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Concept

As with many concepts in physics, energy—along with the related ideas of work and power—has a meaning much more specific, and in some ways quite different, from its everyday connotation. According to the language of physics, a person who strains without success to pull a rock out of the ground has done no work, whereas a child playing on a playground produces a great deal of work. Energy, which may be defined as the ability of an object to do work, is neither created nor destroyed; it simply changes form, a concept that can be illustrated by the behavior of a bouncing ball.

How It Works

In fact, it might actually be more precise to say that energy is the ability of "a thing" or "something" to do work. Not only tangible objects (whether they be organic, mechanical, or electromagnetic) but also non-objects may possess energy. At the subatomic level, a particle with no mass may have energy. The same can be said of a magnetic force field.

One cannot touch a force field; hence, it is not an object—but obviously, it exists. All one has to do to prove its existence is to place a natural magnet, such as an iron nail, within the magnetic field. Assuming the force field is strong enough, the nail will move through space toward it—and thus the force field will have performed work on the nail.

Work: What It Is and Is Not

Work may be defined in general terms as the exertion of force over a given distance. In order for work to be accomplished, there must be a displacement in space—or, in colloquial terms, something has to be moved from point A to point B. As noted earlier, this definition creates results that go against the common-sense definition of "work."

A person straining, and failing, to pull a rock from the ground has performed no work (in terms of physics) because nothing has been moved. On the other hand, a child on a playground performs considerable work: as she runs from the slide to the swing, for instance, she has moved her own weight (a variety of force) across a distance. She is even working when her movement is back-and-forth, as on the swing. This type of movement results in no net displacement, but as long as displacement has occurred at all, work has occurred.

Similarly, when a man completes a full push-up, his body is in the same position—parallel to the floor, arms extended to support him—as he was before he began it; yet he has accomplished work. If, on the other hand, he at the end of his energy, his chest is on the floor, straining but failing, to complete just one more push-up, then he is not working. The fact that he feels as though he has worked may matter in a personal sense, but it does not in terms of physics.

Calculating Work

Work can be defined more specifically as the product of force and distance, where those two vectors are exerted in the same direction. Suppose one were to drag a block of a certain weight across a given distance of floor. The amount of force one exerts parallel to the floor itself, multiplied by the distance, is equal to the amount of work exerted. On the other hand, if one pulls up on the block in a position perpendicular to the floor, that force does not contribute toward the work of dragging the block across the floor, because it is not par allel to distance as defined in this particular situation.

Similarly, if one exerts force on the block at an angle to the floor, only a portion of that force counts toward the net product of work—a portion that must be quantified in terms of trigonometry. The line of force parallel to the floor may be thought of as the base of a triangle, with a line perpendicular to the floor as its second side. Hence there is a 90°-angle, making it a right triangle with a hypotenuse. The hypotenuse is the line of force, which again is at an angle to the floor.

The component of force that counts toward the total work on the block is equal to the total force multiplied by the cosine of the angle. A cosine is the ratio between the leg adjacent to an acute (less than 90°) angle and the hypotenuse. The leg adjacent to the acute angle is, of course, the base of the triangle, which is parallel to the floor itself. Sizes of triangles may vary, but the ratio expressed by a cosine (abbreviated cos) does not. Hence, if one is pulling on the block by a rope that makes a 30°-angle to the floor, then force must be multiplied by cos 30°, which is equal to 0.866.

Note that the cosine is less than 1; hence when multiplied by the total force exerted, it will yield a figure 13.4% smaller than the total force. In fact, the larger the angle, the smaller the cosine; thus for 90°, the value of cos = 0. On the other hand, for an angle of 0°, cos = 1. Thus, if total force is exerted parallel to the floor—that is, at a 0°-angle to it—then the component of force that counts toward total work is equal to the total force. From the standpoint of physics, this would be a highly work-intensive operation.

Gravity and Other Peculiarities of Work

The above discussion relates entirely to work along a horizontal plane. On the vertical plane, by contrast, work is much simpler to calculate due to the presence of a constant downward force, which is, of course, gravity. The force of gravity accelerates objects at a rate of 32 ft (9.8 m)/sec². The mass (m) of an object multiplied by the rate of gravitational acceleration (g) yields its weight, and the formula for work done against gravity is equal to weight multiplied by height (h) above some lower reference point: mgh.

Distance and force are both vectors—that is, quantities possessing both magnitude and direction. Yet work, though it is the product of these two vectors, is a scalar, meaning that only the magnitude of work (and not the direction over which it is exerted) is important. Hence mgh can refer either to the upward work one exerts against gravity (that is, by lifting an object to a certain height), or to the downward work that gravity performs on the object when it is dropped. The direction of h does not matter, and its value is purely relative, referring to the vertical distance between one point and another.

The fact that gravity can "do work"—and the irrelevance of direction—further illustrates the truth that work, in the sense in which it is applied by physicists, is quite different from "work" as it understood in the day-to-day world. There is a highly personal quality to the everyday meaning of the term, which is completely lacking from its physics definition.

If someone carried a heavy box up five flights of stairs, that person would quite naturally feel justified in saying "I've worked." Certainly he or she would feel that the work expended was far greater than that of someone who had simply allowed the the elevator to carry the box up those five floors. Yet in terms of work done against gravity, the work done on the box by the elevator is exactly the same as that performed by the person carrying it upstairs. The identity of the "worker"—not to mention the sweat expended or not expended—is irrelevant from the standpoint of physics.

Measurement of Work and Power

In the metric system, a newton (N) is the amount of force required to accelerate 1 kg of mass by 1 meter per second squared (m/s²). Work is measured by the joule (J), equal to 1 newton-meter (N · m). The British unit of force is the pound, and work is measured in foot-pounds, or the work done by a force of 1 lb over a distance of one foot.

