HEAT TRANSFER HEAT TRANSFER - Youngbull Science …science.telosrtc.com/uploads/1/6/5/9/16598904/chapter_22.pdf · ferred through the metal by conduction. Conduction of heat is the

THE BIG

IDEA ......

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HEAT TRANSFER

The spontaneous transfer of heat is always from warmer objects to cooler objects. If several

objects near one another have dif-ferent temperatures, then those that are warm become cooler and those that are cool become warmer, until all have a common temperature. This equalization of temperatures is brought about in three ways: by conduction, by convection, and by radiation.

Heat can be transferred by conduction, by convection, and by radiation.

Does White Ever Appear Black?1. Using a paper punch or sharp pencil, make

a small hole in the center of a black sheet of construction paper.

2. Place the paper on top of a polystyrene coffee cup or any cup that is all white inside.

Analyze and Conclude1. Observing Which is darker, the construction

paper or the hole?

2. Predicting What do you think will happen if you enlarge the hole?

3. Making Generalizations Why do openings such as the pupil of the eye and doorways of distant houses appear black even in the daytime?

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HEAT TRANSFER

Objectives• Explain how conduction works.

(22.1)

• Explain how convection works. (22.2)

• Explain how heat can be transmitted through empty space. (22.3)

• Identify which substances emit radiant energy. (22.4)

• Compare the ability of an object to emit radiant energy with its ability to absorb radiant energy. (22.5)

• Relate the temperature difference between an object and its surroundings to the rate at which it cools. (22.6)

• Identify the main driver of global warming and climate change. (22.7)

discover!

MATERIALS black construction paper, hole punch or pencil, white polystyrene cup

EXPECTED OUTCOME Even though the inside of the cup is white, the hole looks black.

ANALYZE AND CONCLUDE

Both are the same.

The hole would no longer appear dark.

Light entering a small opening is reflected from the inside surfaces many times. Some of the light is partially absorbed at each reflection until none remains.

TEACHING TIP If the aperture is made too large, some light entering the hole will find its way out of the cavity. Students may also find that the hole will not appear black if viewed under a bright light.

1.

2.

3.

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22.1 ConductionIf you hold one end of an iron rod in a flame, as shown in Figure 22.1, before long the rod will become too hot to hold. Heat has trans-ferred through the metal by conduction. Conduction of heat is the transfer of energy within materials and between different materials that are in direct contact. Materials that conduct heat well are known as heat conductors. Metals are the best conductors. Among the common metals, silver is the most conductive, followed by copper, aluminum, and iron.

Conduction is explained by collisions between atoms or mol-ecules, and the actions of loosely bound electrons. In conduction, collisions between particles transfer thermal energy, without any overall transfer of matter. When the end of an iron rod is held in a flame, the atoms at the heated end vibrate more rapidly. These atoms vibrate against neighboring atoms, which in turn do the same. More important, free electrons that can drift through the metal are made to jostle and transfer energy by colliding with atoms and other free elec-trons within the rod.

Conductors Materials composed of atoms with “loose” outer elec-trons are good conductors of heat (and electricity also). Because met-als have the “loosest” outer electrons, they are the best conductors of heat and electricity.

Touch a piece of metal and a piece of wood in your immediate vicinity. Which one feels colder? Which is really colder? Your answers should be different. If the materials are in the same vicinity, they should have the same temperature, room temperature. Thus nei-ther is really colder. Yet, the metal feels colder because it is a better conductor, like the tile in Figure 22.2; heat easily moves out of your warmer hand into the cooler metal. Wood, on the other hand, is a poor conductor. Little heat moves out of your hand into the wood, so your hand does not sense that it is touching something cooler. Wood, wool, straw, paper, cork, and polystyrene are all poor heat conduc-tors. Instead, they are called good insulators.

think!

CHAPTER 22 HEAT TRANSFER 431

FIGURE 22.1 �Heat from the flame causes atoms and free electrons in the end of the metal to move faster and jostle against others. Those particles do the same and increase the energy of vibrating atoms along the length of the rod.

� FIGURE 22.2The tile floor feels cold to the bare feet, while the carpet at the same temperature feels warm. This is because tile is a better conductor than carpet.

If you hold one end of a metal bar against a piece of ice, the end in your hand will soon become cold. Does cold flow from the ice to your hand?Answer: 22.1.1

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22.1 Conduction

Key Terms conduction, conductors, insulator

Common Misconception Surfaces that feel cooler than others must have a lower temperature.

FACT Surfaces that have been in the same vicinity for some time should all have the same temperature—that of the vicinity! One surface may feel colder than another simply because it is a better conductor.

� Teaching Tip Explain that the physics of the phenomenon of walking harmlessly on red-hot wooden coals with bare feet is the same as the physics that allows one to momentarily place one’s hand in a very hot oven without harm—not because the temperature is low but because air is a poor conductor of heat. Conductivity, not only temperature, must be considered. Explain that since wood has low heat conductivity, it is used for handles on cooking utensils. Wood is a poor conductor, even when it’s red hot. After the surface of a red-hot coal of low-conductivity wood gives up its heat, perhaps to a bare foot that has just stepped on it, more than 1 second passes before appreciable internal energy from the inside reheats the surface. So although the coal has a very high temperature, it gives up very little heat in a brief contact with a cooler surface. The physics of hot-coal walking! The result would be very different indeed should a person try to walk over red-hot pieces of iron. Caution: Warn your students not to try either of these themselves!


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Insulators Liquids and gases generally make poor conductors—they are good insulators. An insulator is any material that is a poor conductor of heat and that delays the transfer of heat. Air is a very good insulator. Porous materials having many small air spaces are good insulators. The good insulating properties of materials such as wool, fur, and feathers are largely due to the air spaces they con-tain. Birds vary their insulation by fluffing their feathers to create air spaces. Be glad that air is a poor conductor, for if it were not, you’d feel quite chilly on a 25°C (77°F) day!

Snowflakes imprison a lot of air in their crystals and are good in-sulators. Snow slows the escape of heat from Earth’s surface, shields Eskimo dwellings from the cold, and provides protection from the cold to animals on cold winter nights. Snow, like the blanket in Figure 22.3, is not a source of heat; it simply prevents any heat from escaping too rapidly.

Heat is energy and is tangible. Cold is not; cold is simply the absence of heat. Strictly speaking, there is no “cold” that passes through a conductor or an insulator. Only heat is transferred. We don’t insulate a home, such as some of those in Figure 22.4, to keep the cold out; we insulate to keep the heat in. If the home becomes colder, it is because heat flows out.

