturechanges would be more dramaticbecause there would be less waterto heat up. With 250 mL, the tem-perature changes would be muchsmaller and more difficult to notice.

3. It would heat and cool more slowly.

Real-World Physics1. In general, oils heat up and cool

down more quickly than water. Thespecific heat of canola oil is about2000 J/kg�K compared to a specificheat of 4180 J/kg�K for water.

2. No, because it takes longer forobjects to cool after they have beenheated by an external source.

333

To Make this Lab an Inquiry Lab: Ask students how the temperature of a mass of a liquid changesin the presence (and absence) of a heat source. Students may wish to study the time/temperaturerelationship of different masses of water, different liquids, different amounts of time, or different levelsof a heat source. Students may even be able to use home cooking examples as part of their study (forexample, does it help if you cut a 400-g potato before you cook it, or do five 25-mL ice cubes meltquicker than one 125-mL ice cube?).

Time (min)

25.020.00.0

Tem

per

atu

re (

�C)

2 144 6 8 10 12

30.035.040.045.050.055.060.0

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■ PurposeStudents will learn about the prin-ciples of thermodynamics throughan application using heat pumps.

■ BackgroundHeat pumps were originally smallwindow-mounted units known as“reversible air conditioners.” Theyare still used to heat and coolmany motel rooms. If the air-conditioner unit in a motel roomhas both “heat” and “cool” con-trols on it, it is probably a heatpump. The heat pumps that areused to heat and cool largehouses have very large compres-sors, evaporators, and condensers.In a central air-conditioning unit,the condenser is always outside,located in a box with the com-pressor and a large fan.

■ Visual LearningIf the weather is warm, take theclass outside to investigate variousair conditioning units and to seehow the air that the units blowout through their condensers ishotter than the temperature of theoutside air. If the weather is cold,ask the students to discuss theexperience of having walked pasta window air conditioner on avery hot day. They should men-tion that they were heated furtherby the air from the condenser.

■ ExtensionsHave students research how anairplane is heated and cooled.Students should note that the out-side temperature at an averagecruising altitude is about �70°F.

334 How It Works

The Heat Pump

Heat pumps, also called reversible air conditioners,were invented in the 1940s. They are used to heat andcool homes and hotel rooms. Heat pumps change fromheaters to air conditioners by reversing the flow ofrefrigerant through the system.

1. Observe Trace the flow of refrigerantthrough the entire system for bothheating and cooling. Start at the compressor.

2. Analyze Would a heat pump be ableto heat an entire house when the out-side temperature drops to extremelycold levels?

Thinking Critically

Air grating

Compressor pumprefrigerant

1 4

3 2

Receiver: tankstores refrigerant

Fanmotor

Unitcabinet

Airflowfromrooms

Airflow torooms

Inside Outside

Airgrating

Fan motor

1 Cooling The thin capillary tube sprays liquid refrigerant into a larger coil inside.

2 Cooling Valves 1 and 2 are opened and valves 3 and 4 are closed for cooling. The refrigerant flows downward. The inside coil functions as an evaporator and the outside coil functions as a condenser.

3 Heating The thin capillary tube sprays liquid refrigerant into a larger diameter pipe in an outer coil for heating.

Heating Valves 3 and 4 are opened and valves 1 and 2 are closed for heating. The refrigerant flows upward. The inside coil functions as a condenser and the outside coil functions as an evaporator.

4

5 The fan cools the coil during cooling and warms the coil during heating.

334

Thinking Critically

1. In this diagram, the flow of the refrigerantthrough the heat-pump system when it isheating is generally clockwise, and the flowwhen it is cooling is counterclockwise.

2. The heat provided by a heat pump isextracted from the air outside the house.In extremely cold temperatures, a heat

pump often cannot keep up with thedemands of the occupants of the houseand with the loss of thermal energy fromthe house to the environment. Thus, anauxiliary furnace sometimes is used tosupplement the output from a heat pumpin very cold weather.