Power, the rate at which work is accomplished over time, is the same as work divided by time. It can also be calculated in terms of force multiplied by speed, much like the force-multiplied-by-distance formula for work. However, as with work, the force and speed must be in the same direction. Hence, the formula for power in these terms is F · cos θ · v, where F=force, v=speed, and cos θ is equal to the cosine of the angle θ (the Greek letter theta) between F and the direction of v.

The metric-system measure of power is the watt, named after James Watt (1736-1819), the Scottish inventor who developed the first fully viable steam engine and thus helped inaugurate the Industrial Revolution. A watt is equal to 1 joule per second, but this is such a small unit that it is more typical to speak in terms of kilowatts, or units of 1,000 watts.

Ironically, Watt himself—like most people in the British Isles and America—lived in a world that used the British system, in which the unit of power is the foot-pound per second. The latter, too, is very small, so for measuring the power of his steam engine, Watt suggested a unit based on something quite familiar to the people of his time: the power of a horse. One horsepower (hp) is equal to 550 foot-pounds per second.

Sorting Out Metric and British Units

The British system, of course, is horridly cumbersome compared to the metric system, and thus it long ago fell out of favor with the international scientific community. The British system is the product of loosely developed conventions that emerged over time: for instance, a foot was based on the length of the reigning king's foot, and in time, this became standardized. By contrast, the metric system was created quite deliberately over a matter of just a few years following the French Revolution, which broke out in 1789. The metric system was adopted ten years later.

During the revolutionary era, French intellectuals believed that every aspect of existence could and should be treated in highly rational, scientific terms. Out of these ideas arose much folly—especially after the supposedly "rational" leaders of the revolution began chopping off people's heads—but one of the more positive outcomes was the metric system. This system, based entirely on the number 10 and its exponents, made it easy to relate one figure to another: for instance, there are 100 centimeters in a meter and 1,000 meters in a kilometer. This is vastly more convenient than converting 12 inches to a foot, and 5,280 feet to a mile.

For this reason, scientists—even those from the Anglo-American world—use the metric system for measuring not only horizontal space, but volume, temperature, pressure, work, power, and so on. Within the scientific community, in fact, the metric system is known as SI, an abbreviation of the French Système International d'Unités—that is, "International System of Units."

Americans have shown little interest in adopting the SI system, yet where power is concerned, there is one exception. For measuring the power of a mechanical device, such as an automobile or even a garbage disposal, Americans use the British horsepower. However, for measuring electrical power, the SI kilowatt is used. When an electric utility performs a meter reading on a family's power usage, it measures that usage in terms of electrical "work" performed for the family, and thus bills them by the kilowatt-hour.

Three Types of Energy

Kinetic and Potential Energy Formulae

Earlier, energy was defined as the ability of an object to accomplish work—a definition that by this point has acquired a great deal more meaning. There are three types of energy: kinetic energy, or the energy that something possesses by virtue of its motion; potential energy, the energy it possesses by virtue of its position; and rest energy, the energy it possesses by virtue of its mass.

The formula for kinetic energy is KE = ½ mv². In other words, for an object of mass m, kinetic energy is equal to half the mass multiplied by the square of its speed v. The actual derivation of this formula is a rather detailed process, involving reference to the second of the three laws of motion formulated by Sir Isaac Newton (1642-1727.) The second law states that F = ma, in other words, that force is equal to mass multiplied by acceleration. In order to understand kinetic energy, it is necessary, then, to understand the formula for uniform acceleration. The latter is v_f² = v₀² + 2as, where v_f² is the final speed of the object, v₀² its initial speed, a acceleration and s distance. By substituting values within these equations, one arrives at the formula of ½ mv² for kinetic energy.

The above is simply another form of the general formula for work—since energy is, after all, the ability to perform work. In order to produce an amount of kinetic energy equal to ½ mv² within an object, one must perform an amount of work on it equal to Fs. Hence, kinetic energy also equals Fs, and thus the preceding paragraph simply provides a means for translating that into more specific terms.

The potential energy (PE) formula is much simpler, but it also relates to a work formula given earlier: that of work done against gravity. Potential energy, in this instance, is simply a function of gravity and the distance h above some reference point. Hence, its formula is the same as that for work done against gravity, mgh or wh, where w stands for weight. (Note that this refers to potential energy in a gravitational field; potential energy may also exist in an electromagnetic field, in which case the formula would be different from the one presented here.)

Rest Energy and Its Intriguing Formula

Finally, there is rest energy, which, though it may not sound very exciting, is in fact the most intriguing—and the most complex—of the three. Ironically, the formula for rest energy is far, far more complex in derivation than that for potential or even kinetic energy, yet it is much more well-known within the popular culture.

Indeed, E = mc² is perhaps the most famous physics formula in the world—even more so than the much simpler F = ma. The formula for rest energy, as many people know, comes from the man whose Theory of Relativity invalidated certain specifics of the Newtonian framework: Albert Einstein (1879-1955). As for what the formula actually means, that will be discussed later.

Real-Life Applications

Falling and Bouncing Balls

One of the best—and most frequently used—illustrations of potential and kinetic energy involves standing at the top of a building, holding a baseball over the side. Naturally, this is not an experiment to perform in real life. Due to its relatively small mass, a falling baseball does not have a great amount of kinetic energy, yet in the real world, a variety of other conditions (among them inertia, the tendency of an object to maintain its state of motion) conspire to make a hit on the head with a baseball potentially quite serious. If dropped from a great enough height, it could be fatal.