It is important to note that no insulator can totally prevent heat from getting through it. An insulator just reduces the rate at which heat penetrates. Even the best-insulated warm homes in winter will gradually cool. Insulation slows down heat transfer.

CONCEPTCHECK ...

... How does conduction transfer heat?

think!

FIGURE 22.4 �Snow lasts longest on the roof of a well-insulated house. Thus, the snow pat-terns reveal the conduction, or lack of conduction, of heat through the roof. The houses with more snow on the roof are better insulated.

FIGURE 22.3 �A “warm” blanket does not provide you with heat; it simply slows the transfer of your body heat to the surroundings.

You can place your hand into a hot pizza oven for several seconds without harm, whereas you’d never touch the metal inside surfaces for even a second. Why?Answer: 22.1.2


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Place blobs of wax or butter on rods of various metals. Place each rod a similar distance from a hot flame with the blob of wax or butter at the end of each rod farther from the flame. Notice how the heat is conducted along the rods at different rates. This demonstration illustrates the relative conductivities of the different metals.

� Teaching Tip Discuss the poor conductivity of air, and its role in insulating materials, e.g., down-filled sleeping bags and sportswear, spun glass and Styrofoam insulation, fluffy blankets, and even snow.

In conduction, collisions between

particles transfer thermal energy, without any overall transfer of matter.

T e a c h i n g R e s o u r c e s

• Reading and Study Workbook

• PresentationEXPRESS

• Interactive Textbook

• Next-Time Question 22-1

• Conceptual Physics Alive! DVDs Heat Transfer

DemonstrationDemonstration

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You can hold your fingers beside the candle flame withoutharm, but not above the flame. Why?Answer: 22.2

22.2 ConvectionConduction involves the transfer of energy from molecule to mol-ecule. Energy moves from one place to another, but the molecules themselves do not. Another means of heat transfer is by movement of the hotter substance. Air in contact with a hot stove rises and warms the region above. Water heated in a boiler in the basement rises to warm the radiators in the upper floors. This is convection, a means of heat transfer by movement of the heated substance itself, such as by currents in a fluid.

In convection, heat is transferred by movement of the hot-ter substance from one place to another. A simple demonstration illustrates the difference between conduction and convection. With a bit of steel wool, trap a piece of ice at the bottom of a test tube nearly filled with water. Hold the tube by the bottom with your bare hand and place the top in the flame of a Bunsen burner, as shown in Figure 22.5. The water at the top will come to a vigorous boil while the ice below remains unmelted. The hot water at the top is less dense and remains at the top. Any heat that reaches the ice must be trans-ferred by conduction, and we see that water is a poor conductor of heat. If you repeat the experiment, only this time holding the test tube at the top by means of tongs and heating the water from below while the ice floats at the surface, the ice will melt quickly. Heat gets to the top by convection, for the hot water rises to the surface, carry-ing its energy with it to the ice.

Can You See Convection?1. Bring a beaker full of water to a boil.

2. Drop a small amount of dark dye or food coloring into the water. What path does it take as it flows through the water?

3. Think Give three other examples of where you can see the paths of convection.

discover!

think!

� FIGURE 22.5 When the test tube is heated at the top, convection is prevented and heat can reach the ice by con-duction only. Since water is a poor conductor, the top water will boil without melting the ice.

Convection ovens are simply ovens with a fan inside, which speeds up cooking by circulating the warmed air.

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22.2 Convection

Key Termconvection

Do the activity in Figure 22.5, with ice wedged at the bottom of a test tube. Some steel wool will hold the ice at the bottom of the tube. It is impressive to see that the water at the top is brought to a boil while the ice below barely melts! (Convection, or better, the lack of convection, is illustrated here. If heating were at the bottom and the ice cube at the top, the ice would quickly melt.)

discover!

MATERIALS beaker, water, heat source, dark dye

EXPECTED OUTCOME Though the dye disperses quite rapidly, if they watch carefully, students will see that it follows the convection flow pattern.

THINK In smoke, steam, and in the air over a hot stove



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Convection occurs in all fluids, whether liquid or gas. Whether we heat water in a pan or heat air in a room, the process is the same, as shown in Figure 22.6. When the fluid is heated, it expands, becomes less dense, and rises. Warm air or warm water rises for the same reason that a block of wood floats in water and a helium-filled balloon rises in air. In effect, convection is an application of Archimedes’ principle, for the warmer fluid is buoyed upward by denser surrounding fluid. Cooler fluid then moves to the bottom, and the process continues. In this way, convection currents keep a fluid stirred up as it heats. Convection currents also have a large influence on the air in the atmosphere.

Moving Air Convection currents stirring the atmosphere produce winds. Some parts of Earth’s surface absorb heat from the sun more readily than others. The uneven absorption causes uneven heating of the air near the surface and creates convection currents. This phenom-enon is often evident at the seashore. In the daytime the shore warms more easily than the water. Air over the shore rises, and cooler air from above the water takes its place. The result is a sea breeze, as shown in Figure 22.7.

At night the process reverses as the shore cools off more quickly than the water—the warmer air is now over the sea. If you build a fire on the beach you’ll notice that the smoke sweeps inward in the day and seaward at night.

b

FIGURE 22.6 �Convection occurs in all fluids. a. Convection currents transfer heat in air. b. Convection currents transfer heat in liquid.

FIGURE 22.7 �Convection currents are pro-duced by uneven heating.

a. During the day, the land is warmer than the air, and a sea breeze results.

b. At night, the land is cooler than the water, so the air flows in the other direction.


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� Teaching Tip Explain that the lack of convection in orbiting vehicles such as the space shuttle has interesting consequences. For example, in orbit, one cannot light a match without it snuffing out very quickly. This is because of the absence of convection in orbit. Much of the convection in fluids depends on buoyancy, which in turn depends on gravity. In orbit the local effects of gravity are not there (because the shuttle and everything in the shuttle are freely falling around Earth). With no convection, hot gases are not buoyed upward away from a flame but remain around the flame, preventing the entry of needed oxygen. The flame burns out.

� Teaching Tip Discuss the role of convection in climates. Call attention to the shift in winds as shown in Figure 22.7.

Ask Why does the direction of coastal winds change from day to night? Land warms faster than water, and in the day the land and the air above it are warmer than the water and the air above it. The air rises and results in a sea breeze from water to land. At night, the reverse happens.