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12.1 Temperature and Thermal Energy

Vocabulary• conduction (p. 315)

• thermal equilibrium (p. 315)

• heat (p. 317)

• convection (p. 317)

• radiation (p. 317)

• specific heat (p. 318)


Vocabulary• heat of fusion (p. 324)

• heat of vaporization (p. 324)

• first law of thermodynamics (p. 326)

• heat engine (p. 326)

• entropy (p. 328)

• second law of thermodynamics (p. 330)

Key Concepts• The temperature of a gas is proportional to the average kinetic energy of

its particles.

• Thermal energy is a measure of the internal motion of an object’s particles.

• A thermometer reaches thermal equilibrium with the object that it comes in contact with, and then a temperature-dependent property of thethermometer indicates the temperature.

• The Celsius and Kelvin temperature scales are used in scientific work. Themagnitude of 1 K is equal to the magnitude of 1°C.

• At absolute zero, no more thermal energy can be removed from a substance.

• Heat is energy transferred because of a difference in temperature.

• Specific heat is the quantity of heat required to raise the temperature of 1 kgof a substance by 1 K.

• In a closed, isolated system, heat may flow and change the thermal energy of parts of the system, but the total energy of the system is constant.

EA � EB � constant

Q � mC�T � mC(Tf � Ti)

Key Concepts• The heat of fusion is the quantity of heat needed to change 1 kg of a

substance from its solid to liquid state at its melting point.

• The heat of vaporization is the quantity of heat needed to change 1 kg of a substance from its liquid to gaseous state at its boiling point.

• Heat transferred during a change of state does not change the temperature of a substance.

• The change in energy of an object is the sum of the heat added to it minusthe work done by the object.

• A heat engine continuously converts thermal energy to mechanical energy.

• A heat pump and a refrigerator use mechanical energy to transfer heat froma region of lower temperature to one of higher temperature.

• Entropy is a measure of the disorder of a system.

• The change in entropy of an object is defined to be the heat added to theobject divided by the temperature of the object.

�S � �QT

�

�U � Q � W

Q � mHv

Q � mHf

335physicspp.com/vocabulary_puzzlemaker

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For additional helpwith vocabulary, havestudents access the

Vocabulary PuzzleMakeronline.

physicspp.com/vocabulary_puzzlemaker

Key ConceptsSummary statements can beused by students to review themajor concepts of the chapter.

335

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35. Complete the following concept map using thefollowing terms: heat, work, internal energy.

Mastering Concepts36. Explain the differences among the mechanical

energy of a ball, its thermal energy, and itstemperature. (12.1)

37. Can temperature be assigned to a vacuum? Explain.(12.1)

38. Do all of the molecules or atoms in a liquid havethe same speed? (12.1)

39. Is your body a good judge of temperature? On acold winter day, a metal doorknob feels muchcolder to your hand than a wooden door does.Explain why this is true. (12.1)

40. When heat flows from a warmer object in contactwith a colder object, do the two have the sametemperature changes? (12.1)

41. Can you add thermal energy to an object withoutincreasing its temperature? Explain. (12.2)

42. When wax freezes, does it absorb or release energy?(12.2)

43. Explain why water in a canteen that is surroundedby dry air stays cooler if it has a canvas cover that is kept wet. (12.2)

44. Which process occurs at the coils of a running airconditioner inside a house, vaporization orcondensation? Explain. (12.2)

Applying Concepts45. Cooking Sally is cooking pasta in a pot of boiling

water. Will the pasta cook faster if the water isboiling vigorously or if it is boiling gently?

46. Which liquid would an ice cube cool faster, water ormethanol? Explain.

47. Equal masses of aluminum and lead are heated to thesame temperature. The pieces of metal are placed ona block of ice. Which metal melts more ice? Explain.

48. Why do easily vaporized liquids, such as acetoneand methanol, feel cool to the skin?

49. Explain why fruit growers spray their trees withwater when frost is expected to protect the fruitfrom freezing.

50. Two blocks of lead have the same temperature.Block A has twice the mass of block B. They aredropped into identical cups of water of equaltemperatures. Will the two cups of water have equaltemperatures after equilibrium is achieved? Explain.

51. Windows Often, architects design most of thewindows of a house on the north side. How doesputting windows on the south side affect theheating and cooling of the house?

