energy - john wiley & sons

= applications of the great ideadiscussed in this chapter

= other applications, some of whichare discussed in other chapters

PHYSICS

When a bowlerbowls a strike, someof the bowling ball’s

kinetic energy istransferred to scatter

the pins.

BIOLOGY

Plants convertthe radiant energyof sunlight into the

chemical energynecessary to sustainlife for organisms at

every trophiclevel.

CHEMISTRY

Stored chemicalenergy in fossil

fuels (coal, gas, andoil) is converted toheat energy during

the process ofburning.

ENVIRONMENT

Wind and rain obtaintheir energy throughthe conservation of

the Sun’s radiantenergy. (Ch. 18)

Vigorous exerciseconverts the body’s

stored chemicalenergy into kineticenergy and heat.

HEALTH & SAFETY

During anearthquake,

elastic potentialenergy stored in rockis suddenly convertedto kinetic energy as

the rock breaks.(Ch. 17)

GEOLOGY

Stars convert theelement hydrogen

into helium andradiate energy

through the processof nuclear fusion.

(Ch. 14)

ASTRONOMY

A newgeneration ofpowerful and

lightweight batteries thatconvert chemical

potential energy intoelectricity is needed to

power electric cars.(Ch. 15)

TECHNOLOGY

GREAT IDEA

The many differentforms of energy are

interchangeable, and thetotal amount of energyin an isolated system

is conserved.

3Energy

Why must animals eat to stay alive?

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Hundreds of millions of years ago, a bit of energy was generated in the core of the Sun.For thousands of years, that energy percolated outward to the Sun’s surface; then, in amere eight minutes, it made the trip through empty space to Earth in the form of sun-light. Unlike other bits of energy that were reflected back into space by clouds or sim-ply served to warm Earth’s soil, this particular energy was absorbed by organisms knownas algae floating on the warm ocean surface.

Through the process of photosynthesis (see Chapter 22),these algae transformed the Sun’s energy into the chemical energyneeded to hold together its complex molecules. Eventually thesealgae died and sank to the bottom of the ocean, where, over longeons, they were buried deeper and deeper. Under the influence ofpressure and heat, the dead algae were eventually transformedinto fossil fuel—petroleum.

Then, a short while ago, engineers pumped that petroleumwith its stored energy up out of the ground. At a refinery, thelarge molecules were broken down into gasoline, and the gasolinewas shipped to your town. A few days ago you put it into the tankof your car. The last time you drove you burned that gasoline,converting the stored energy into the engine’s mechanical energythat moved your car. When you parked the car, the hot engineslowly cooled, and that bit of heat, after having been delayed fora few hundred million years, was radiated out into space to con-

The daily routine begins. You turn on the overhead light, squinting asyour eyes adjust to the brightness. Then you take your morning

shower; it feels great to just stand there and let the hot water wash over you.Soon you’ll boil water for coffee, eat a hearty breakfast, and then drive tothe beach.

During every one of these ordinary actions—indeed, every momentof every day—you use energy in its many varied and interchangeableforms.

Science Through the Day Morning Routine

The Great Chain of Energy

This oil pump in Colorado is bringingup solar energy stored millions ofyears ago.

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tinue its voyage away from the solar system. As you read these words, the energy youfreed yesterday has long since left the solar system and is out in the depths of interstel-lar space.

Scientifically SpeakingAt this moment, trillions of cells in your body are hard at work turning the chemicalenergy of the food you ate yesterday into the chemical energy that will keep you alivetoday. Energy in the atmosphere generates sweeping winds and powerful storms, whilethe ocean’s energy drives mighty currents and incessant tides. Meanwhile, deep withinEarth, energy in the form of heat is moving the continent on which you are standing.

All situations where energy is expended have one thing in common. If you look atthe event closely enough, you will find that, in accord with Newton’s laws of motion(Chapter 2), a force is being exerted on an object to make it move. When your car burnsgasoline, the fuel’s energy ultimately turns the wheels of your car, which then exert aforce on the road; the road exerts an equal and opposite force on the car, pushing it for-ward. When you climb the stairs, your muscles exert a force that lifts you upward againstgravity. Even in your body’s cells, a force is exerted on molecules in chemical reactions.Energy thus is intimately connected with the application of a force.

In everyday conversation we speak of someone having lots of energy, but in sciencethe term energy has a precise definition that is somewhat different from the ordinarymeaning. To see what scientists mean when they talk about energy, we must first intro-duce the familiar concept of work.

WorkScientists say that work is done whenever a force is exerted over a distance. Pick up thisbook and raise it a foot. Your muscles applied a force equal to the weight of the bookover a distance of a foot. You did work.

This definition of work differs considerably from everyday usage. From a physicist’spoint of view, if you accidentally drive into a tree and smash your fender, work has beendone because a force deformed the car’s metal a measurable distance. On the otherhand, a physicist would say that you haven’t done any work if you spend an hour in afutile effort to move a large boulder, no matter how tired you get. Even though youhave exerted a considerable force, the distance over which you exerted it is negligible.

Physicists provide an exact mathematical definition of their notion of work.

� In words: Work is equal to the force that is exerted times the distanceover which it is exerted.

� In equation form:

work (joules) = force (newtons) × distance (meters)

where a joule is the unit of work, as defined in the following paragraph.� In symbols:

W = F × d

In practical terms, even a small force can do a lot of work if it is exertedover a long distance.

As you might expect from this equation, units of work are equal to aforce unit times a distance unit (Figure 3-1). In the metric system of units,where force is measured in newtons (abbreviated N), work is measured innewton-meters (N-m). For reference, a Newton is roughly equal to theforce exerted on your hand by a baseball (or by 7 Fig Newtons!).

This unit is given the special name “joule,” after the English scientistJames Prescott Joule (1818–1889), one of the first people to understand

The Great Chain of Energy | 51

Work is done when a force is exertedover a distance.

d(m)F(N)

• Figure 3-1 A weightlifter appliesa force (in Newtons) over a distance(in meters).

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the properties of energy. One joule is defined as the amount of work done when a forceof one newton is exerted through a distance of one meter.

1 joule of work = 1 N of force × 1 m of distance

In the English system of units (see Appendix B), where force is measured in pounds,work is measured in a unit called the foot-pound (usually abbreviated ft-lb).

52 | CHAPTER 3 | Energy

Working Against GravityHow much work do you do when you carry a 20-kg television set up a flight of stairs(about 4 meters)?

Reasoning: We must first calculate the force exerted by a 20-kg mass before we can deter-mine work. From the previous chapter, we know that to lift a 20-kg mass against the accel-eration of gravity (9.8 m/s2) requires a force given by

force = mass × g= 20 kg × 9.8 m/s2

= 196 newtons

Solution: Then, from the equation for work,

work = force × distance= 196 N × 4m= 784 joules

EXAMPLE 3-1

EnergyEnergy is defined as the ability to do work. If a system is capable of exerting a forceover a distance, then that system possesses energy. The amount of a system’s energy,which can be recorded in joules or foot-pounds (the same units used for work), is ameasure of how much work the system might do. When a system runs out of energy, itsimply can’t do any more work.