Ask Is fog a low-altitude cloud, or is a cloud high-altitude fog? They are the same. Both are water-saturated air at different altitudes.


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Cooling Air Rising warm air, like a rising balloon, expands. Why? Because less atmospheric pressure squeezes on it at higher altitudes. As the air expands, it cools—just the opposite of what happens when air is compressed. If you’ve ever compressed air with a tire pump, you probably noticed that the air and pump became quite hot. The oppo-site happens when air expands. Expanding air cools.

We can understand the cooling of expanding air by thinking of molecules of air as tiny balls bouncing against one another. Speed is picked up by a ball when it is hit by another that approaches with a greater speed. When a ball collides with one that is receding, its rebound speed is reduced, as shown in Figure 22.8. Likewise for a table-tennis ball moving toward a paddle; it picks up speed when it hits an approaching paddle, but loses speed when it hits a receding paddle. This also applies to a region of air that is expanding; mol-ecules collide, on the average, with more molecules that are receding than are approaching, as shown in Figure 22.9. Thus, in expanding air, the average speed of the molecules decreases and the air cools.22.2

CONCEPTCHECK ...

... How does convection transfer heat?

Is Your Breath Warm or Cold?1. With your mouth open wide, blow on your hand.

Note the temperature of your breath.

2. Now pucker your lips to make a small opening with your mouth and blow on your hand again. Does the temperature of your breath feel the same?

3. Think In which case does your exhaled breath expand more— when blowing with your mouth open wide or when blowing with your lips puckered? When did the air on your hand feel cooler? Explain why.

discover!

FIGURE 22.8 �

When a molecule collides with a target molecule that is receding, its rebound speed after the collision is less than it was before the collision.

On a much larger scale, convection due to uneven solar heat-ing of Earth’s surface combines with the effects of Earth’s rotation to contribute to overall global wind patterns.

FIGURE 22.9 �Molecules in a region of expanding air collide more often with receding mol-ecules than with approaching ones.

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EXPECTED OUTCOME When the student blows on his or her hand through the smaller gap in the lips, the air feels cooler.

THINK The warm breath expands more when blown through a narrow gap. Expanding air cools and so feels cooler when on the hand.

� Teaching Tip Explain that when a portion of air is heated, it expands and becomes less dense than the surrounding air. The buoyancy force becomes greater than the weight and the warm air rises. When it rises, it expands and cools.

Ask Since warm air rises, why are mountain tops cold and snow covered, and the valleys below relatively warm and green? Shouldn’t it be the other way around? No, nature is correct—as warm air rises, it cools. The cool tops of mountains are a consequence of rising warm air, not a contradiction!

Hold your fingers beside a flame. Ask students why you cannot do the same with your fingers above the flame. (The air above the flame is hotter than the air beside it because of the convection flow.)

In convection, heat is transferred by

movement of the hotter substance from one place to another.


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22.3 RadiationHow does the sun warm Earth’s surface? It can’t be through conduc-tion, because there is 150 million kilometers of virtually nothing between Earth and the sun. Nor can it be by convection, because there is nothing between the sun and Earth to expand and rise. The sun’s heat is transmitted by another process—by radiation.22.3.1 Radiation is energy transmitted by electromagnetic waves, as shown in Figure 22.10. What is being radiated from the sun is primarily light.

Radiant energy is any energy that is transmitted by radiation. In radiation, heat is transmitted in the form of radiant energy,

or electromagnetic waves. Radiant energy includes radio waves, microwaves, infrared radiation (such as the heat from the fireplace in Figure 22.11), visible light, ultraviolet radiation, X-rays, and gamma rays. These types of radiant energy are listed in order of wavelength, from longest to shortest.22.3.2

CONCEPTCHECK ...

... How does radiation transmit heat?

Why Do Glasses Keep You Cool?

1. Sit close to a fire in a fireplace and feel the heat on your closed eyelids.

2. Now slip a pair of glasses over your eyes. How do your eyes feel?

3. Think Why did the glasses cause your eyes to feel a different temperature?

discover!

FIGURE 22.10 �Radiant energy is transmitted as electromagnetic waves.

FIGURE 22.11 �Most of the heat from a fire-place goes up the chimney by convection. The heat that warms us comes to us by radiation.

a. Radio waves send signals through the air.

b. You feel infrared waves as heat.

c. A visible form of radiant energy is light waves.


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22.3 Radiation

Key Termsradiation, radiant energy

� Teaching Tip Discuss the radiation one feels from red-hot coals in a fireplace and how the intensity of radiation decreases with distance. Consider the radiation one feels when stepping from shade to sunshine. The heat one feels is not so much because of the sun’s temperature, but because the sun is big!

� Teaching Tip Explain that Earth is warmer at the equator than at the poles because of greater solar energy per unit area (not because it is closer to the sun). Ask students to compare the rays of sunlight striking Earth with rain that strikes two pieces of paper—one held horizontally and the other held at an angle in the rain. Dispel the misconception that the paper held horizontally must get wetter than the paper held at an angle because it is closer to the clouds!

discover!

MATERIALS heat source, pair of glasses

EXPECTED OUTCOME Students will find that the effects of the heat are less when they put on the glasses.

THINK The lenses do not transmit the infrared waves (or heat) from the fire.

In radiation, heat is transmitted in the

form of radiant energy, or electromagnetic waves.

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22.4 Emission of Radiant EnergyAll substances continuously emit radiant energy in a mixture

of wavelengths. Objects at low temperatures emit long waves, just as long, lazy waves are produced when you shake a rope with little energy as shown in Figure 22.12. Higher-temperature objects emit waves of shorter wavelengths. Objects of everyday temperatures emit waves mostly in the long-wavelength end of the infrared region, which is between radio and light waves. Shorter-wavelength infrared waves absorbed by our skin produce the sensation of heat. Thus, when we speak of heat radiation, we are speaking of infrared radiation.

The fact that all objects in our environment continuously emit infrared radiation underlies infrared thermometers such as the one in Figure 22.13. How nice it is that you simply point the thermometer at something whose temperature you want, press a button, and a digital temperature reading appears. The radiation emitted by the object whose temperature you wish to know provides the reading. Typical classroom infrared thermometers operate in the range of about –30°C to 200°C.