When one holds the baseball over the side of the building, potential energy is at a peak, but once the ball is released, potential energy begins to decrease in favor of kinetic energy. The relationship between these, in fact, is inverse: as the value of one decreases, that of the other increases in exact proportion. The ball will only fall to the point where its potential energy becomes 0, the same amount of kinetic energy it possessed before it was dropped. At the same point, kinetic energy will have reached maximum value, and will be equal to the potential energy the ball possessed at the beginning. Thus the sum of kinetic energy and potential energy remains constant, reflecting the conservation of energy, a subject discussed below.

It is relatively easy to understand how the ball acquires kinetic energy in its fall, but potential energy is somewhat more challenging to comprehend. The ball does not really "possess" the potential energy: potential energy resides within an entire system comprised by the ball, the space through which it falls, and the Earth. There is thus no "magic" in the reciprocal relationship between potential and kinetic energy: both are part of a single system, which can be envisioned by means of an analogy.

Imagine that one has a 20-dollar bill, then buys a pack of gum. Now one has, say, $19.20. The positive value of dollars has decreased by $0.80, but now one has increased "non-dollars" or "anti-dollars" by the same amount. After buying lunch, one might be down to $12.00, meaning that "anti-dollars" are now up to $8.00. The same will continue until the entire $20.00 has been spent. Obviously, there is nothing magical about this: the 20-dollar bill was a closed system, just like the one that included the ball and the ground. And just as potential energy decreased while kinetic energy increased, so "non-dollars" increased while dollars decreased.

Bouncing Back

The example of the baseball illustrates one of the most fundamental laws in the universe, the conservation of energy: within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. An interesting example of this comes from the case of another ball and another form of vertical motion.

This time instead of a baseball, the ball should be one that bounces: any ball will do, from a basketball to a tennis ball to a superball. And rather than falling from a great height, this one is dropped through a range of motion ordinary for a human being bouncing a ball. It hits the floor and bounces back—during which time it experiences a complex energy transfer.

As was the case with the baseball dropped from the building, the ball (or more specifically, the system involving the ball and the floor) possesses maximum potential energy prior to being released. Then, in the split-second before its impact on the floor, kinetic energy will be at a maximum while potential energy reaches zero.

So far, this is no different than the baseball scenario discussed earlier. But note what happens when the ball actually hits the floor: it stops for an infinitesimal fraction of a moment. What has happened is that the impact on the floor (which in this example is assumed to be perfectly rigid) has dented the surface of the ball, and this saps the ball's kinetic energy just at the moment when the energy had reached its maximum value. In accordance with the energy conservation law, that energy did not simply disappear: rather, it was transferred to the floor.

Meanwhile, in the wake of its huge energy loss, the ball is motionless. An instant later, however, it reabsorbs kinetic energy from the floor, undents, and rebounds. As it flies upward, its kinetic energy begins to diminish, but potential energy increases with height. Assuming that the person who released it catches it at exactly the same height at which he or she let it go, then potential energy is at the level it was before the ball was dropped.

When a Ball Loses Its Bounce

The above, of course, takes little account of energy "loss"—that is, the transfer of energy from one body to another. In fact, a part of the ball's kinetic energy will be lost to the floor because friction with the floor will lead to an energy transfer in the form of thermal, or heat, energy. The sound that the ball makes when it bounces also requires a slight energy loss; but friction—a force that resists motion when the surface of one object comes into contact with the surface of another—is the principal culprit where energy transfer is concerned.

Of particular importance is the way the ball responds in that instant when it hits bottom and stops. Hard rubber balls are better suited for this purpose than soft ones, because the harder the rubber, the greater the tendency of the molecules to experience only elastic deformation. What this means is that the spacing between molecules changes, yet their overall position does not.

If, however, the molecules change positions, this causes them to slide against one another, which produces friction and reduces the energy that goes into the bounce. Once the internal friction reaches a certain threshold, the ball is "dead"—that is, unable to bounce. The deader the ball is, the more its kinetic energy turns into heat upon impact with the floor, and the less energy remains for bouncing upward.

Varieties of Energy in Action

The preceding illustration makes several references to the conversion of kinetic energy to thermal energy, but it should be stressed that there are only three fundamental varieties of energy: potential, kinetic, and rest. Though heat is often discussed as a form unto itself, this is done only because the topic of heat or thermal energy is complex: in fact, thermal energy is simply a result of the kinetic energy between molecules.

To draw a parallel, most languages permit the use of only three basic subject-predicate constructions: first person ("I"), second person ("you"), and third person ("he/she/it.") Yet within these are endless varieties such as singular and plural nouns or various temporal orientations of verbs: present ("I go"); present perfect ("I have gone"); simple past ("I went"); past perfect ("I had gone.") There are even "moods," such as the subjunctive or hypothetical, which permit the construction of complex thoughts such as "I would have gone." Yet for all this variety in terms of sentence pattern—actually, a degree of variety much greater than for that of energy types—all subject-predicate constructions can still be identified as first, second, or third person.

One might thus describe thermal energy as a manifestation of energy, rather than as a discrete form. Other such manifestations include electromagnetic (sometimes divided into electrical and magnetic), sound, chemical, and nuclear. The principles governing most of these are similar: for instance, the positive or negative attraction between two electromagnetically charged particles is analogous to the force of gravity.

Mechanical Energy

One term not listed among manifestations of energy is mechanical energy, which is something different altogether: the sum of potential and kinetic energy. A dropped or bouncing ball was used as a convenient illustration of interactions within a larger system of mechanical energy, but the example could just as easily have been a roller coaster, which, with its ups and downs, quite neatly illustrates the sliding scale of kinetic and potential energy.