PowerPower provides a measure of both the amount of work done (or, equivalently, theamount of energy expended) and the time it takes to do that work. In order to com-plete a physical task quickly, you must generate more power than if you do the sametask slowly. If you run up a flight of stairs, your muscles need to generate more powerthan they would if you walked up the same flight, even though you expend the sameamount of energy in either case. A power hitter in baseball swings the bat faster, con-verting the chemical energy in his muscles to kinetic energy more quickly than mostother players.

Scientists define power as the rate at which work is done, or the rate at whichenergy is expended.

� In words: Power is the amount of work done divided by the time it takes to do thatwork.� In equation form:

where the watt is the unit of power, as defined in the following paragraph.

work (joules)power (watts) = ———————

time (seconds)

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� In symbols:

If you do more work in a given span of time, or do a task in a shortertime, you use more power.

In the metric system, power is measured in watts, after James Watt(1736–1819), the Scottish inventor who developed the modern steamengine that powered the Industrial Revolution. The watt, a unit ofmeasurement that you probably encounter every day, is defined as theexpenditure of 1 joule of energy in 1 second:

The unit of 1000 watts (corresponding to an expenditure of 1000 joules per second) iscalled a kilowatt and is a commonly used measurement of electrical power. The Englishsystem, on the other hand, uses the more colorful unit horsepower, which is defined as550 foot-pounds per second.

The familiar rating of a lightbulb (60 watts or 100 watts, for example) is a measureof the rate of energy that the lightbulb consumes when it is operating. As another famil-iar example, most electric hand tools or appliances in your home will be labeled with apower rating in watts.

The equation we have introduced defining power as energy divided by time may berewritten as follows:

energy (joules) = power (watts) × time (seconds)

This important equation allows you (and the electric company) to calculate how muchenergy you consume (and how much you have to pay for). Note from this equation that,while the joule is the standard scientific unit for energy, energy can also be measured inunits of power × time, such as the familiar kilowatt-hour (often abbreviated kwh) thatappears on your electric bill. Table 3-1 summarizes the important terms we’ve used forforce, work, energy, and power.

(1 joule of energy)1 watt of power = ————————

(1 second of time)

WP = —–

t

The Great Chain of Energy | 53

Athletes must release their energyquickly and with great power to suc-ceed in events such as the javelinthrow.

Table 3-1 Important Terms

Quantity Definition Units

Force mass × acceleration newtons

Work force × distance joules

Energy ability to do work joules

Energy power × time joules

Power wattswork energy–—— = ———time time

James Watt boiling water in his fireplace.

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Science in the Making •James Watt and the HorsepowerThe horsepower, a unit of power with a colorful history, was devised by James Watt sothat he could sell his steam engines. Watt knew that the main use of his engines wouldbe in mines, where owners traditionally used horses to drive pumps that removed water.The easiest way to promote his new engines was to tell the mining engineers how manyhorses each engine would replace. Consequently, he did a series of experiments to deter-mine how much energy a horse could generate over a given amount of time. Watt foundthat an average, healthy horse can do 550 ft-lb of work every second over an averageworking day—a unit he defined to be the horsepower, and so he rated his enginesaccordingly. We still use this unit (the engines of virtually all cars and trucks are rated inhorsepower), although we seldom build engines to replace horses these days. •


Paying the PiperA typical CD system uses 250 watts of electrical power. If you play your system for threehours in an evening, how much energy do you use? If energy costs 12 cents a kilowatt-hour, how much do you owe the electrical company?

Reasoning and Solution: The total amount of energy you use will be given by

energy = power × time= 250 W × 3 h= 750 Wh

Because 750 watts equals 0.75 kilowatt,

energy = 0.75 Kwh

The cost will be as follows:

cost = 12 cents per Kwh × 0.75 Kwh= 9 cents

EXAMPLE 3-2

Forms of Energy

Energy, the ability to do work, appears in all natural systems, and it comes in manyforms. The identification of these forms posed a great challenge to scientists in the nine-teenth century. Ultimately, they recognized two very broad categories. Kinetic energyis energy associated with moving objects, whereas stored or potential energy is energywaiting to be released.

Kinetic EnergyThink about a cannonball flying through the air. When it hits a wooden target, the ballexerts a force on the fibers in the wood, splintering and pushing them apart and creat-ing a hole. Work has to be done to make that hole; fibers have to be moved aside, whichmeans that a force must be exerted over the distance they move. When the cannonballhits the wood, it does work, and so a cannonball in flight clearly has the ability to dowork—that is, it has energy—because of its motion. This energy of motion is what wecall kinetic energy.

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You can find countless examples of kinetic energy in nature. A fishmoving through water, a bird flying, and a predator catching its preyall have kinetic energy. So do a speeding car, a flying Frisbee, a fallingleaf, and anything else that is moving.

Our intuition tells us that two factors govern the amount ofkinetic energy contained in any moving object. First, heavier objectsthat are moving have more kinetic energy than lighter ones: a bowl-ing ball traveling 10 m/s (a very fast sprint) carries a lot more kineticenergy than a golf ball traveling at the same speed. In fact, kineticenergy is directly proportional to mass: if you double the mass, thenyou double the kinetic energy.

Second, the faster something is moving, the greater the force it iscapable of exerting and the greater energy it possesses. A high-speedcollision causes much more damage than a fender bender in a parkinglot. It turns out that an object’s kinetic energy increases as the square of its speed. A carmoving 40 mph has four times as much kinetic energy as one moving 20 mph, while at60 mph a car carries nine times as much kinetic energy as at 20 mph. Thus a modestincrease in speed can cause a large increase in kinetic energy.

These ideas are combined in the equation for kinetic energy.

� In words: Kinetic energy equals the mass of the moving object times the square ofthat object’s speed, times the constant 1–

2.


kinetic energy (joules) = 1–2

× mass (kg) × [speed (m/s)]2

� In symbols:

EK = 1–2

× m × v2

Forms of Energy | 55

This breaching humpback whale haskinetic energy because he is moving.

Bowling Balls and BaseballsWhat is the kinetic energy of a 4-kg (about 8-lb) bowling ball rolling down a bowling laneat 10 m/s (about 22 mph)? Compare this energy with that of a 250-gram (about half-a-pound) baseball traveling 50 m/s (almost 110 mph). Which object would hurt more if ithit you (i.e., which object has the greater kinetic energy)?

Reasoning: We have to substitute numbers into the equation for kinetic energy.

Solution: For the 4-kg bowling ball traveling at 10 m/s:



= 1–2

× 4 kg × (10 m/s)2

= 1–2

× 4 kg × 100 m2/s2

= 200 kg-m2/s2

Note that

200 kg-m2/s2 = 200 (kg-m/s2) × m= 200 N × m= 200 joules

EXAMPLE 3-3

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Even though the bowling ball is much more massive than the baseball, a hard-hit base-ball carries more kinetic energy than a typical bowling ball because of its high speed.

Potential EnergyAlmost every mountain range in the country has a “balancing rock”—a boulder precar-iously perched on top of a hill so that it looks as if a little push would send it tumblingdown the slope. If the balancing rock were to fall, it would clearly acquire kinetic energy,and it would do “work” on anything it smashed. The balancing rock has the ability todo work even though it’s not doing work right now, and even though it’s not necessar-ily going to be doing work any time in the near future. The boulder possesses energyjust by virtue of its position.