The average frequency f of radiant energy is directly propor-tional to the Kelvin temperature T of the emitter:

People, with a surface temperature of 310 K, emit light in the low-frequency infrared part of the spectrum, which is why we can’t see each other in the dark. If an object is hot enough, some of the radi-ant energy it emits is in the range of visible light. At a temperature of about 500°C an object begins to emit the longest waves we can see, red light. Higher temperatures produce a yellowish light. At about 1500°C all the different waves to which the eye is sensitive are emitted and we see an object as “white hot.” You can see this relationship in the temperatures of the stars. A blue-hot star is hotter than a white-hot star, and a red-hot star is less hot. Since the color blue has nearly twice the frequency of red, a blue-hot star has nearly twice the surface temperature of a red-hot star. The radiant energy emitted by the stars is called stellar radiation.

� FIGURE 22.12 Shorter wavelengths are produced when the rope is shaken more rapidly.

Everything around you both radiates and absorbs energy continuously!

FIGURE 22.13 �An infrared thermometer measures the infrared radiant energy emitted by a body and converts it to temperature.

f T

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22.4 Emission of Radiant Energy

Key Termssteller radiation, terrestrial radiation

Common MisconceptionOnly hot things radiate energy.

FACT All objects continually emit radiant energy in a mixture of wavelengths.

If time is short, Sections 22.4 and 22.5 may be omitted without consequence.


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The surface of the sun has a high temperature (5500°C) and therefore emits radiant energy at a high frequency—much of it in the visible portion of the electromagnetic spectrum. The surface of Earth, by comparison, is relatively cool, and so the radiant energy it emits consists of frequencies lower than those of visible light. Radiant energy that is emitted by Earth is called terrestrial radiation, which is in the form of infrared waves—below our threshold of sight. The source of the sun’s radiant energy involves thermonuclear fusion in its deep interior. In contrast, much of Earth’s supply of energy is fueled by radioactive decay in its interior. So we see that both the sun and Earth glow—the sun at high visible frequencies and Earth at low infrared frequencies. And both glows are related to nuclear processes in their interiors. (We’ll treat radioactive decay in Chapter 39 and thermonuclear fusion in Chapter 40.)

When radiant energy encounters objects, it is partly reflected and partly absorbed. The part that is absorbed increases the internal energy of the objects.

CONCEPTCHECK ...

... What substances emit radiant energy?

22.5 Absorption of Radiant EnergyIf everything is emitting energy, why doesn’t everything finally run out of it? The answer is that everything also absorbs energy from its environment.

Absorption and Emission For example, a book sitting on your desk is both absorbing and radiating energy at the same rate. It is in thermal equilibrium with its environment. Imagine that you move the book out into the bright sunshine. If the book’s temperature doesn’t change, it radiates the same amount of energy as before. But because the sun shines on it, the book absorbs more energy than it radiates. Its temperature increases. As the book gets hotter, it radiates more energy, eventually reaching a new thermal equilibrium. Then it radi-ates as much energy as it receives. In the sunshine the book remains at this new higher temperature.

If you move the book back indoors, the opposite process occurs. The hot book initially radiates more energy than it receives from its surroundings. So it cools. In cooling, it radiates less energy. At a sufficiently lowered temperature it radiates no more energy than it receives from the room. It stops cooling. It has reached thermal equi-librium again.

think!Why is it that light radi-ated by the sun is yellow-ish, but light radiated by Earth is infrared?Answer: 22.4

A hot pizza placed out-side on a winter day is a net emitter. The same pizza placed in a hotter oven is a net absorber.


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All substances continuously emit

radiant energy in a mixture of wavelengths.





22.5 Absorption of Radiant Energy

� Teaching Tip Explain that some materials absorb better than others. The good absorbers are easy to spot, because they absorb visible radiation and so appear black.

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Make the distinction that objects don’t absorb because they’re black, but are black because they absorb so well. Cause precedes effect.

� Teaching Tip Explain that though there are various colors of eyes, all have one thing in common: The pupils are black. This is because the light that enters the eyes through the pupils is absorbed. (An exception to this is that flash photography can sometimes produce photos that show people with red eyes. This happens because the bright flash can be reflected from the retina of the eye if the eye does not have time to adjust to the bright light. Some cameras have a “red-eye reduction” setting. This setting produces multiple flashes that give the eyes time to adjust before the photograph is taken.)


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Good emitters of radiant energy are also good absorbers; poor emitters are poor absorbers. For example, a radio antenna con-structed to be a good emitter of radio waves is also, by its very design, a good receiver (absorber) of them. A poorly designed transmitting antenna is also a poor receiver.

A blacktop pavement and dark automobile body may remain hotter than their surroundings on a hot day. But at nightfall these dark objects cool faster! Sooner or later, all objects in thermal contact come to thermal equilibrium. So a dark object that absorbs radiant energy well emits radiation equally well.22.5

Absorption and Reflection Absorption and reflection are opposite processes. Therefore, a good absorber of radiant energy reflects very little radiant energy, including the range of radiant energy we call light. So a good absorber appears dark. A perfect absorber reflects no radiant energy and appears perfectly black. The pupil of the eye, for example, allows radiant energy to enter with no reflection and appears perfectly black. (The red “pupils” that appear in some flash portraits are from direct light reflected off the retina at the back of the eyeball.)

Look at the open ends of pipes in a stack. The holes appear black. Look at open doorways or windows of distant houses in the daytime, and they too look black. Openings appear black, as in Figure 22.14, because the radiant energy that enters is reflected from the inside walls many times and is partly absorbed at each reflection until very little or none remains to come back out. You can see this illustrated in Figure 22.15.

think!

If a good absorber of radiant energy were a poor emitter, how would its temperature compare with its surroundings?Answer: 22.5

� FIGURE 22.14Even though the interior of the box has been painted white, the hole looks black.

FIGURE 22.15 �Radiant energy that enters an opening has little chance of leaving before it is completely absorbed.

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� Teaching Tip Emphasize that everything emits radiation—everything that has any temperature—but everything does not become progressively cooler because everything also absorbs radiation. We live in a sea of radiation, everything emitting and everything absorbing. When emission rate equals absorption rate, temperature remains constant. Some materials, because of their molecular design, emit better than others.

Cut a hole in a sturdy box as shown in Figure 22.14. Paint the interior of the box white. When the box is open, the interior, as seen through the hole, appears white. However, when the box is closed, the interior appears black because the light that enters through the hole is reflected from the inside walls many times, and is partly absorbed at each reflection until very little (or none) comes back out.