Likewise, the relationship of Earth to the Sun is one of potential and kinetic energy transfers: as with the baseball and Earth itself, the planet is pulled by gravitational force toward the larger body. When it is relatively far from the Sun, it possesses a higher degree of potential energy, whereas when closer, its kinetic energy is highest. Potential and kinetic energy can also be illustrated within the realm of electromagnetic, as opposed to gravitational, force: when a nail is some distance from a magnet, its potential energy is high, but as it moves toward the magnet, kinetic energy increases.

Energy Conversion in a Dam

A dam provides a beautiful illustration of energy conversion: not only from potential to kinetic, but from energy in which gravity provides the force component to energy based in electromagnetic force. A dam big enough to be used for generating hydroelectric power forms a vast steel-and-concrete curtain that holds back millions of tons of water from a river or other body. The water nearest the top—the "head" of the dam—thus has enormous potential energy.

Hydroelectric power is created by allowing controlled streams of this water to flow downward, gathering kinetic energy that is then transferred to powering turbines. Dams in popular vacation spots often release a certain amount of water for recreational purposes during the day. This makes it possible for rafters, kayakers, and others downstream to enjoy a relatively fast-flowing river. (Or, to put it another way, a stream with high kinetic energy.) As the day goes on, however, the sluice-gates are closed once again to build up the "head." Thus when night comes, and energy demand is relatively high as people retreat to their homes, vacation cabins, and hotels, the dam is ready to provide the power they need.

Other Manifestations of Energy

Thermal and electromagnetic energy are much more readily recognizable manifestations of energy, yet sound and chemical energy are two forms that play a significant part as well. Sound, which is essentially nothing more than the series of pressure fluctuations within a medium such as air, possesses enormous energy: consider the example of a singer hitting a certain note and shattering a glass.

Contrary to popular belief, the note does not have to be particularly high: rather, the note should be on the same wavelength as the glass's own vibrations. When this occurs, sound energy is transferred directly to the glass, which is shattered by this sudden net intake of energy. Sound waves can be much more destructive than that: not only can the sound of very loud music cause permanent damage to the ear drums, but also, sound waves of certain frequencies and decibel levels can actually drill through steel. Indeed, sound is not just a by-product of an explosion; it is part of the destructive force.

As for chemical energy, it is associated with the pull that binds together atoms within larger molecular structures. The formation of water molecules, for instance, depends on the chemical bond between hydrogen and oxygen atoms. The combustion of materials is another example of chemical energy in action.

With both chemical and sound energy, however, it is easy to show how these simply reflect the larger structure of potential and kinetic energy discussed earlier. Hence sound, for instance, is potential energy when it emerges from a source, and becomes kinetic energy as it moves toward a receiver (for example, a human ear). Furthermore, the molecules in a combustible material contain enormous chemical potential energy, which becomes kinetic energy when released in a fire.

Rest Energy and Its Nuclear Manifestation

Nuclear energy is similar to chemical energy, though in this instance, it is based on the binding of particles within an atom and its nucleus. But it is also different from all other kinds of energy, because its force component is neither gravitational nor electromagnetic, but based on one of two other known varieties of force: strong nuclear and weak nuclear. Furthermore, nuclear energy—to a much greater extent than thermal or chemical energy—involves not only kinetic and potential energy, but also the mysterious, extraordinarily powerful, form known as rest energy.

Throughout this discussion, there has been little mention of rest energy; yet it is ever-present. Kinetic and potential energy rise and fall with respect to one another; but rest energy changes little. In the baseball illustration, for instance, the ball had the same rest energy at the top of the building as it did in flight—the same rest energy, in fact, that it had when sitting on the ground. And its rest energy is enormous.

Nuclear Warfare

This brings back the subject of the rest energy formula: E = mc², famous because it made possible the creation of the atomic bomb. The latter, which fortunately has been detonated in warfare only twice in history, brought a swift end to World War II when the United States unleashed it against Japan in August 1945. From the beginning, it was clear that the atom bomb possessed staggering power, and that it would forever change the way nations conducted their affairs in war and peace.

Yet the atom bomb involved only nuclear fission, or the splitting of an atom, whereas the hydrogen bomb that appeared just a few years after the end of World War II used an even more powerful process, the nuclear fusion of atoms. Hence, the hydrogen bomb upped the ante to a much greater extent, and soon the two nuclear superpowers—the United States and the Soviet Union—possessed the power to destroy most of the life on Earth.

The next four decades were marked by a superpower struggle to control "the bomb" as it came to be known—meaning any and all nuclear weapons. Initially, the United States controlled all atomic secrets through its heavily guarded Manhattan Project, which created the bombs used against Japan. Soon, however, spies such as Julius and Ethel Rosenberg provided the Soviets with U.S. nuclear secrets, ensuring that the dictatorship of Josef Stalin would possess nuclear capabilities as well. (The Rosenbergs were executed for treason, and their alleged innocence became a celebrated cause among artists and intellectuals; however, Soviet documents released since the collapse of the Soviet empire make it clear that they were guilty as charged.)

Both nations began building up missile arsenals. It was not, however, just a matter of the United States and the Soviet Union. By the 1970s, there were at least three other nations in the "nuclear club": Britain, France, and China. There were also other countries on the verge of developing nuclear bombs, among them India and Israel. Furthermore, there was a great threat that a terrorist leader such as Libya's Muammar al-Qaddafi would acquire nuclear weapons and do the unthinkable: actually use them.