This kind of energy, which could result in the exertion of a force over distancebut is not doing so now, is called potential energy. In the case of the balancing rock,it is called gravitational potential energy because the force of gravity gives the rockthe capability of exerting its own force. An object that has been lifted above Earth’ssurface possesses an amount of gravitational potential energy exactly equal to thetotal amount of work you would have to do to lift it from the ground to its presentposition.

� In words: The gravitational potential energy of any object equals its weight (thegravitational force exerted downward by the object) times its height above theground.


gravitational potential energy (joules) = mass (kg) × g (m/s2) × height (m)

where g is the acceleration due to gravity at Earth’s surface (see Chapter 2).� In symbols:

EP = m × g × h

In Example 3-1 we saw that it requires 784 joules of energy to carry a 20-kg televisionset 4 meters distance up the stairs. Thus 784 joules is the amount of work that wouldbe done if the television set were allowed to fall, and it is the amount of gravitationalpotential energy stored in the elevated television set.

We encounter many other kinds of potential energy besides the gravitational kind inour daily lives. Chemical potential energy is stored in the gasoline that moves your car,the batteries that power your radio, and the food you eat. All animals depend on thechemical potential energy of food, and all living things rely on molecules that storechemical energy for future use. In each of these situations, potential energy is stored inthe chemical bonds between atoms (see Chapter 9).


For the 250-g baseball traveling at 50 m/s:



= 1–2

× 250 g × (50 m/s)2

A gram is a thousandth of a kilogram, so 250 g = 0.25 kg:


× 0.25 kg × 2500 m2/s2

= 312.5 kg-m2/s2

= 312.5 joules

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Wall outlets in your home and at work provide a means to tap into electrical poten-tial energy, waiting to turn a fan or drive a vacuum cleaner. A tightly coiled spring, aflexed muscle, and a stretched rubber band contain elastic potential energy, while arefrigerator magnet carries magnetic potential energy. In every case, energy is stored,ready to do work (Figure 3-2).

Heat, or Thermal EnergyTwo centuries ago, scientists understood the basic behavior of kinetic and potentialenergy, but the nature of heat was far more mysterious. It’s easy to feel and measure theeffects of heat, but what are the physical causes underlying the behavior of hot and coldobjects?

We now know that all matter is made of minute objects called atoms, which oftenclump together into discrete collections of two or more atoms called molecules. We’llexamine details of the structure and behavior of atoms and molecules, which are muchtoo small to be seen with an ordinary microscope, in Chapters 8 through 10. A key dis-covery regarding these minute particles is that the properties of all the materials in ourenvironment depend on their constituent atoms and how they’re linked together. Thecontrast between solid ice, liquid water, and gaseous steam, all of which are made frommolecules of three atoms (two hydrogen atoms linked to one oxygen atom, or H2O),for example, is a consequence of how strongly adajacent atoms or molecules interactwith each other (Chapter 10).

The key to understanding the nature of heat is that all atoms and molecules are inconstant random motion. These particles that make up all matter move around andvibrate, and therefore these particles possess kinetic energy. The tiny forces that theyexert are experienced only by other atoms and molecules, but the small scale doesn’tmake the forces any less real. If molecules in a material begin to move more rapidly, thenthey have more kinetic energy and are capable of exerting greater forces on each otherin collisions. If you touch an object whose molecules are moving fast, then the collisionsof those molecules with molecules in your hand will exert greater force, and you willperceive the object to be hot. By contrast, if the molecules in your hand are movingfaster than those of the object you touch, then you will perceive the object to be cold.What we normally call heat, therefore, is simply thermal energy—the random kineticenergy of atoms and molecules.

Forms of Energy | 57

• Figure 3-2 Potential energy comes in many forms.

Jack Hollingsworth/PhotoDisc, Inc./Getty Images Vladimir Pcholkin/Taxi/Getty Images, Inc.Dennis Galante/Taxi/Getty Images, Inc.

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Science in the Making •Discovering the Nature of HeatWhat is heat? How would you apply the scientific method to determine its origins? Thatwas the problem facing scientists 200 years ago.

In many respects, they realized, heat behaves like a fluid. It flows from place toplace, and it seems to spread out evenly like water that has been spilled on the floor.Some objects soak up heat faster than others, and many materials seem to swell up whenheated, just like waterlogged wood. Thus, in 1800, after years of observations andexperiments, many physicists mistakenly accepted the theory that heat is an invisiblefluid—they called it “caloric.” According to the caloric theory of heat, the best fuels,such as coal, are saturated with caloric, while ice is virtually devoid of the substance.

One of the most influential investigators of heat was the Massachusetts-born Ben-jamin Thompson (1752–1814), who led a remarkably adventurous life. At the age of 19he married an extremely wealthy widow, 14 years his senior. He sided with the Britishduring the Revolutionary War, first working as a spy, then as an officer in the BritishArmy of Occupation in New York. After the Americans won the war, Thompson aban-doned his wife and infant daughter and fled to Europe, where he was knighted by KingGeorge III. Later in his turbulent life he was forced to flee England on suspicion of spy-ing for the French, and he eventually wound up in the employ of the Elector of Bavaria,where his duties included the manufacture and machining of cannons.

If heat is a fluid, then each object must contain a fixed quantity of that substance.But Thompson noted that the increase in temperature that accompanies boring a can-non had nothing at all to do with the quantity of brass to be drilled. Sharp tools, hefound, cut brass quickly with minimum heat generation, while dull tools made slowprogress and produced prodigious amounts of heat.

Thompson proposed an alternative hypothesis. He suggested that the increase intemperature in his brass was a consequence of the mechanical energy of friction, notsome theoretical, invisible fluid. He proved his point by immersing an entire cannon-boring machine in water, turning it on, and watching the heat that was generated turnthe water to steam. British chemist and popular science lecturer Sir Humphry Davy(1778–1829) further dramatized Thompson’s point when he generated heat by rubbingpieces of ice together on a cold London day.

The work of Thompson, Davy, and others inspired English researcher James PrescottJoule to devise a special experiment to test the predictions of the rival theories. As shownin Figure 3-3, Joule’s apparatus employed a weight that was lifted up and attached to arope. The rope turned a paddle wheel immersed in a tub of water. The weight had gravi-tational potential energy, and, as it fell, that energy was converted into kinetic energy ofthe rotating paddle. The paddle wheel’s kinetic energy, in turn, was transferred to kineticenergy of water molecules. As Joule suspected, the water heated up by an amount equalto the gravitational potential energy released by the weights. Heat, he declared, is justanother form of energy. •

Wave EnergyAnyone who has watched surf battering a seashore has firsthand knowledge of waveenergy. In the case of water waves, the type of energy involved is obvious. Largeamounts of water are in rapid motion and therefore possess kinetic energy. It is thisenergy that we see released when waves hit the shore.

Other kinds of waves possess energy, as well. For example, when a sound wave is gen-erated, molecules in the air are set in motion and the energy of the sound wave is associ-ated with the kinetic energy of those molecules. Similar sound waves traveling through thesolid earth, called seismic waves, can carry the potentially destructive energy that isunleashed in earthquakes (see Chapter 17). In Chapter 6 we will meet another importantkind of wave, the kind associated with electromagnetic radiation, such as the radiantenergy (light) that streams from the Sun. This kind of wave stores its energy in changingelectrical and magnetic fields.