Mastering Problems12.1 Temperature and Thermal Energy

52. How much heat is needed to raise the temperatureof 50.0 g of water from 4.5°C to 83.0°C?

53. A 5.00�102-g block of metal absorbs 5016 J of heatwhen its temperature changes from 20.0°C to30.0°C. Calculate the specific heat of the metal.

54. Coffee Cup A 4.00�102-g glass coffee cup is 20.0°Cat room temperature. It is then plunged into hotdishwater at a temperature of 80.0°C, as shown inFigure 12-18. If the temperature of the cup reachesthat of the dishwater, how much heat does the cupabsorb? Assume that the mass of the dishwater islarge enough so that its temperature does notchange appreciably.

55. A 1.00�102-g mass of tungsten at 100.0°C is placedin 2.00�102 g of water at 20.0°C. The mixturereaches equilibrium at 21.6°C. Calculate the specificheat of tungsten.

4.00�102 g

20.0°C 80.0°C

Concept Mapping

336 Chapter 12 Thermal Energy For more problems, go to Additional Problems, Appendix B.

First law ofthermodynamics

temperatureentropy externalforces

■ Figure 12-18

Concept Mapping35. See Solutions Manual.

Mastering Concepts36. The mechanical energy is the

sum of the potential and kineticenergies of the ball consideredas one mass. The thermalenergy is the sum of the poten-tial and kinetic energies of theindividual particles that makeup the mass of the ball. Thetemperature is a measure of theinternal energy of the ball.

37. No, there are no particles thathave energy in a vacuum.

38. No. There is a distribution of ve-locities of the atoms or molecules.

39. Your skin measures heat flow toor from itself. The metal door-knob absorbs heat from yourskin faster than the woodendoor, so it feels colder.

40. The two objects will changetemperatures depending ontheir masses and specific heats.The temperature changes arenot necessarily the same foreach.

41. When you melt a solid or boil a liquid, you add thermal energy without changing thetemperature.

42. In freezing, wax releases energy.

43. When the water in the coverevaporates into the dry air, itmust absorb an amount ofenergy proportional to its heatof fusion. In doing so, it coolsoff the canteen.

44. Inside the house, the coolant isevaporating in the coils toabsorb energy from the rooms.

Applying Concepts45. It should make no difference.

Either way, the water is at thesame temperature.

46. methanol, because it has alower specific heat. For a givenmass and heat transfer, it gen-erates a bigger �T, since Q �mC �T.

336

47. The specific heat of aluminum is muchgreater than that of lead; therefore, it meltsmore ice.

48. As they evaporate, they absorb their heat ofvaporization from the skin.

49. The water on the leaves will not freeze untilit can release its heat of fusion. This processkeeps the leaves warmer longer. The heat

capacity of the ice slows down the coolingbelow 0°C.

50. The cup with block A will be hotter becauseblock A contains more thermal energy.

51. In the northern hemisphere, the sunlightcomes from the south. The Sun's light wouldhelp heat the house in the winter but wouldalso heat the house in the summer.

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56. A 6.0�102-g sample of water at 90.0°C is mixedwith 4.00�102 g of water at 22.0°C. Assume thatthere is no heat loss to the surroundings. What isthe final temperature of the mixture?

57. A 10.0-kg piece of zinc at 71.0°C is placed in acontainer of water, as shown in Figure 12-19. Thewater has a mass of 20.0 kg and a temperature of10.0°C before the zinc is added. What is the finaltemperature of the water and the zinc?

58. The kinetic energy of a compact car moving at 100 km/h is 2.9�105 J. To get a feeling for theamount of energy needed to heat water, whatvolume of water (in liters) would 2.9�105 J ofenergy warm from room temperature (20.0°C) toboiling (100.0°C)?

59. Water Heater A 3.0�102-W electric immersionheater is used to heat a cup of water, as shown inFigure 12-20. The cup is made of glass, and itsmass is 3.00�102 g. It contains 250 g of water at15°C. How much time is needed to bring the waterto the boiling point? Assume that the temperatureof the cup is the same as the temperature of thewater at all times and that no heat is lost to the air.