Though other nations acquired nuclear weapons, however, the scale of the two super-power arsenals dwarfed all others. And at the heart of the U.S.-Soviet nuclear competition was a sort of high-stakes chess game—to use a metaphor mentioned frequently during the 1970s. Soviet leaders and their American counterparts both recognized that it would be the end of the world if either unleashed their nuclear weapons; yet each was determined to be able to meet the other's ever-escalating nuclear threat.

United States President Ronald Reagan earned harsh criticism at home for his nuclear buildup and his hard line in negotiations with Soviet President Mikhail Gorbachev; but as a result of this one-upmanship, he put the Soviets into a position where they could no longer compete. As they put more and more money into nuclear weapons, they found themselves less and less able to uphold their already weak economic system. This was precisely Reagan's purpose in using American economic might to outspend the Soviets—or, in the case of the proposed multi-trillion-dollar Strategic Defense Initiative (SDI or "Star Wars")—threatening to outspend them. The Soviets expended much of their economic energy in competing with U.S. military strength, and this (along with a number of other complex factors), spelled the beginning of the end of the Communist empire.

E = Mc²

The purpose of the preceding historical brief is to illustrate the epoch-making significance of a single scientific formula: E = mc². It ended World War II and ensured that no war like it would ever happen again—but brought on the specter of global annihilation. It created a superpower struggle—yet it also ultimately helped bring about the end of Soviet totalitarianism, thus opening the way for a greater level of peace and economic and cultural exchange than the world has ever known. Yet nuclear arsenals still remain, and the nuclear threat is far from over.

So just what is this literally earth-shattering formula? E stands for rest energy, m for mass, and c for the speed of light, which is 186,000 mi (297,600 km) per second. Squared, this yields an almost unbelievably staggering number.

Hence, even an object of insignificant mass possesses an incredible amount of rest energy. The baseball, for instance, weighs only about 0.333 lb, which—on Earth, at least—converts to 0.15 kg. (The latter is a unit of mass, as opposed to weight.) Yet when factored into the rest energy equation, it yields about 3.75 billion kilowatt-hours—enough to provide an American home with enough electrical power to last it more than 156,000 years!

How can a mere baseball possess such energy? It is not the baseball in and of itself, but its mass; thus every object with mass of any kind possesses rest energy. Often, mass energy can be released in very small quantities through purely thermal or chemical processes: hence, when a fire burns, an almost infinitesimal portion of the matter that went into making the fire is converted into energy. If a stick of dynamite that weighed 2.2 lb (1 kg) exploded, the portion of it that "disappeared" would be equal to 6 parts out of 100 billion; yet that portion would cause a blast of considerable proportions.

As noted much earlier, the derivation of Einstein's formula—and, more to the point, how he came to recognize the fundamental principles involved—is far beyond the scope of this essay. What is important is the fact, hypothesized by Einstein and confirmed in subsequent experiments, that matter is convertible to energy, a fact that becomes apparent when matter is accelerated to speeds close to that of light.

Physicists do not possess a means for propelling a baseball to a speed near that of light—or of controlling its behavior and capturing its energy. Instead, atomic energy—whether of the wartime or peacetime varieties (that is, in power plants)—involves the acceleration of mere atomic particles. Nor is any atom as good as another. Typically physicists use uranium and other extremely rare minerals, and often, they further process these minerals in highly specialized ways. It is the rarity and expense of those minerals, incidentally—not the difficulty of actually putting atomic principles to work—that has kept smaller nations from developing their own nuclear arsenals.

Where to Learn More

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Berger, Melvin. Sound, Heat and Light: Energy at Work. Illustrated by Anna DiVito. New York: Scholastic, 1992.

Gardner, Robert. Energy Projects for Young Scientists. New York: F. Watts, 1987.

"Kinetic and Potential Energy" Thinkquest (Web site). <http://library.thinkquest.org/2745/data/ke.htm> (March 12, 2001).

Snedden, Robert. Energy. Des Plaines, IL: Heinemann, Library, 1999.

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

"Work and Energy" (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/energy/energtoc.html> (March 12, 2001).

World of Coasters (Web site). <http://www.worldofcoasters.com> (March 12, 2001).

Zubrowski, Bernie. Raceways: Having Fun with Balls and Tracks. Illustrated by Roy Doty. New York: Morrow, 1985.

The ability of one system to do work on another system. There are many kinds of energy: chemical energy from fossil fuels, electrical energy distributed by a utility company, radiant energy from the Sun, and nuclear energy from a reactor. The units of energy include ergs, joules, foot-pounds, and foot-poundals. Work and heat have the same units as energy, but are entirely different physical concepts. See also Heat; Work.

Any particle or system of particles subject to conservative forces has two kinds of energy, potential energy and kinetic energy. Potential energy is the energy due to position or configuration, and kinetic energy is the energy due to motion.

Energy is conserved for all isolated mechanical systems. This is because if a system A is isolated, there is no other system B that it can give any energy to, and its total energy must remain constant. This system A can convert kinetic energy to potential energy, and it can convert one form of potential energy to another, but the total energy must remain the same. The meaning of conserved total energy is that the system has the same value of total energy at all times. See also Conservation of energy.

In 1905 A. Einstein showed that at high velocities near the speed of light important modifications must be made in physical concepts. One particularly radical idea which he advanced was that space and time are not independent, but rather are two aspects of the same object, a space-time manifold. This necessitated a reexamination of the concept of energy and led to the conclusion that the inertia, or mass m, depends upon its energy through the mass-energy relation shown below, where c is the speed of light in vacuum. Furthermore, energy and momentum conservation become joined in a single four-momentum conservation law in special relativity. See also Internal energy; Relativity.