Benjamin Thompson, Count Rumford, ina Bavarian cannon foundry in 1798, call-ing attention to the transformation ofmechanical energy into heat.

• Figure 3-3 Joule’s experimentdemonstrated that heat is another form ofenergy by showing that the kinetic energyof a paddle wheel is transferred to thermalenergy of the agitated water.

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Mass as EnergyThe discovery that certain atoms, such as uranium, spontaneously release energy as theydisintegrate—the phenomenon of radioactivity—led to the realization in the early twen-tieth century that mass is a form of energy. This principle is the focus of Chapter 7, butthe main idea is summarized in Albert Einstein’s most famous equation.

� In words: Every object at rest contains potential energy equivalent to the product ofits mass times a constant, which is the speed of light squared.


energy (joules) = mass (kg) × [speed of light (m/s)]2

� In symbols:

E = mc2

where c is the symbol for the speed of light, a constant equal to 300,000,000 meters persecond (3 × 108 m/s).

This equation, which has achieved the rank of a cultural icon, tells us that it is pos-sible to transform mass into energy and to use energy to create mass. (Note: This equa-tion does not mean the mass has to be traveling at the speed of light; the mass is assumedto be at rest.) Furthermore, because the speed of light is so great, the energy stored ineven a tiny amount of mass is enormous.

The Interchangeability of Energy | 59

Lots of PotentialAccording to Einstein’s equation, how much potential energy is contained in the mass ofa grain of sand with a mass of 0.001 gram?

Reasoning and Solution: Substitute the mass, 0.001 gram, into Einstein’s famous equation.Remember that 1 gram is a thousandth of a kilogram, so a thousandth of a gram equals amillionth of a kilogram (10–6 kg). Also, the speed of light is a constant, 3 × 108 m/s.

energy (joules) = mass (kg) × [speed of light (m/s)]2

= 10–6 kg × (3 × 108 m/s)2

= 10–6 × 9 × (1016 kg-m2/s2)= 9 × 1010 joules

The energy contained in the mass of a single grain of sand is prodigious: almost 100 bil-lion joules, which is 25,000 kilowatt-hours. The average American family uses about 1000kilowatt-hours of electricity per month, so a sand grain—if we had the means to convertits mass entirely to electrical energy (which we don’t)—could satisfy your home’s energyneeds for the next two years!

In practical terms, Einstein’s equation showed that mass could be used to generate elec-tricity in nuclear power plants, in which a few pounds of nuclear fuel is enough to poweran entire city.

EXAMPLE 3-4

The Interchangeability of Energy

You know from everyday experience that energy can be changed from one form toanother (Table 3-2). Plants absorb light streaming from the Sun and convert that radi-ant energy into the stored chemical energy of cells and plant tissues. You eat plants andconvert the chemical energy into the kinetic energy of your muscles—energy of motion

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that in turn can be converted into gravitational potential energy when you climb a flightof stairs, elastic potential energy when you stretch a rubber band, or heat when you rubyour hands together. The lesson from these examples is clear.

Energy in one form can be converted into others.Bungee jumping provides a dramatic illustration of this rule (Figure 3-4). Bungee

jumpers climb to a high bridge or platform, where elastic cords are attached to theirankles. Then they launch themselves into space and fall toward the ground until thecords stretch, slow them down, and stop their fall.


Table 3-2 Some Forms of Energy

Potential Energy Kinetic Energy Other

Gravitational Moving objects Mass

Chemical Heat

Elastic Sound and other waves

Electromagnetic

The many different forms of energy are interchangeable.

Fullystretchedcord

FallingAt restafterjump

G K E T G K E T G K E TG K E T

(a) (b) (c) (d)

• Figure 3-4 Energy changesform during a bungee jump,though the total energy is con-stant. Histograms display thedistribution of energy amonggravitational potential (G),kinetic (K), elastic potential (E),and thermal (T). Initially (a), allof the energy to be used in thejump is stored as gravitationalpotential energy. During thedescent (b), the gravitationalpotential energy is converted tokinetic energy. At the bottom ofthe jump, the bungee cordstretches (c), so that mostenergy is in the form of elasticpotential. At the end of thejump (d) most of the energywinds up as heat.

A Slinky provides a dramatic example of energy changingfrom one form to another. Can you identify some of thekinds of energy changes involved?

Andy Washnik

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From an energy point of view, a bungee jumper uses the chemical potential energygenerated from food to walk up to the launching platform. The work that had beendone against gravity provides the jumper with gravitational potential energy. During thelong descent, the gravitational potential energy diminishes, while the jumper’s kineticenergy simultaneously increases. As the cords begin to stretch, the jumper slows downand kinetic energy gradually is converted to stored elastic potential energy in the cords.Eventually, the gravitational potential energy that the jumper had at the beginning iscompletely transferred to the stretched elastic cords, which then rebound, convertingsome of the stored elastic energy back into kinetic energy and gravitational potentialenergy. All the time, some of the energy is also converted to thermal energy: increasedtemperature in the stressed cord, on the jumper’s ankles, and the air as it is pushed aside.

One of the most fundamental properties of the universe in which we live is thatevery form of energy on our list can be converted to every other form of energy.

The Science of Life •Energy for Life and Trophic LevelsAll of Earth’s systems, both living and nonliving, transform the Sun’s radiant energy intoother forms. Just how much energy is available, and how is it used by living organisms?

At the top of Earth’s atmosphere, the Sun’s incoming energy is 1400 watts persquare meter. To calculate the total energy of this solar power, we first need to calculateEarth’s cross-sectional area in square meters. Earth’s radius is 6375 kilometers(6,375,000 meters), and so the cross-sectional area is

area of a circle = pi × (radius)2

= 3.14 × (6,375,000 m)2

= 1.28 × 1014 m2

Thus the total power received at the top of Earth’s atmosphere is

power = solar energy per m2 × Earth’s cross-sectional area= 1400 watts/m2 × 1.28 × 1014 m2

= 1.79 × 1017 watts

Each second, the top of Earth’s atmosphere receives 1.79 × 1017 joules of energy, butthat is more than twice the amount that reaches the ground. When solar radiationencounters the top of the atmosphere, about 25% of it is immediately reflected back intospace. Another 25% is absorbed by gases in the atmosphere, and Earth’s surface reflectsan additional 5% back into space. These processes leave about 45% of the initial amountto be absorbed at Earth’s surface.

All living systems take their energy from this 45% but absorb only a small portionof this amount—only about 4% to run photosynthesis and supply the entire food chain.A much larger portion heats the ground or air, or evaporates water from lakes, rivers,and oceans.

The concept of the food chain and its trophic levels is particularly useful when track-ing the many changes of energy as it flows through living systems of Earth. A trophiclevel consists of all organisms that get their energy from the same source (Figure 3-5).

The Interchangeability of Energy | 61

Solar photovoltaic cells, like this arrayin Albuquerque, New Mexico, con-vert the energy in sunlight directlyinto electrical current.

Big CarnivoresCarnivores

Herbivores

Producers – Photosynthetic Organisms

Fourth trophic levelThird trophic level

Second trophic level

First trophic level

Mass of living materials per unit of area

• Figure 3-5 The food chain. Livingorganisms are arranged in trophic levelsaccording to how they obtain energy. Thefirst trophic level consists of plants that pro-duce energy from photosynthesis. In thehigher trophic levels, animals get their energyby feeding on organisms from the next low-est level.