60. Car Engine A 2.50�102-kg cast-iron car enginecontains water as a coolant. Suppose that theengine’s temperature is 35.0°C when it is shut off,and the air temperature is 10.0°C. The heat given off by the engine and water in it as they cool to airtemperature is 4.40�106 J. What mass of water is used to cool the engine?


61. Years ago, a block of ice with a mass of about 20.0 kgwas used daily in a home icebox. The temperatureof the ice was 0.0°C when it was delivered. As itmelted, how much heat did the block of ice absorb?

62. A 40.0-g sample of chloroform is condensed from avapor at 61.6°C to a liquid at 61.6°C. It liberates9870 J of heat. What is the heat of vaporization ofchloroform?

63. A 750-kg car moving at 23 m/s brakes to a stop. Thebrakes contain about 15 kg of iron, which absorbsthe energy. What is the increase in temperature ofthe brakes?

64. How much heat is added to 10.0 g of ice at�20.0°C to convert it to steam at 120.0°C?

65. A 4.2-g lead bullet moving at 275 m/s strikes a steelplate and comes to a stop. If all its kinetic energy isconverted to thermal energy and none leaves thebullet, what is its temperature change?

66. Soft Drink A soft drink from Australia is labeled“Low-Joule Cola.” The label says “100 mL yields 1.7 kJ.” The can contains 375 mL of cola. Chandradrinks the cola and then wants to offset this inputof food energy by climbing stairs. How high wouldChandra have to climb if she has a mass of 65.0 kg?

Mixed Review67. What is the efficiency of an engine that produces

2200 J/s while burning enough gasoline to produce5300 J/s? How much waste heat does the engineproduce per second?

68. Stamping Press A metal stamping machine in afactory does 2100 J of work each time it stamps outa piece of metal. Each stamped piece is then dippedin a 32.0-kg vat of water for cooling. By how manydegrees does the vat heat up each time a piece ofstamped metal is dipped into it?

69. A 1500-kg automobile comes to a stop from25 m/s. All of the energy of the automobile isdeposited in the brakes. Assuming that the brakesare about 45 kg of aluminum, what would be thechange in temperature of the brakes?

15°C

250 g

3.00�102 W

3.00�102 g

20.0 kg

10.0°C

10.0

kg

Chapter 12 Assessment 337physicspp.com/chapter_test

■ Figure 12-19

■ Figure 12-20

Mastering Problems12.1 Temperature and Thermal

Energy

Level 152. 1.64�104 J

53. 1.00�103 J/kg�K

54. 2.02�104 J

55. 171 J/kg�K

56. 63°C

57. 12.7°C

Level 258. 0.87 L

59. 6.1 min

60. 15 kg

12.2 Changes of State and theLaws of Thermodynamics

Level 161. 6.68�106 J

62. 2.47�105 J/kg

63. 29°C

Level 264. 3.09�104 J

65. 290°C

66. 1.0�101 m

Mixed ReviewLevel 167. 42%; 2900 J

68. 0.016°C

69. 12°C

70. 1.1 kg; thus, you need slightlymore ice than tea, but this ratiowould make watery tea. Let thetea cool to room temperaturebefore adding the ice.

Level 271. The copper block has 2.3 times

as much mass as the aluminumblock.

72. 12 m/s

337

Level 373. 2.0�10�5 kg

Thinking Critically74. a. 0.0313 J/K

b. 0.103 J/K; the total entropy change inthe reservoirs, and in the universe, hasincreased approximately by a factor of three.

75. 0.0478 kg

76. 4.8�10�19 J/molecule

77. Student answers will vary. Answers shouldreflect changing average temperatures onEarth, different weather patterns, plant andanimal species dying out, etc.

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70. Iced Tea To make iced tea, you start by brewing thetea with hot water. Then you add ice. If you startwith 1.0 L of 90°C tea, what is the minimumamount of ice needed to cool it to 0°C? Would it be better to let the tea cool to room temperaturebefore adding the ice?

71. A block of copper at 100.0°C comes in contact witha block of aluminum at 20.0°C, as shown in Figure 12-21. The final temperature of the blocks is60.0°C. What are the relative masses of the blocks?

72. A 0.35-kg block of copper sliding on the floor hitsan identical block moving at the same speed fromthe opposite direction. The two blocks come to astop together after the collision. Their temperaturesincrease by 0.20°C as a result of the collision. Whatwas their velocity before the collision?