The ability to do work. The SI unit of energy is the joule, and nutritionally relevant amounts of energy are kilojoules (kJ, 1000 J) and megajoules (MJ, 1, 000, 000 J). The calorie is still widely used in nutrition; 1 cal = 4.186 J (approximated to 4.2). While it is usual to speak of the calorie or joule content of a food it is more correct to refer to the energy yield.

The total chemical energy in a food, as released by complete combustion (in the bomb calorimeter) is gross energy. Allowing for the losses of unabsorbed food in the faeces gives digestible energy. Allowing for loss in the urine due to incomplete combustion in the body (e.g. urea from the incomplete combustion of proteins) gives metabolizable energy. Allowing for the loss due to diet-induced thermogenesis gives net energy, i.e. the actual amount available for use in the body.

The following factors are used for energy yields of foods: protein 17 kJ (4 kcal); fat, 37 kJ (9 kcal); carbohydrate, 16 kJ (4 kcal); alcohol, 29 kJ (7 kcal); sugar alcohols, 10 kJ (2.4 kcal); organic acids, 13 kJ (3 kcal).

noun

Capacity or power for work or vigorous activity: animation, force, might, potency, power, puissance, sprightliness, steam, strength. Informal get-up-and-go, go, pep, peppiness, zip. See action/inaction.

Definition: person's spirit and vigor
Antonyms: idleness, inactivity, laziness, lethargy, tiredness

Energy means work. It refers to the effort required to move a weight for some distance. The heavier the weight or the longer the distance, the more energy is required. Energy is measured in units called "joules," or sometimes as the heat equivalent to these joules, called "calories." In nutrition, both terms are used. A calorie is the amount of heat needed to warm one gram of water by one degree centigrade. A more convenient unit is the kilocalorie (kcal), which equals one thousand calories. In physical terms, energy has several forms, all of which can be converted into heat. These include potential energy, kinetic energy, chemical energy, and heat energy.

(SEE ALSO: Fats; Krebs Cycle; Nutrition)

— GEORGE A. BRAY

The physical capacity for doing work. Nearly all our energy derives from the sun, and technical progress has reflected more and more sophisticated uses of energy, from wind and water, through fossil fuels, to nuclear power. In the early stages of industrialization, the consumption of energy is closely related to levels of economic development, and hence per capita GNP, although mature economies tend to be more energy-efficient, perhaps because technology improves and the emphasis shifts to service industries. Nevertheless, the advanced economies still account for most of the world's energy consumption. The breakdown of the European Union's energy consumption in 1997 was: oil 42.2%, natural gas 22.15%, solid fuels 16%, nuclear 15.8%, hydroelectricity 1.2%, and other renewable energy 2.7% (http://www.eurogas.org/site/statis/statcons.htm).

World demand for energy has increased so much that an energy crisis—a potential shortage of energy—has now been identified and this, together with the adverse environmental effects associated with the burning of fossil fuels (greenhouse effect, acid rain) has led to increased emphasis on energy conservation.

Energy resources are commonly divided into non-renewable (fossil fuels) and renewable (wind, water, and solar energy). See also geothermal heat.

The capacity to do work; the amount of work that a system is capable of doing.

The capacity of something to generate work, itself defined as the product of force times distance. In the seventeenth century dispute arose between the Cartesians, who held that energy should be measured by mass times velocity (later separately identified as momentum), and Leibniz, who held that it was proportional to mass times the square of the velocity. Later potential energy, stored in a system such as a mass at a height, or a coiled spring, became distinguished from the original idea of kinetic energy. More subtle concepts of energy evolve in special and general relativity theory.

The capacity for doing work. The SI unit for energy is the joule, although the calorie is still commonly used in nutritional studies. There are many different interconvertible forms of energy, including chemical energy, mechanical energy. electrical energy, heat energy, nuclear energy, and radiant energy.

Sufficient dietary energy is essential to the survival and health of all animals. For understanding the biology and health of humans, energy is particularly important for a number of reasons. First, food and energy represent critical points of interaction between humans and their environment. The environments in which humans live determine the range of food resources that are available and how much energy and effort are necessary to procure those resources. Indeed, the dynamic between energy intake and energy expenditure is quite different for a subsistence farmer of Latin America than it is for an urban executive living in the United States. Beyond differences in the physical environment, social, cultural, and economic variation also shape aspects of energy balance. Social and cultural norms are important for shaping food preferences, whereas differences in subsistence behavior and socioeconomic status strongly influence food availability and the effort required to obtain food.

Additionally, the balance between energy expenditure and energy acquired has important adaptive consequences for both survival and reproduction. Obtaining sufficient food energy has been an important stressor throughout human evolutionary history, and it continues to strongly shape the biology of traditional human populations today.

This article examines aspects of energy expenditure and energy intake in humans. How energy is measured is first considered, with a look at how both the energy content of foods and the energy requirements for humans are determined. Next, aspects of energy consumption and the chemical sources of energy in different food items are examined. Third, the physiological basis of variation in human energy requirements is explored, specifically a consideration of the different factors that determine how much energy a person must consume to sustain him- or herself. Finally, patterns of variation in energy intake and expenditure among modern human populations are examined, with the different strategies that humans use to fulfill their dietary energy needs highlighted.

Calorimetry: Measuring Energy

The study of energy relies on the principle of calorimetry, the measurement of heat transfer. In food and nutrition, energy is most often measured in kilocalories (kcal). One kilocalorie is the amount of heat required to raise the temperature of 1 kilogram (or 1 liter) of water 1°C. Thus, a food item containing 150 kilocalories (two pieces of bread, for example) contains enough stored chemical energy to increase the temperature of 150 liters of water by 1°C. Another common unit for measuring energy is the joule or the kilojoule (1 kilojoule [kJ] = 1,000 joules). The conversion between calories and joules is as follows: 1 kilocalorie equals 4.184 kilojoules.