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In this ranking scheme, all plants that produce energy from photosynthesis are in thefirst trophic level. These plants all absorb energy from sunlight and use it to drive chem-ical reactions that make plant tissues and other complex molecules subsequently used asenergy sources by organisms in higher trophic levels.

The second trophic level includes all herbivores—animals that get their energy by eat-ing plants of the first trophic level. Cows, rabbits, and many insects occupy this level.The third trophic level, as you might expect, consists of carnivores—animals that get theirenergy by eating organisms in the second trophic level. This third level includes suchfamiliar animals as wolves, eagles, and lions, as well as insect-eating birds, blood-suckingticks and mosquitoes, and many other organisms.

A few more groups of organisms fill out the scheme of trophic levels on Earth. Car-nivores that eat other carnivores, such as killer whales, occupy the fourth trophic level.Termites, vultures, and a host of bacteria and fungi get their energy from feeding ondead organisms and are generally placed in a trophic level separate from the four we havejust described. (The usual convention is that this trophic level is not given a numberbecause the dead organisms can come from any of the other trophic levels.)

A number of animals and plants span the trophic levels. Human beings, raccoons,and bears, for example, are omnivores that gain energy from plants and from organismsin other trophic levels, while the Venus flytrap is a green plant that supplements its dietwith trapped insects. •

Although you might expect it to be otherwise, the efficiency with which solar energy isused by Earth’s organisms is very low, despite the struggle by all these organisms to useenergy efficiently. When sunlight falls, for example, on a cornfield in the middle of Iowain August—arguably one of the best situations in the world for plant growth—only asmall percentage of the solar energy striking the field is actually transformed as chemi-cal energy in the plants. All the rest of the energy is reflected, heats up the soil, evapo-rates water, or performs some other function. It is a general rule that no plants anywheretransform as much as 10% of solar energy available to them.

The same situation applies to trophic levels above the first. Typically, less than 10%of a plant’s chemical potential energy winds up as tissue in the animal of the secondtrophic level that eats the plants. That is, less than about 1% (10% of 10%) of the origi-nal energy in sunlight is transformed into chemical energy of the second trophic level.Continuing with the same pattern, animals in the third trophic level also use less than10% of the energy available from the second level.

You can do a rough verification of this statement in your supermarket. Whole grains(those that have not been processed heavily) typically cost about one-tenth as much perpound as fresh meat. Examined from an energy point of view, this cost differential is notsurprising. It takes 10 times as much energy to make a pound of beef as it does to makea pound of wheat or rice, and this fact is reflected in the price.

One of the most interesting examples of energy flow through trophic levels canbe seen in the fossils of dinosaurs. In many museum exhibits, the most dramatic andmemorable specimen is a giant carnivore—a Tyrannosaurus or Allosaurus with 6-inchdagger teeth and powerful claws. So often are these impressive skeletons illustratedthat you might get the impression that these finds are common. In fact, fossil carni-vores are extremely rare and represent only a small fraction of known dinosaur speci-mens. Our knowledge of the fearsome Tyrannosaurus, for example, is based on onlyabout a dozen skeletons, and most of those are quite fragmentary. By contrast, pale-ontologists have found hundreds of skeletons of plant-eating dinosaurs. This distribu-tion is hardly chance. Carnivorous dinosaurs, like modern lions and tigers, wererelatively scarce compared to their herbivorous victims. In fact, statistical studies of alldinosaur skeletons reveal a roughly 10:1 herbivore-to-carnivore ratio, a value


Stop and Think! From which trophic levels did you obtain energy during thepast 24 hours?

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approaching what we find today for the ratio of warm-blooded herbivores to warm-blooded carnivores, and much higher than the herbivore-to-carnivore ratio observedin modern cold-blooded reptiles. This pattern is cited by many paleontologists as evi-dence that dinosaurs were warm-blooded.

The First Law of Thermodynamics: Energy Is Conserved | 63

The First Law of Thermodynamics: Energy Is Conserved

Scientists are always on the lookout for attributes of the ever-changing universe that areconstant and unchanging. If the total number of atoms, electrons, or electrical chargesis constant, then that attribute is said to be conserved. Any statement that an attributeis conserved is called a conservation law. (Note that these meanings of “conserved” and“conservation” are different from the more common uses of the words associated withmodest consumption and recycling.)

Before describing the conservation law that relates to energy, we must first intro-duce the idea of a system. You can think of a system as an imaginary box into whichyou put some matter and some energy that you would like to study. Scientists mightwant to study a system containing only a pan of water, or one consisting of a forest, oreven the entire planet Earth. Doctors examine your nervous system, astronomersexplore the solar system, and biologists observe a variety of ecosystems. In each case,the investigation of nature is simplified by focusing on one small part of the universe.

If the system under study can exchange matter and energy with its surroundings—a pan full of water that is heated on a stove and gradually evaporates, for example—thenit is an open system. An open system is like an open box where you can take things outand put things back in. Alternatively, if matter and energy in a system do not freelyexchange with their surroundings, as in a tightly shut box, then the system is said to beclosed or isolated. Earth and its primary source of energy, the Sun, together make a sys-tem that may be thought of for most purposes as closed, because there are no signifi-cant amounts of matter or energy being added from outside sources.

The most important conservation law in the sciences is the law of conservation ofenergy. This law is also called the first law of thermodynamics. (Thermodynamics—lit-erally the study of the movement of heat—is a term used for the science of heat, energy,and work.) The law can be stated as follows:

This law tells us that, although the kind of energy in a given system can change, thetotal amount cannot. For example, when a bungee jumper hurls herself into space, thegravitational potential energy she had at the beginning of the fall is converted to anequal amount of other kinds of energy. When she’s moving, some of the gravitationalpotential energy changes into kinetic energy, some into elastic potential energy, andsome into the increased temperature of the surroundings. At each point during the fall,however, the sum of kinetic, elastic potential, gravitational potential, and heat energieshas to be the same as the gravitational energy at the beginning.

Energy is something like an economy with an absolutely fixed amount of money.You can earn it, store it in a bank or under your pillow, and spend it here and therewhen you want to. But the total amount of money doesn’t change just because itpasses through your hands. Likewise, in any physical situation you can shuffle energyfrom one place to another. You could take it out of the account labeled “kinetic” andput it into the account labeled “potential”; you could spread it around into accountslabeled “chemical potential,” “elastic potential,” “heat,” and so on; but the first law of

In an isolated system the total amount of energy, including heat, isconserved.

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thermodynamics tells us that, in a closed system, you can never have more or lessenergy than you started with.

To many scientists of the nineteenth century the first law of thermodynamics rep-resented more than just a useful statement about energy. For them it carried a profoundsignificance about the underlying symmetry—even beauty—of the natural order. Jouledescribed the first law in the following poetic way: “Nothing is destroyed, nothing isever lost, but the entire machinery, complicated as it is, works smoothly and harmo-niously . . . Everything may appear complicated in the apparent confusion and intricacyof an almost endless variety of causes, effects, conversions, and arrangements, yet is themost perfect regularity preserved—the whole being governed by the sovereign will ofGod.” To Joule, the first law was nothing less than proof of the beneficence of the Cre-ator—a natural law analogous to the immortality of the soul.