Good emitters of radiant energy are

also good absorbers; poor emitters are poor absorbers.


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Good reflectors, on the other hand, are poor absorbers, like the toaster in Figure 22.16. Light-colored objects reflect more light and heat than dark-colored ones. In summer, light-colored clothing keeps people cooler.

On a sunny day Earth’s surface is a net absorber. At night it is a net emitter. On a cloudless night its “surroundings” are the frigid depths of space and cooling is faster than on a cloudy night, where the surroundings are nearby clouds. Record-breaking cold nights occur when the skies are clear.

The next time you’re in the direct light of the sun, step in and out of the shade. You’ll note the difference in the radiant energy you receive. Then think about the enormous amount of energy the sun emits to reach you some 150,000,000 kilometers distant. Is the sun unusually hot? Not as hot as some welding torches in auto shops. You feel the sun’s heat not because it is hot (which it is), but primar-ily because it is big. Really big!

CONCEPTCHECK ...

... How does an object’s emission rate compare with its absorption rate?

22.6 Newton’s Law of CoolingAn object hotter than its surroundings eventually cools to match the surrounding temperature. When considering how quickly (or slowly) something cools, we speak of its rate of cooling—how many degrees change per unit of time.

The rate of cooling of an object depends on how much hotter the object is than the surroundings. The colder an object’s sur-roundings, the faster the object will cool. The temperature change per minute of a hot apple pie will be more if the hot pie is put in a cold freezer than if put on the kitchen table because the temperature difference is greater. A warm home will lose heat to the cold outside at a greater rate when there is a larger difference between the inside and outside temperatures. Keeping the inside of your home at a high temperature on a cold day is more costly than keeping it at a lower temperature. If you keep the temperature difference small, the rate of cooling will be correspondingly low.

think!

� FIGURE 22.16Anything with a mirrorlike surface reflects most of the radiant energy it encounters. That’s why it is a poor absorber of radiant energy.

Since a hot cup of tea loses heat more rapidly than a lukewarm cup of tea, would it be correct to say that a hot cup of tea will cool to room temper-ature before a lukewarm cup of tea will? Explain.Answer: 22.6

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22.6 Newton’s Law of Cooling

Key TermNewton’s law of cooling

� Teaching Tip Relate the rate of cooling to the black and silver containers that are cooling and warming. We see the difference between a proportionality sign and an equals sign for the formula here, for the rate of cooling or warming is proportional not only to the difference in temperatures but also to the differences in the “emissivities” of the surfaces.

� Teaching Tip Point out that D means “the change in.”

� Teaching Tip Relate Newton’s law of cooling to Think and Explain 34 (cream in the coffee), 35 (cooling a beverage in the fridge), and 37 (thermostat on a cold day). These questions make excellent discussion topics.

Fill a beaker with warm water and a similar beaker with boiling water. Record the temperatures of the two beakers at regular intervals as they cool to room temperature. Note the different rates of cooling.

Ask Does Newton’s law of cooling apply to the warming of a cold object in a warm environment? Yes

The colder an object’s surroundings, the

faster the object will cool.


• Laboratory Manual 59

• Probeware Lab Manual 10


CONCEPTCHECK ...

...CONCEPTCHECK ...

...



This principle is known as Newton’s law of cooling. (Guess who is credited with discovering this?) Newton’s law of cooling states that the rate of cooling of an object—whether by conduction, convection, or radiation—is approximately proportional to the temperature dif-ference DT between the object and its surroundings:

rate of cooling T

Newton’s law of cooling also holds for heating. If an object is cooler than its surroundings, its rate of warming up is also propor-tional to DT. Frozen food warms up faster in a warmer room.

CONCEPTCHECK ...

... What causes an object to cool faster?

22.7 Global Warming and the Greenhouse Effect

An automobile sitting in the bright sun on a hot day with its win-dows rolled up can get very hot inside—appreciably hotter than the outside air. This is an example of the greenhouse effect, so named for the same temperature-raising effect in florists’ glass greenhouses. The greenhouse effect is the warming of a planet’s surface due to the trapping of radiation by the planet’s atmo-sphere. Understanding the greenhouse effect requires knowing about two concepts.

Causes of the Greenhouse Effect The first concept has been previously stated—that all things radiate, and the frequency and wavelength of radiation depends on the temperature of the object emitting the radiation. High-temperature objects radiate short waves; low-temperature objects radiate long waves. The second concept we need to know is that the transparency of things such as air and glass depends on the wavelength of radiation. Air is transparent to both infrared (long) waves and visible (short) waves, unless the air con-tains excess carbon dioxide and water vapor, in which case it absorbs infrared waves. Glass is transparent to visible light waves but absorbs infrared waves. (This is discussed later, in Chapter 27.)

Now to why that car gets so hot in bright sunlight: Compared with the car, the sun’s temperature is very high. This means the wavelengths of waves the sun radiates are very short. These short waves easily pass through both Earth’s atmosphere and the glass windows of the car. So energy from the sun gets into the car interior, where, except for some reflection, it is absorbed. The interior of the car warms up.

Newton’s law of cool-ing is an empirical rela-tionship and not a fundamental law like Newton’s laws of motion.

EcologistThe greenhouse effect is of particular con-cern to the ecologist. Ecologists study the relationship between the living and nonliving factors in an ecosys-tem. Ecologists need to use physics when they analyze changes in atmospheric tem-peratures over time. Understanding the relationships between energy, temperature, and greenhouse gases enables ecologists to identify processes that interfere with Earth’s natural processes. Ecologists can find opportunities in gov-ernment and privately funded projects.

Physics on the Job

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22.7 Global Warming and the Greenhouse Effect

Key Termgreenhouse effect

Common MisconceptionThe greenhouse effect on Earth is undesirable.

FACT The greenhouse effect provides a temperature that supports life as we know it. Without it, the average temperature of Earth would be about 218ºC. What is undesirable is an increase in this effect.

� Teaching Tip Discuss the greenhouse effect, first for florists’ greenhouses, and then for Earth’s atmosphere. The key idea is that the medium (glass for the greenhouse, atmosphere for Earth) is transparent to high-frequency (short wavelength) electromagnetic waves but opaque to low-frequency (long wavelength) electromagnetic waves.

� Teaching Tip Point out that Earth’s atmosphere is primarily warmed by terrestrial radiation, not solar radiation. That’s why air near the ground is warmer than air above. The opposite would be the case if the sun were the primary warmer of air!