To directly measure the energy content of foods, scientists use an instrument known as a bomb calorimeter. This instrument burns a sample of food in the presence of oxygen and measures the amount of heat released (that is, kilocalories or kilojoules). This heat of combustion represents the total energetic value of the food.

Basic principles of calorimetry are also used to measure energy expenditure (or requirements) in humans and other animals. Techniques for measuring energy expenditure involve either measuring heat loss directly (direct calorimetry) or measuring a proxy of heat loss such as oxygen consumption (O₂) or carbon dioxide (CO₂) production (indirect calorimetry). Direct calorimetry is done under controlled laboratory conditions in insulated chambers that measure changes in air temperature associated with the heat being released by a subject. Although quite accurate, direct calorimetry is not widely used because of its expense and technical difficulty.

Thus, methods of indirect calorimetry are more commonly used to quantify human energy expenditure. The most widely used of these techniques involve measuring oxygen consumption. Because the body's energy production is dependent on oxygen (aerobic respiration), O₂ consumption provides a very accurate indirect way of measuring a person's energy expenditure. Every liter of O₂ consumed by the body is equivalent to an energy cost of approximately 5 kilocalories. Consequently, by measuring O₂ use while a person is performing a particular task (for example, standing, walking, or running on a treadmill), the energy cost of the task can be determined.

With the Douglas bag method for measuring O₂ uptake, subjects breathe through a valve that allows them to inhale room air and exhale into a large collection bag. The volume and the O₂ and CO₂ contents of the collected air sample are then measured to determine the total amount of oxygen consumed by the subject. Recent advances in computer technology allow for the determination of O₂ consumption more quickly without having to collect expired air samples. One computerized system for measuring oxygen consumption, like the Douglas bag method, determines energy costs by measuring the volume and the O₂ and CO₂ concentrations of expired air samples.

Sources of Food Energy

The main chemical sources of energy in our foods are carbohydrates, protein, and fats. Collectively, these three energy sources are known as macronutrients. Vitamins and minerals (micronutrients) are required in much smaller amounts and are important for regulating many aspects of biological function.

Carbohydrates and proteins have similar energy contents; each provides 4 kilocalories of metabolic energy per gram. In contrast, fat is more calorically dense; each gram provides about 9 to 10 kilocalories. Alcohol, although not a required nutrient, also can be used as an energy source, contributing 7 kcal/g. Regardless of the source, excess dietary energy can be stored by the body as glycogen (a carbohydrate) or as fat. Humans have relatively limited glycogen stores (about 375–475 grams) in the liver and muscles. Fat, however, represents a much larger source of stored energy, accounting for approximately 13 to 20 percent of body weight in men and 25 to 28 percent in women.

The largest source of dietary energy for most humans is carbohydrates (45–50 percent of calories in the typical American diet). The three types of carbohydrates are monosaccharides, disaccharides, and polysaccharides. Monosaccharides, or simple sugars, include glucose, the body's primary metabolic fuel; fructose (fruit sugar); and galactose. Disaccharides, as the name implies, are sugars formed by a combination of two monosaccharides. Sucrose (glucose and fructose), the most common disaccharide, is found in sugar, honey, and maple syrup. Lactose, the sugar found in milk, is composed of glucose and galactose. Maltose (glucose and glucose), the least common of the disaccharides, is found in malt products and germinating cereals. Polysaccharides, or complex carbohydrates, are composed of three or more simple sugar molecules. Glycogen is the polysaccharide used for storing carbohydrates in animal tissues. In plants, the two most common polysaccharides are starch and cellulose. Starch is found in a wide variety of foods, such as grains, cereals, and breads, and provides an important source of dietary energy. In contrast, cellulose—the fibrous, structural parts of plant material—is not digestible by humans and passes through the gastrointestinal tract as fiber.

Fats provide the largest store of potential energy for biological work in the body. They are divided into three main groups: simple, compound, and derived. The simple or "neutral fats" consist primarily of triglycerides. A triglyceride consists of two component molecules: glycerol and fatty acid. Fatty acid molecules, in turn, are divided into two broad groups: saturated and unsaturated. These categories reflect the chemical bonding pattern between the carbon atoms of the fatty acid molecule. Saturated fatty acids have no double bonds between carbons, thus allowing for the maximum number of hydrogen atoms to be bound to the carbon (that is, the carbons are "saturated" with hydrogen atoms). In contrast, unsaturated fatty acids have one (monounsaturated) or more (polyunsaturated) double bonds. Saturated fats are abundant in animal products, whereas unsaturated fats predominate in vegetable oils.

Compound fats consist of a neutral fat in combination with some other chemical substance (for example, a sugar or a protein). Examples of compound fats include phospholipids and lipoproteins. Phospholipids are important in blood clotting and insulating nerve fibers, whereas lipoproteins are the main form of transport for fat in the bloodstream.

Derived fats are substances synthesized from simple and compound fats. The best known derived fat is cholesterol. Cholesterol is present in all human cells and may be derived from foods (exogenous) or synthesized by the body (endogenous). Cholesterol is necessary for normal development and function because it is critical for the synthesis of such hormones as estradiol, progesterone, and testosterone.

Proteins, in addition to providing an energy source, are also critical for the growth and replacement of living tissues. They are composed of nitrogen-containing compounds known as amino acids. Of the twenty different amino acids required by the body, nine (leucine, isoleucine, valine, lysine, threonine, methionine, phenylalanine, tryptophan, and histidine) are known as "essential" because they cannot be synthesized by the body and thus must be derived from food. Two others, cystine and tyrosine, are synthesized in the body from methionine and phenylalanine, respectively. The remaining amino acids are called "nonessential" because they can be produced by the body and need not be derived from the diet.