Science by the Numbers •Diet and CaloriesThe first law of thermodynamics has a great deal to say about the American obsessionwith weight and diet. Human beings take in energy with their food, energy we usuallymeasure in calories. (Note that the calorie we talk about in foods is defined as theamount of energy needed to raise the temperature of a kilogram of water 1° Celsius, aunit we will later call a kilocalorie.) When a certain amount of energy is taken in, the firstlaw says that only one of two things can happen to it: It can be converted into work andincreased temperature of the surroundings, or it can be stored. If we take in more energythan we expend, the excess is stored in fat. If, on the other hand, we take in less thanwe expend, energy must be removed from storage to meet the deficit, and the amountof body fat decreases.

Here are a couple of rough rules you can use to calculate calories in your diet:

1. Under most circumstances, normal body maintenance uses up about 15 calories perday for each pound of body weight.

2. You must consume about 3500 calories to gain a pound of fat.

Suppose you weigh 150 pounds. To keep your weight constant, you have to take in

150 pounds × 15 calories/pound = 2250 calories per day

If you wanted to lose one pound (3500 calories) a week (7 days), you would have toreduce your daily calorie intake by

Another way of saying this is that you would have to reduce your calorie intake to 1750calories—the equivalent of skipping dessert every day.

Alternatively, the first law says you can increase your energy use through exercise.Roughly speaking, to burn off 500 calories you would have to run 5 miles, bike 15miles, or swim for an hour.

It’s a whole lot easier to refrain from eating than to burn off the weight by exercise.In fact, most researchers now say that the main benefit of exercise in weight control hasto do with its ability to help people control their appetites. •

Science in the Making •Lord Kelvin and Earth’s AgeThe first law of thermodynamics provided physicists with a powerful tool for describingand analyzing their universe. Every isolated system, the law tells us, has a fixed amount

3500 calories—————— = 500 calories per day

7days


William Thomson, Lord Kelvin(1824–1907)

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of energy. Naturally, one of the first systems that scientists considered was the Sun andEarth.

British physicist William Thomson (1824–1907), enobled as Lord Kelvin, asked asimple question: How much energy could be stored inside Earth? And, given the pres-ent rate at which energy radiates out into space, how old might Earth be? Though sim-ple, these questions had profound implications for philosophers and theologians whohad their own ideas about Earth’s relative antiquity. Some biblical scholars believed thatEarth could be no more than a few thousand years old. Most geologists, on the otherhand, saw evidence in layered rocks to suggest an Earth at least hundreds of millions ofyears old. Biologists also required vast amounts of time to account for the gradual evo-lution of life on Earth. Who was correct?

Kelvin assumed, as did most of his contemporaries, that Earth had formed from acontracting cloud of interstellar dust (see Chapter 16). He thought that Earth began asa hot body because impacts of large objects on it early in its history must have convertedhuge amounts of gravitational potential energy into thermal energy. He used new devel-opments in mathematics to calculate how long it took for a hot Earth to cool to its pres-ent temperature. He assumed that there were no sources of energy inside Earth, andfound that Earth’s age had to be less than about 100 million years. He soundly rejectedthe geologists’ and biologists’ claims of an older Earth because these claims seemed toviolate the first law of thermodynamics.

Seldom have scientists come to such a bitter impasse. Two competing theoriesabout Earth’s age, each supported by seemingly sound observations, were at odds. Thecalculations of the physicist seemed unassailable, yet the observations of biologists andgeologists in the field were equally meticulous. What could possibly resolve thedilemma? Had the scientific method failed? The solution came from a totally unexpectedsource when scientists discovered in the 1890s that rocks hold a previously unknownsource of energy, radioactivity (see Chapter 11), in which thermal energy is generatedby the conversion of mass. Lord Kelvin’s rigorous age calculations were in error onlybecause he and his contemporaries were unaware of this critical component of Earth’senergy budget. Earth’s deep interior, we now know, gains approximately half of its ther-mal energy from radioactive decay. Revised calculations suggest an Earth several billionsof years old, in conformity with geological and biological observations. •

The United States and Its Energy Future | 65

The United States and Its Energy Future

The growth of modern technological societies since the Industrial Revolution has beendriven by the availability of cheap, high-grade sources of energy. When fuel woodbecame expensive and scarce at the end of the eighteenth century, men like James Wattfigured out how to tap into the solar energy stored in coal. In the early twentieth cen-tury, the development of the internal combustion engine and other new technologiesmade petroleum the fuel of choice. Both of these transitions took about 30 years.

Fuels like oil (petroleum), coal, and natural gas are called fossil fuels because they arethe result of processes that happened long ago. As you can see from Figure 3-6, theeconomy of the United States today depends almost completely on the burning of fos-sil fuels. This state of affairs leads to two difficult problems. One characteristic of fossilfuels is that they are not replaceable—once you burn a ton of coal or a barrel of oil, itis gone as far as any timescale meaningful to human beings is concerned. Another char-acteristic, as we shall discuss in Chapter 19, is that an inevitable result of burning fossilfuels is the addition of carbon dioxide to the atmosphere. This, in turn, may well leadto long-term climate change. Thus, the search for alternate energy sources to drive oureconomy is well under way.

The two most important alternate energy sources being considered are solarenergy and wind. Because they are constantly being replaced, solar energy and wind are

Nuclear (5%) Hydroelectric (7%)

Coal (30%)

Oil (38%)

Natural gas(20%)

• Figure 3-6 Sources of energy forthe United States and other industrialnations. Note that most of our energycomes from fossil fuels.

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usually classed as renewable energy sources. Neither contributes to global warming, andboth are considered to be part of the process of weaning ourselves from fossil fuels.

The question of when these energy sources will be available in commercially usefulquantities is a complicated mix of technology and economics. As an example, thinkabout generating electricity from these sources. Commercial electrical generation in theUnited States can be divided into two types—base load and peak load. Base load is elec-tricity that has to be delivered day in and day out to run essential services like lightingand manufacturing. Peak load refers to the extra electricity that has to be delivered on,for example, a hot day when everyone turns on his or her air conditioner. Typically, baseload power is delivered by large coal or nuclear plants. These plants are expensive tobuild, but since the construction cost is spread out over a long time period, the net costper kilowatt-hour is low. Peak load, on the other hand, is typically delivered by systemssuch as gas turbines. These plants are cheap to build but expensive to operate becausethey typically use more expensive fuels. Thus, peak load electricity is usually more expen-sive than base load. (You probably don’t see this difference in your electricity billbecause the costs are folded together). Thus, the best place for alternate energy sourcesto enter the economy is in the peak load market.

The United States has enormous solar and wind resources. A “wind belt” runs fromthe Dakotas to New Mexico, and, of course, the deserts of the American Southwest havesunlight in plenty. Enormous improvements in windmill technology over the past fewdecades have lowered the cost of wind power to the point where it is competitive withconventional forms of generation. This is why you see windmill “farms” springing up allover the place.

Solar energy is further behind. In 2005, the cost of solar-generated electricity was24 cents per kilowatt hour versus about 4 cents for coal. Some experts estimate that by2025, the cost of solar energy will have dropped to 6 cents per kilowatt-hour and thatabout half of all new electrical generation in the United States will be solar.