� Teaching Tip Explain that terrestrial radiation also cools Earth, especially on clear nights. Clouds reradiate terrestrial radiation. Farmers sometimes use smudge pots in orchards to create a cloud close to the ground. This enables terrestrial radiation (absorbed by the smoke) to be reradiated to the ground resulting in a longer cooling time for the ground. This helps crops survive nights without freezing.


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The car interior radiates its own waves, but since it is not as hot as the sun, the radiated waves are longer. The reradiated long waves encounter glass windows that aren’t transparent to them. So most of the reradiated energy remains in the car, which makes the car’s interior even warmer. (That is why leaving your pet in a car on a hot sunny day is a no-no.) As hot as the interior gets, it won’t be hot enough to radiate waves that can pass through glass (unless it glows red or white hot!).

The same effect occurs in Earth’s atmosphere, which is transpar-ent to solar radiation, as shown in Figure 22.17. The surface of Earth absorbs this energy, and reradiates part of this at longer wavelengths, as shown in Figure 22.18. Energy that Earth radiates is called terrestrial radiation. Atmospheric gases (mainly water vapor, carbon dioxide, and methane) absorb and re-emit much of this long-wavelength terrestrial radiation back to Earth. So the long-wavelength radia-tion that cannot escape Earth’s atmosphere warms Earth. This global warming process is very nice, for Earth would be a frigid –18°C oth-erwise. Our present environmental concern is that increased levels of carbon dioxide and other atmospheric gases in the atmosphere may further increase the temperature and produce a new thermal balance unfavorable to the biosphere.22.7

Consequences of the Greenhouse Effect Averaged over a few years, the amount of solar radiation that strikes Earth exactly balances the terrestrial radiation Earth emits into space. This bal-ance results in the average temperature of Earth—a temperature that presently supports life as we know it. We now see that over a period of decades, Earth’s average temperature can be changed—by natural causes and also by human activity.

FIGURE 22.17 �Earth’s temperature depends on the energy balance between incoming solar radiation and outgoing terrestrial radiation.

FIGURE 22.18 �Earth’s atmosphere acts as a sort of one-way valve. It allows visible light from the sun in, but because of its water vapor and carbon dioxide content, it prevents terrestrial radiation from leaving.


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� Teaching Tip Briefly discuss the idea of wave frequency. Review Figure 22.12, showing the relationship of wave frequency to wavelength. The origin of electromagnetic waves is vibrating electrons in matter. Explain that the frequency of electromagnetic radiation emitted by a source increases with the temperature of the source. Electrons vibrate at greater frequencies in hot matter than in cold matter. The sun is so hot that the frequency of electromagnetic waves it emits is high enough to activate our visible receptors. Write f , T in big letters to indicate large values of both frequency and temperature. This radiation is visible light. It is absorbed by Earth, which in turn emits its own radiation. Write f , T in small letters to indicate low values of both frequency and temperature.


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Adding materials such as those from the burning of fossil fuels to the atmosphere changes the absorption and reflection of solar radiation. Except where the source of energy is solar, wind, or water, increased energy consumption on Earth adds heat. These activities can change the radiative balance and change Earth’s average temperature.

The near unanimous view of climate scientists is that human activity is a main driver of global warming and climate change. Thisview is the outcome of a long, painstaking road of successively more sophisticated climate models.

Confidence in the models, run by more and more sophisticated computers, is bolstered by an intriguing outcome: data gathered ear-lier about Earth and its atmosphere that were fed into the models successfully “predicted” the recent climate of the past twenty years.

Although water vapor is the main greenhouse gas, CO2 is the gas

most rapidly increasing in the atmosphere. Concern doesn’t stop there, for further warming by CO

2 can produce more water vapor as

well. The greater concern is the combination of growing amounts of both these greenhouse gases.

An important credo is “You can never change only one thing.” Change one thing, and you change another. Burn fossil fuels and you warm the planet. Increase global temperature and you increase storm activity. Changed climate means changed rainfall patterns, changed coastal boundaries, and changes in insect breeding patterns. How these changes upon changes will play out, we don’t know.

What we do know is that energy consumption is related to popula-tion size. We are seriously questioning the idea of continued growth. (Please take the time to read Appendix E, “Exponential Growth and Doubling Time”—very important stuff.)

CONCEPTCHECK ...

... How does human activity affect climate change?

� FIGURE 22.19Shorter-wavelength radiant energy from the sun enters through the glass roof of the greenhouse. The soil emits long-wavelength radi-ant energy, which is unable to pass through the glass. Income exceeds outgo, so the interior is warmed.

Volcanoes put more particulate matter into the atmosphere than industries and all human activity. But when it comes to carbon dioxide, the impact of humans is big enough to affect climate.

For:Visit:Web Code: –

Links on global warming www.SciLinks.org csn 2207

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The near unanimous view of climate

scientists is that human activity is a main driver of global warming and climate change.



• Laboratory Manual 60

• Transparency 43




• Conceptual Physics Alive! DVDs Heat Radiation

CONCEPTCHECK ...

...CONCEPTCHECK ...

...

The carbon that is spewed by burning is the same carbon that is absorbed by tree growth. So a realistic step in the solution to the increased greenhouse effect is simply to grow more trees (while decreasing the rate at which they are cut down)! This would not be an end-all to the problem, however, because the carbon returns to the biosphere when the trees ultimately decay.


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Concept Summary ••••••

• In conduction, collisions between parti-cles transfer thermal energy, without any overall transfer of matter.

• In convection, heat is transferred by movement of the hotter substance from one place to another.

• In radiation, heat is transmitted in the form of radiant energy, or electromag-netic waves.

• All substances continuously emit radiant energy in a mixture of wavelengths.

• Good emitters of radiant energy are also good absorbers; poor emitters are poor absorbers.

• The colder an object’s surroundings, the faster the object will cool.

• The near unanimous view of climate scientists is that human activity is a main driver of global warming and climate change.

Key Terms ••••••

conduction (p. 431)

conductors (p. 431)

insulator (p. 432)

convection (p. 433)

radiation (p. 436)

radiant energy (p. 436)

stellar radiation (p. 437)

terrestrial radiation (p. 438)

Newton’s law of cooling (p. 441)

greenhouse effect(p. 441)

22.1.1 Cold does not flow from the ice to your hand. Heat flows from your hand to the ice. The metal is cold to your touch because you are transferring heat to the metal.