73. A 2.2-kg block of ice slides across a rough floor. Its initial velocity is 2.5 m/s and its final velocity is 0.50 m/s. How much of the ice block melted as a result of the work done by friction?

Thinking Critically74. Analyze and Conclude A certain heat engine

removes 50.0 J of thermal energy from a hotreservoir at temperature TH � 545 K and expels 40.0 J of heat to a colder reservoir at temperature TL � 325 K. In the process, it also transfers entropyfrom one reservoir to the other. a. How does the operation of the engine change

the total entropy of the reservoirs?b. What would be the total entropy change in the

reservoirs if TL � 205 K?

75. Analyze and Conclude During a game, themetabolism of basketball players often increases byas much as 30.0 W. How much perspiration must aplayer vaporize per hour to dissipate this extrathermal energy?

76. Analyze and Conclude Chemists use calorimetersto measure the heat produced by chemicalreactions. For instance, a chemist dissolves 1.0�1022 molecules of a powdered substance into a calorimeter containing 0.50 kg of water. Themolecules break up and release their binding energyto the water. The water temperature increases by2.3°C. What is the binding energy per molecule forthis substance?

77. Apply Concepts All of the energy on Earth comesfrom the Sun. The surface temperature of the Sun is approximately 104 K. What would be the effect on our world if the Sun’s surface temperature were103 K?

Writing in Physics78. Our understanding of the relationship between heat

and energy was influenced by a soldier namedBenjamin Thompson, Count Rumford; and abrewer named James Prescott Joule. Both relied onexperimental results to develop their ideas.Investigate what experiments they did and evaluatewhether or not it is fair that the unit of energy iscalled the Joule and not the Thompson.

79. Water has an unusually large specific heat and largeheats of fusion and vaporization. Our weather andecosystems depend upon water in all three states.How would our world be different if water’sthermodynamic properties were like other materials,such as methanol?

Cumulative Review80. A rope is wound around a drum with a radius of

0.250 m and a moment of inertia of 2.25 kg m2.The rope is connected to a 4.00-kg block. (Chapter 8)a. Find the linear acceleration of the block.b. Find the angular acceleration of the drum.c. Find the tension, FT , in the rope.d. Find the angular velocity of the drum after the

block has fallen 5.00 m.

81. A weight lifter raises a 180-kg barbell to a height of 1.95 m. How much work is done by the weightlifter in lifting the barbell? (Chapter 10)

82. In a Greek myth, the man Sisyphus is condemnedby the gods to forever roll an enormous rock up ahill. Each time he reaches the top, the rock rollsback down to the bottom. If the rock has a mass of 215 kg, the hill is 33 m in height, and Sisyphuscan produce an average power of 0.2 kW, how manytimes in 1 h can he roll the rock up the hill?(Chapter 11)

Copper Aluminum

Copper Aluminum

60.0°C60.0°C

20.0°C100.0°C

338 Chapter 12 Thermal Energy For more problems, go to Additional Problems, Appendix B.

■ Figure 12-21

338

Writing in Physics78. In 1799 heat was thought to be

a liquid that flowed from oneobject to another. However,Count Rumford thought thatheat was caused by the motionof particles in the metal cannon.He did not do any quantitativemeasurements and his ideaswere not widely accepted. In1843 Joule, doing careful mea-surements, measured thechange in temperature causedby adding heat or doing workon a quantity of water. Heproved that heat is a flavor ofenergy and that energy is con-served. Joule deserves thecredit and the eponymic unit.

79. The large specific heat andlarge heats of fusion and vapor-ization mean that water, ice, andwater vapor can store a lot ofthermal energy without chang-ing their temperatures toomuch. The implications aremany. The oceans and largelakes moderate the temperaturechanges in nearby regions on adaily and seasonal basis. Theday to night temperature varia-tion near a lake is much smallerthan the day to night tempera-ture variation in the desert. Thelarge heat of fusion of watercontrols the change of seasonsin the far north and south. Theabsorption of energy by freezingwater in the fall and its releasein the spring slows the tempera-ture changes in the atmosphere.Water absorbs and stores a lotof energy as it vaporizes. Thisenergy can be used to drivemeteorological events such asthunderstorms and hurricanes.