To understand why this practice makes sense, you have to realize that the cost ofelectricity is only a small portion of the cost of maintaining something like a trafficcounter. Typically, the major expense is the installation itself. As one engineer told theauthors, “You can just drop these in place where you want them. You don’t have tobring in electricians to connect them, and that makes them a lot cheaper.”

Most analysts think that the energy future of the United States will involve somemix of coal, oil, natural gas, nuclear, wind, and solar, with an eventual shift to com-pletely renewable sources. The magnitude of the effort required to accomplish such atransition should not be underestimated, however. To generate all of America’s elec-tricity by wind power would require a windmill every quarter mile over the entirestates of North and South Dakota. Similarly, to generate the same amount of energyfrom sunlight would require covering an area four times that of Massachusetts withsolar collectors. Neither of these tasks would be a trivial undertaking, and no one asyet has given serious thought to the environmental or social consequences of an engi-neering project of this scale.

Another area of energy use is in transportation, which consumes about a third of theUnited States’ energy budget. Much of this energy is used to run gasoline-poweredinternal combustion engines (ICE) in cars and trucks. There is at the moment a tremen-dous technological ferment as engineers advocating different ways of replacing ICEwork hard to make their systems as good as they can be. Some leading contenders areas follows.


Electricity generated from this sort ofwind turbine is starting to becomeeconomically competitive in theUnited States.

Stop and Think! You often see highway signs and traffic counters beingpowered by solar cells. Given the high cost of solar energy, why do you supposethese devices are used even in areas where it would be easy to hook up to theordinary electrical power grid?Solar photovoltaeic cells, like those

shown, are semiconducting diodesthat convert the energy in sunlight toelectrical current. They are alreadyused in niche markets in the UnitedStates, but require more developmentto become a major source of electricalpower.

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Electric cars Batteries power these cars, so that their energy actually derives fromthe electrical power grid. There are many small electric vehicles in the United States(think of golf carts) and a number of prototype passenger cars. The problem withelectric cars is primarily technological because the best current batteries don’t storea lot of energy per pound of weight. It would, for example, take about 800 poundsof ordinary car batteries to store as much energy as is found in a gallon of gasoline.Because of this problem, the distance that electric cars can go (a quantity referredto as “range”) is significantly less than cars with ICE. As new, high-efficiency, light-weight batteries are developed, however, you can expect to see electric cars play abigger role in the country’s transportation system.

Hybrids A hybrid vehicle is one in which a small gasoline motor operates a gen-erator that charges a bank of batteries that, in turn, power the electric motor thatdrives the car. Because the batteries are constantly being recharged, the car canoperate with fewer batteries than are required in a fully electric vehicle. Because thedrive system can take the energy of motion of the car during deceleration and useit to generate electricity, a hybrid vehicle uses much less gasoline than a conventionalICE. The first hybrid to enter the American market was the Toyota Prius, which wasfollowed by many other models.

Fuel Cell Cars A fuel cell is a device in which hydrogen combines with oxygen toform water, producing heat energy in the process. This process is very efficient, andsince the only exhaust product is water, it’s very clean as well. Engineers considertwo approaches to a fuel cell transportation system: one in which pure hydrogen isfed into the fuel cell and one in which the hydrogen is carried into the engine aspart of a larger molecule like methanol. In both cases, energy has to be expendedto provide the hydrogen. In the case of pure hydrogen fuel, this energy is usually inthe form of the electricity needed to separate hydrogen from water molecules. Inthe case of methanol, it’s the energy needed to run the farms that grow the plants(often corn) from which the molecule is made. In both cases, a new distribution sys-tem would be needed for the new fuel.

The United States and Its Energy Future | 67

Hybrid cars, like this one, are starting tobecome popular in the United States.They use a gasoline engine to charge thebatteries that run the electric motor thatdrives the car. These cars have high gasmileage and ranges comparable to ordi-nary internal combustion cars.

Fossil Fuels

All life is rich in the element carbon, which plays a key role invirtually all the chemicals that make up our cells. Life uses theSun’s energy, directly through photosynthesis or indirectlythrough food, to form these carbon-based substances thatstore chemical potential energy. When living things die, theymay collect in layers at the bottoms of ponds, lakes, or oceans.Over time, as the layers become buried, Earth’s temperatureand pressure may alter the chemicals of life into deposits offossil fuels.

Geologists estimate that it takes tens of millions of years ofgradual burial under layers of sediments, combined with thetransforming effects of temperature and pressure, to form acoal seam or petroleum deposit. Coal forms from layer uponlayer of plants that thrived in vast ancient swamps, while petro-leum represents primarily the organic matter once contained inplankton, microscopic organisms that float near the ocean’s

surface. While these natural processes continue today, the rateof coal and petroleum formation in Earth’s crust is only asmall fraction of the fossil fuels being consumed. For this rea-son, fossil fuels are classified as nonrenewable resources.

One consequence of this situation is clear. Humans cannotcontinue to rely on fossil fuels forever. Reserves of high-gradecrude oil and the cleanest-burning varieties of coal may lastless than 100 more years. Less efficient forms of fossil fuels,including lower grades of coal and oil shales in which petro-leum is dispersed through solid rock, could be depleted withina few centuries. All the energy now locked up in those valuableenergy reserves will still exist, but in the form of unusable heatradiating far into space. Given the irreversibility of burning upour fossil fuel reserves, what steps should we take to promoteenergy conservation? Should energy be taxed at a higher rate?Should we assume that new energy sources will become avail-able as they are needed?

Thinking More About Energy

EPA/Marijan Murat/Landov/Landov LLC

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Work, measured in joules (or foot-pounds), is defined as a forceapplied over a distance. You do work every time you move an object.Every action of our lives requires energy (also measured in joules),which is the ability to do work. Power, measured in watts or kilo-watts, indicates the rate at which energy is expended.

Energy comes in several forms. Kinetic energy is the energyassociated with moving objects such as cars or cannonballs. Potentialenergy, on the other hand, is stored, ready-to-use energy, such as thechemical energy of coal, the elastic energy of a coiled spring, thegravitational energy of dammed-up water, or the electrical energy inyour wall socket. Thermal energy or heat is the form of kinetic energyassociated with vibrating atoms and molecules. Energy can also takethe form of wave energy, such as sound waves or light waves. Andearly in the twentieth century it was discovered that mass is also a

form of energy. All around us energy constantly shifts from one formto another, and all of these kinds of energy are interchangeable.

Energy from the Sun is used by photosynthetic plants in the firsttrophic level; these plants provide the energy for animals in highertrophic levels. Roughly speaking, only about 10% of the energy avail-able at one trophic level finds its way to the next.

The most fundamental idea about energy, expressed in thefirst law of thermodynamics, is that it is conserved: the total amountof energy in an isolated system never changes. Energy can shift backand forth between the different kinds, but the sum of all energy isconstant.

At present, most industrialized countries use fossil fuels to runtheir economies. Alternative sources for the future include solar andwind energy and, for transportation, electric and fuel cell cars.