22.1.2 Air is a poor conductor, so the rate of heat flow from the hot air to your relatively cool hand is low. But touching the metal parts is a different story. Metal conducts heat very well, and a lot of heat in a short time is conducted into your hand when thermal contact is made.

22.2 Heat travels upward by convection. Air is a poor conductor, so very little heat travels sideways.

22.4 The answer is that the sun has a higher temperature than Earth. Earth radiates in the infrared because its temperature is relatively low compared to the sun.

22.5 If a good absorber were not also a good emitter, there would be a net absorption of radiant energy and the temperature of a good absorber would remain higher than the temperature of the surroundings. Things around us approach a common temperature only because good absorbers are, by their very nature, also good emit-ters.

22.6 No! Although the rate of cooling is greater for the hotter cup, it has farther to cool to reach thermal equilibrium. The extra time is equal to the time the hotter cup takes to cool to the initial temperature of the luke-warm cup of tea. Cooling rate and cooling time are not the same.

think! Answers

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REVIEW


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• Conceptual Physics Alive! DVDs Heat Transfer; Heat Radiation


CHAPTER 22 HEAT TRANSFER 445CHAPTER 22 HEAT TRANSFER 445

ASSESS

Check Concepts ••••••

Section 22.1 1. What is the role of “loose” electrons in

heat conductors?

2. Why does a piece of room-temperature metal feel cooler to the touch than paper, wood, or cloth?

3. What is the difference between a conductor and an insulator?

4. Why are materials such as wood, fur, feathers, and even snow good insulators?

5. What is meant by saying that cold is not a tangible thing?

Section 22.2 6. How does Archimedes’ principle relate to

convection?

7. Why does the direction of coastal winds change from day to night?

8. How does the temperature of a gas change when it is compressed? When it expands?

Section 22.3 9. Dominoes are placed upright in a row, one

next to another. When one is tipped over, it knocks against its neighbor, which does the same in cascade fashion until the whole row collapses. Which of the three types of heat transfer is this most similar to?

10. What is radiant energy?

Section 22.4 11. How does the predominant frequency of

radiant energy vary with the absolute tem-perature of the radiating source?

12. Is a good absorber of radiation a good emit-ter or a poor emitter?

13. Which will normally cool faster, a black pot of hot tea or a silvered pot of hot tea?

Section 22.5 14. Why does a good absorber of radiant

energy appear black?

15. Why do eye pupils appear black?

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ASSESS

Check Concepts 1. They transfer energy through

the conducting material.

2. It is a better conductor and draws more energy from a person’s skin.

3. A conductor moves heat quickly, whereas an insulator moves heat slowly.

4. They have many air spaces and air is a good insulator.

5. Cold is the absence of heat.

6. Warmed air is less dense and is buoyed upward.

7. The land is warmer than the water during the day, so the air rises. The opposite happens at night.

8. Increases; decreases, if adiabatic

9. Conduction

10. The energy in electromagnetic waves

11. Higher temperature sources produce waves of higher frequencies.

12. Good; otherwise there would be no thermal equilibrium.

13. Black is a better emitter, and so will cool faster.

14. It absorbs rather than reflects light.

15. Light entering is absorbed.




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ASSESS (continued)

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Section 22.6 16. Which will undergo the greater rate of cool-

ing, a red-hot poker in a warm oven or a red-hot poker in a cold room (or do both cool at the same rate)?

17. Does Newton’s law of cooling apply to warming as well as to cooling?

Section 22.7 18. What is terrestrial radiation?

19. Solar radiant energy is composed of short waves, yet terrestrial radiation is composed of relatively longer waves. Why?

20. a. What does it mean to say that the green-house effect is like a one-way valve?

b. Is the greenhouse effect more pronounced for florists’ greenhouses or for Earth’s surface?

Think and Explain ••••••

21. At what common temperature will both a block of wood and a piece of metal feel neither hot nor cool when you touch them with your hand?

22. If you stick a metal rod in a snowbank, the end in your hand will soon become cold. Does cold flow from the snow to your hand?

23. Wood is a better insulator than glass. Yet fiberglass is commonly used as an insulator in wooden buildings. Explain.

24. Visit a snow-covered cemetery and note that the snow does not slope upward against the gravestones but, instead, forms depressions around them, as shown. Make a hypothesis explaining why this is so.

25. Wood is a poor conductor, which means that heat is slow to transfer—even when wood is very hot. Why can firewalkers safely walk barefoot on red-hot wooden coals, but not safely walk barefoot on red-hot pieces of iron?

26. When a space shuttle is in orbit and there appears to be no gravity in the cabin, why can a candle not stay lit?

27. A friend says that, in a mixture of gases in thermal equilibrium, the molecules have the same average kinetic energy. Do you agree or disagree? Defend your answer.

28. A friend says that, in a mixture of gases in thermal equilibrium, the molecules have the same average speed. Do you agree or disagree? Defend your answer.

29. In a mixture of hydrogen and oxygen gases at the same temperature, which molecules move faster? Why?


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16. Cold room; greater DT

17. Yes

18. Radiant energy emitted by Earth

19. Earth’s temperature is lower, so it produces waves of longer length.

20. a. Only short wavelengths pass back out. b. Earth

Think and Explain 21. Same temperature as your

hand

22. No, energy flows from your hand via the rod to the snow.

23. Fiberglass is a good insulator because of trapped air.

24. Heat from warm ground conducted by stone melts snow in contact.

25. Iron transfers internal energy very fast.

26. No convection; the CO2 around the candle cuts off the oxygen supply.

27. Agree; at thermal equilibrium, gases have same temperature, which means same average KE.

28. Disagree; having same KE doesn’t mean same speed, unless all molecules have equal masses.

29. H2 molecules are faster. KE 5 1/2 mv2. For fixed KE, less mass means more speed.


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ASSESS


30. Which atoms have the greater average speed in a mixture, U-238 or U-235? How would this affect diffusion through a porous mem-brane of otherwise identical gases made from these isotopes?

31. Notice that a desk lamp often has small holes near the top of the metal lampshade. How do these holes keep the lamp cool?

32. Turn an incandescent lamp on and off quickly while you are standing near it. You feel its heat, but you find when you touch the bulb that it is not hot. Explain why you felt heat from the lamp.

33. In Montana, the state highway department spreads coal dust on top of snow. When the sun comes out, the snow rapidly melts. Why?