Cumulative Review80. a. 0.980 m/s2

b. 3.92 rad/s2

c. 35.3 Nd. 12.5 rad/s

81. 3.4�103 J

82. 10 times in one hour.

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312-339 PhyTWEC12-845814 7/12/04 3:05 AM Page 338

1. Which of the following temperatureconversions is incorrect?

�273°C � 0 K 298 K � 571°C

273°C � 546 K 88 K � �185°C

2. What are the units of entropy?

J/K J

K/J kJ

3. Which of the following statements aboutthermal equilibrium is false?

When two objects are at equilibrium, heatradiation between the objects continues to occur.Thermal equilibrium is used to createenergy in a heat engine.The principle of thermal equilibrium isused for calorimetry calculations.When two objects are not at equilibrium,heat will flow from the hotter object to thecooler object.

4. How much heat is required to heat 87 g ofmethanol ice at 14 K to vapor at 340 K?(melting point � �97.6°C, boiling point �64.6°C)

17 kJ 1.4�102 kJ

69 kJ 1.5�102 kJ

5. Which statement is true about energy, entropy,and changes of state?

Freezing ice increases in energy as it gainsmolecular order as a solid.The higher the specific heat capacity of asubstance, the higher its melting point will be.States of matter with increased kineticenergy have higher entropy.Energy and entropy cannot increase at thesame time.

6. How much heat is needed to warm 363 mL ofwater in a baby bottle from 24°C to 38°C?

21 kJ 121 kJ

36 kJ 820 kJ

7. Why is there always some waste heat in a heatengine?

Heat cannot flow from a cold object to a hot object.

Friction slows the engine down.

The entropy increases at each stage.

The heat pump uses energy.

8. How much heat is absorbed from thesurroundings when 81 g of 0.0°C ice in a beaker melts and warms to 10°C?

0.34 kJ 30 kJ

27 kJ 190 kJ

9. You do 0.050 J of work on the coffee in yourcup each time you stir it. What would be theincrease in entropy in 125 mL of coffee at65°C when you stir it 85 times?

0.013 J/K 0.095 J/K

0.050 J 4.2 J

Extended Answer10. What is the difference in heat required to melt

454 g of ice at 0.00°C, and to turn 454 g ofwater at 100.0°C into steam? Is the amount ofthis difference greater or less than the amountof energy required to heat the 454 g of waterfrom 0.00°C to 100.0°C?

m � 81 gIce

Ti � 0.0°C

Multiple Choice

Chapter 12 Standardized Test Practice 339physicspp.com/standardized_test

Your Mistakes Can Teach You

The mistakes you make before the test are helpfulbecause they show you areas in which you needmore work. When calculating the heat needed to melt and warm a substance, remember to calculatethe heat needed for melting as well as the heatneeded for raising the temperature of the substance.

339

Extended Answer10. to melt: 152 kJ; to boil: 1030 kJ; the conver-

sion to steam requires 878 kJ more energy.to heat: 190�102 kJ; the difference inenergy between the phase charges is muchgreater than the energy required to heatwater in the liquid state.

Multiple Choice1. C4. D7. C

2. A5. C8. C

3. B6. A9. A

Points Description

4 The student demonstrates athorough understanding of the physics involved. Theresponse may contain minorflaws that do not detract fromthe demonstration of a thor-ough understanding.

3 The student demonstrates an understanding of the physics involved. The re-sponse is essentially correctand demonstrates an essentialbut less than thorough under-standing of the physics.

2 The student demonstrates only a partial understanding of the physics involved.Although the student mayhave used the correctapproach to a solution or may have provided a correctsolution, the work lacks anessential understanding of the underlying physical concepts.

1 The student demonstrates avery limited understanding ofthe physics involved. Theresponse is incomplete andexhibits many flaws.

0 The student provides a completely incorrect solutionor no response at all.

RubricThe following rubric is a samplescoring device for extendedresponse questions.

Extended Response

312-339 PhyTWEC12-845814 7/21/04 1:18 AM Page 339

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