1. How does the scientific meaning of the words “energy” and“power” differ from their common usage.2. What forms of energy are used in the following sports:a. surfingb. Nascar racingc. hot air ballooningd. sailing

e. tennisf. horse racing3. Does a tablespoon of olive oil have more stored chemicalenergy than a tablespoon of sugar?4. Would it be energy efficient to use a solar water heating systemin Alaska? Why or why not?5. Think about your energy intake today. Pick one food and iden-

SUMMARY •

KEY TERMS •

1. What is the scientific definition of work? How does it differfrom ordinary English usage?2. What is the difference between the watt and the horsepower?3. What is the difference between energy and power?4. List some different kinds of energy. Explain how they differfrom each other.5. What is the relationship between heat, energy, and motion?6. Explain why waves carry energy.7. What does it mean to say that different forms of energy areinterchangeable?

8. Give an example of change of energy from potential to kinetic;from kinetic to potential.9. What is a trophic level? Give some examples.10. What does it mean to say that energy is conserved?11. How did the discovery that mass is a form of energy resolvethe debate over Earth’s age?12. Explain what it means to say, “Energy flows through Earth.”

REVIEW QUESTIONS •

DISCUSSION QUESTIONS •

work (measured in joules)energy (measured in joules)power (measured in watts or

kilowatts)

kinetic energypotential energythermal energy (heat)wave energy

trophic levelconservation lawsystemfirst law of thermodynamics

fuel cell

KEY EQUATIONS •work (joules) = force (newtons) × distance (meters)energy (joules) = power (watts) × time (seconds)kinetic energy (joules) = 1⁄2 mass (kg) × [speed (m/s)]2

gravitational potential energy (joules) = g × mass (kg) × height (m)energy associated with mass at rest (joules) × mass (kg) × [speed of light (m/s)]2

Constantc = 3 × 108 m/s = speed of light

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Investigations | 69

1. How much work against gravity do you do when you bench-press a 75-kg mass a distance of about 1 meter? Compare this workto that done by a 100-watt lightbulb in an hour. How many timeswould you have to press the 75-kg mass to equal the work of thelightbulb in one hour?2. Which has more gravitational potential energy: a 200-kg boul-der 1 meter off the ground, a 50-kg boulder 4 meters off theground, or a 1-kg rock 200 meters off the ground? Which of thesecan do the most work if all the potential energy was converted intokinetic energy?3. Compared to a car moving at 10 miles per hour, how muchkinetic energy does that same car have when it moves at 20 miles perhour? 50? 75? Graph your results. What does your graph suggest toyou about the difficulty of stopping a car as its speed increases?

4. According to Einstein’s famous equation, E = mc2, how muchenergy would be released if a pound of feathers was convertedentirely into energy? a pound of lead? (Note: You will first need toconvert pounds into kilograms.)5. If you eat 500 calories per day (roughly 4 ounces of potatochips) above your energy needs, how long will it take to gain 10pounds? How long would you have to walk (assuming 80 caloriesburned per mile walked) to burn off those 10 pounds?6. Joules and kilowatt-hours are both units of energy. How manyjoules are equal to 1 kilowatt-hour?7. If the price of beef is $2.50 per pound, estimate what the priceof lion meat might be, and give reasons for your prediction.

PROBLEMS •

1. Look at your most recent electric bill and find the cost of onekilowatt-hour in your area. Then,a. Look at the back of your CD player or an appliance and find thepower rating in watts. How much does it cost for you to operatethe device for one hour?b. If you leave a 100-watt lightbulb on all the time, how much willyou pay in a year of electric bills?c. If you had to pay $10 for a high-efficiency bulb that providedthe same light as the 100-watt bulb with only 10 watts of power,how much would you save per year of electric bills, assuming youused the light five hours per day? Would it be worth your while tobuy the energy-efficient bulb if the ordinary bulb cost $1 and eachbulb lasts three years?2. In this chapter we introduced several energy units: the joule,the foot-pound, the kilowatt-hour, and the calorie. There are otherenergy units as well, including the BTU, the erg, the electron-volt,and many more. Look in a science reference book for conversionfactors between different pairs of energy units; you may find morethan a dozen different units. Who uses each of these differentunits? Why are there so many different units for the same phenom-enon—energy?

3. What kind of fuel is used at your local power plant? What arethe implications of the first law of thermodynamics regarding ouruse of fossil fuels? our use of solar energy?4. Keep a record of the calorie content of the food you eat and theamount of exercise you do for a few days. If you wanted to gain apound per month for the next year, how might you change yourcurrent habits?5. Check your household’s electric bills for the past year and calcu-late your total electric consumption for the year.a. How many 50-kg weights would you have to bench-press 1meter to produce a gravitational potential energy equal to this con-sumption?b. How much mass is equal to this consumption (E = mc2)?c. Identify five ways that you might reduce your energy consump-tion without drastically changing your lifestyle.d. Draft a plan by which you reduce your energy consumption by10%. About how much money might this save you per year?6. Investigate the history of the controversy between Lord Kelvinand his contemporaries regarding Earth’s age. When did thedebate begin? How long did it last? What kinds of evidence didbiologists, geologists, and physicists use to support their differing

INVESTIGATIONS •

tify the chain of energy that led to it. What trophic level do youeat from most? Where will the energy that you ingest eventuallywind up?6. What forms of energy are you using when you make a piece oftoast? When you make ice? When you dry your clothes?7. Where does geothermal energy come from? Is it a renewablesource of energy? Is hydroelectricity a renewable form of energy?8. What are the potential environmental drawbacks to the use ofthe following technologies:a. wind [Hint: Think about birds and bats.]b. solarc. geothermald. nucleare. hydro

9. Plants and animals are still dying and falling to the ocean bot-tom today. Why, then, do we not classify fossil fuels as renewableresources?10. Some people say that you lose more calories by eating celerythan you gain. How could that be? Is it possible to eat your way tothinness?11. Ancient human societies are described as labor intensive, whilemodern society is said to be energy intensive. What is meant bythese terms?12. How do “warm-blooded” animals warm their blood? Whatform of energy do “cold-blooded” animals use to warm theirblood and bodies?

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calculations of Earth’s age? Is there still a debate as to the age ofEarth?7. Investigate and find out how your household hot water isheated. Do you use oil, natural gas, solar, or electricity? What isthe most efficient way to heat water in your area? Why?8. Rub your hands together. What conversion of energy is occur-ring?9. The geyser “Old Faithful” in Yellowstone National Park sprayswater and steam hundreds of feet into the air. What form of energyis being used? Will “Old Faithful” ever run out of energy?10. Why do electric and hybrid cars cost more than other compactcars? What is the environemental impact of disposing of large num-bers of batteries? Do you think that the government should offermore incentives for people to buy hybrid and other fuel-efficientvehicles?11. If you work out on a stationary bike at a power output of 100watts for 30 minutes, does this energy output compensate for eat-

ing a 250-calorie jelly-filled doughnut? (Assume that the bodycoverts 20% of the energy input to work and the other 80% is lostas heat and extraneous movements.) 1 food “calorie” = 1 kilocalo-rie; and 1 calorie = 4.2 kilojoules12. The next time you are in an appliance store, check out theefficiency ratings of major appliances such as dryers and dishwash-ers. If you were going to buy one of these appliances, wouldenergy consumption be a factor in your purchase. If one machineis cheaper to run but more expensive to buy, how would you cal-culate which machine is a better buy?13. Different parts of the United States receive varying amountsof sunshine. How much solar energy reaches the ground in yourpart of the country on an average summer day and an average win-ter day? Is solar power a possibility in your area during the sum-mer? During the winter?

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energy - john wiley & sons

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