34. Suppose that a person at a restaurant is served coffee before he or she is ready to drink it. In order that the coffee be hot-test when the person is ready for it, should cream be added to it right away or just before it is drunk?

35. Will a can of beverage cool just as fast in the regular part of the refrigerator as it will in the freezer compartment? (What physical law do you think about in answering this?)

36. Is it important to convert temperatures to the Kelvin scale when we use Newton’s law of cooling? Why or why not?

37. If you wish to save fuel on a cold day, and you’re going to leave your warm house for a half hour or so, should you turn your thermostat down a few degrees, down all the way, or leave it at room temperature?

38. Why is whitewash sometimes applied to the glass of florists’ greenhouses? Would you expect this practice to be more prevalent in winter or summer months?

39. If the composition of the upper atmosphere were changed so that it permitted a greater amount of terrestrial radiation to escape, what effect would this have on Earth’s cli-mate? Conversely, what would be the effect if the upper atmosphere reduced the escape of terrestrial radiation?

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30. Less mass means higher speed, so the U-235 has a greater average speed. Lighter and slightly faster U-235 diffuse better.

31. They allow convection.

32. Heat received is from radiation.

33. The dust absorbs solar energy and melts the snow.

34. Right away, because whiter coffee won’t radiate and cool so quickly; also, the higher the temperature of the coffee compared with its surroundings, the greater will be the rate of cooling. And, increasing the amount of liquid for the same surface area slows the cooling.

35. No, it cools faster in the freezer because its rate of cooling is proportional to the difference in temperature.

36. Not important; either gives same differences.

37. Off altogether; the amount of heat energy, and thus fuel, required to raise the temperature inside again is small compared with the amount of heat energy that continually escapes.

38. Whitewash reduces incoming radiant energy by reflection; good in summer.

39. Earth’s temperature would decrease and cooling of the climate would result. Conversely, warming of Earth’s climate would result.




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ASSESS (continued)

448

Think and Solve ••••••

40. An automobile cooling system holds 12 liters of water. Show that when its temperature rises from 20°C to 70°C, it absorbs 60 kilocalories.

41. Austin places a 50-g aluminum ball into an insulated cup containing 75 g of water at 20°C. The ball and water reach an equilib-rium temperature of 37°C. Austin makes some calculations and reports that the initial temperature of the ball must have been slightly more than 155°C. Do your calculations agree? (Ignore heat transfer to the cup.)

42. Decay of radioactive isotopes of thorium and uranium in granite and other rocks in Earth’s interior provides sufficient energy to keep the interior molten, heat lava, and pro-vide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. Show that 13.3 million years are required for a chunk of thermally insulated granite to increase 500°C in tem-perature. (Use 800 J/kg°C for the specific heat capacity of granite.)

43. In a lab you burn a 0.6-g peanut beneath 50 g of water. Heat from the peanut increases the water temperature from 22°C to 50°C.

a. Assuming 40% efficiency, show that the food value of the peanut is 3500 calories (3.5 Calories).

b. What is the food value in Calories per gram?

44. Pounding a nail into wood makes the nail warmer. Suppose a hammer exerts an aver-age force of 500 N on a 6-cm nail whose mass is 5 grams when it drives into a piece of wood. Work is done on the nail and it be-comes hotter. If all the heat goes to the nail, show that its increase in temperature is slightly more than 13°C. (Use 450 J/kg°C for the specific heat capacity of the nail.)


448

Think and Solve 40. 12 L is 12 kg 5 12,000 g. Q 5

mcDT 5 (12,000 g)(1.0 cal/g°C) 3 (70°C 2 20°C) 5 600,000 cal.

41. Yes; mcDTball lost by ball 5 mcDTwater gained by water.

(50 g)(0.215 cal/g°C)(T 2 37°C) 5 (75 g)(1.0 cal/g°C) 3

(37°C 2 20°C); T 5 155.6°C.

42. From Q 5 mcDT, Q/m 5 cDT 5 (800 J/kg°C)(500°C) 5 400,000 J/kg. Time required is (400,000 J/kg)/(0.03 J/kg?yr) 5 13.3 million years.

43. a. Q 5 mcDT 5 (50.0 g) 3 (1.0 cal/g C°)(50°C 2 22°C) 5 1400 cal. At 40% efficiency 0.4 3 energy from peanut raises water temperature. Heat content is 1400 cal/0.4 5 3500 cal (3.5 Cal).b. Food value is 3.5 Cal/0.6 g 5 5.8 C/g.

44. Work done by hammer is F 3 d; temp change of nail from Q 5 mcDT. (5 grams 5 0.005 kg; 6 cm 5 0.06 m.) Then F 3 d 5 500 N 3 0.06 m

5 30 J, and 30 J 5 (0.005 kg) 3 (450 J/kg°C)(DT). Then DT 5

30 J/(0.005 kg 3 450 J/kg°C) 5 13.3°C.


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ASSESS


More Problem-Solving PracticeAppendix F

45. At a certain location, the solar power per unit area reaching Earth’s surface is 200 W/m2, averaged over a 24-hour day. Consider a house with an average power requirement of 3 kW with solar panels on the roof that convert solar power to electric power with 25 percent efficiency. Show that a solar collector area of 60 square meters will meet the 3 kW requirement.

Activities ••••••

46. Hold the bottom end of a test tube full of cold water in your hand. Heat the top part in a flame until the water boils. The fact that you can still hold the bottom shows that water is a poor conductor of heat. This is even more dramatic when you wedge chunks of ice at the bottom; then the water above can be brought to a boil without melting the ice. Try it and see.

47. If you live where there is snow, do as Benja-min Franklin did more than two centuries ago and lay samples of light and dark cloth on the snow. (If you don’t live in a snowy area, try this using ice cubes.) Describe dif-ferences in the rate of melting beneath the cloths.

48. Wrap a piece of paper around a thick metal bar and place it in a flame. Note that the paper will not catch fire. Can you figure out why? (Hint: Paper generally will not ignite until its temperature reaches about 230°C.)

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45. At 25% efficiency, each square meter of collector supplies 50 W on average. So need (3000 W)/(50 W/m2) 5 60 m2 of collector area.

Activities 46. This is a good demo to show.

Steel wool can be used to wedge the ice at the bottom of the test tube. Be sure to put the top part of the water-filled tube in the flame.

47. The snow under the dark cloth melts faster. The dark cloth absorbs more energy from the sun.

48. The metal must reach 230°C for the paper to do the same.


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