Determinants of Daily Energy Needs

A person's daily energy requirements are determined by several different factors. The major components of an individual's energy budget are associated with resting or basal metabolism, activity, growth, and reproduction. Basal metabolic rate (BMR) represents the minimum amount of energy necessary to keep a person alive. Basal metabolism is measured under controlled conditions while a subject is lying in a relaxed and fasted state.

In addition to basal requirements, energy is expended to perform various types of work, such as daily activities and exercise, digestion and transport of food, and regulating body temperature. The energy costs associated with food handling (i.e., the thermic effect of food) make up a relatively small proportion of daily energy expenditure and are influenced by amount consumed and the composition of the diet (e.g., high-protein meals elevate dietary thermogenesis). In addition, at extreme temperatures, energy must be spent to heat or cool the body. Humans (unclothed) have a thermoneutral range of 25 to 27°C (77–81°F). Within this temperature range, the minimum amount of metabolic energy is spent to maintain body temperature. Finally, during one's lifetime, additional energy is required for physical growth and for reproduction (e.g., pregnancy, lactation).

In 1985 the World Health Organization (WHO) presented its most recent recommendations for assessing human energy requirements. The procedure used for determining energy needs involves first estimating BMR from body weight on the basis of predictive equations developed by the WHO. These equations are presented in Table 1. After estimating BMR, the total daily energy expenditure (TDEE) for adults (18 years old and above) is determined as a multiple of BMR, based on the individual's activity level. This multiplier, known as the physical activity level (PAL) index, reflects the proportion of energy above basal requirements that an individual spends over the course of a normal day. The PALs associated with different occupational work levels for adult men and women are presented in Table 2. The WHO recommends that minimal daily activities such as dressing, washing, and eating are commensurate with a PAL of 1.4 for both men and women. Sedentary lifestyles (e.g., office work) require PALs of 1.55 for men and 1.56 for women. At higher work levels, however, the sex differences are greater. Moderate work is associated with a PAL of 1.78 in men and 1.64 in women, whereas heavy work levels (for example, manual labor, traditional agriculture) necessitate PALs of 2.10 and 1.82 for men and women, respectively.

Table 1

In addition to the costs of daily activity and work, energy costs for reproduction also must be considered. The WHO recommends an additional 285 kcal/day for women who are pregnant and an additional 500 kcal/day for those who are lactating.

Energy requirements for children and adolescents are estimated differently because extra energy is necessary for growth and because relatively less is known about variation in their activity patterns. For children and adolescents between 10 and 18 years old, the WHO recommends the use of age-and sex-specific PALs. In contrast, energy requirements for children under 10 years old are determined by multiplying the child's weight by an ageand sex-specific constant. The reference values for boys and girls under 18 years old are presented in Table 3.

Human Variation in Sources of Food Energy

Compared to most other mammals, humans are able to survive and flourish eating a remarkably wide range of foods. Human diets range from completely vegetarian (as observed in many populations of South Asia) to those based almost entirely on meat and animal foods (for example, traditional Eskimo/Inuit populations of the Arctic). Thus, over the course of evolutionary history, humans have developed a high degree of dietary plasticity.

Table 2

Table 3

This ability to utilize a diverse array of plant and animal resources for food is one of the features that allowed humans to spread and colonize ecosystems all over the world.

Table 4 presents information on per capita energy intakes and the percentage of energy derived from plant and animal foods for subsistence-level (i.e., food-producing) and industrial human societies. The relative contribution of animal foods varies considerably, ranging from less than 10 percent of dietary energy in traditional farming communities of tropical South America, to more than 95 percent among traditionally living Inuit hunters of the Canadian Arctic.

Subsistence-level agricultural populations, as a group, have the lowest consumption of animal foods. Among hunting and gathering populations, the contribution of animal foods to the diet is variable, partly reflecting the environments in which these populations reside. For example, the !Kung San, who live in arid desert environments of southern Africa, have among the lowest levels of animal food consumption among hunter-gatherers. In contrast, hunters of the Arctic rely almost entirely on animal foods for their daily energy. Foragers living in forest and grassland regions of the tropics (for example, the Ache and the Hiwi) have intermediate levels of animal consumption.

Regardless of whether they are from plant or animals, the staple foods in most human societies are calorically dense. Indeed, one of the hallmarks of human evolutionary history has been humankind's success at developing subsistence strategies that maximize the energy returns from available food resources. The initial evolution of human "hunting and gathering" economies some 2 million years ago is an example of this. By incorporating more meat into their diet, man's hominid ancestors were able to increase the energy contents of their diets.

Table 4

With the evolution of agriculture, human populations began to manipulate relatively marginal plant species so as to increase their productivity, digestibility, and energy content. Today, staple agricultural crops such as rice, wheat, and other cereal grains are calorically dense (more than 300 kilocalories per 100 grams), and are much richer sources of energy than the wild plants from which they evolved.

Novel methods of food processing also allow humans to increase the energy content and digestibility of their foods. The most fundamental of these techniques is the use of fire for cooking, a strategy adopted by man's hominid ancestors at least 400,000 years ago. Cooking makes plant foods more digestible by helping to break down complex carbohydrates. Recent work has shown that cooking can increase the energy content of starchy tubers (potatoes, cassava) by more than 70 percent.

Another interesting example of processing food to raise its energy content is seen among populations living in the high Andes of South America. Here, small potatoes are left outside for several days to be repeatedly frozen during the cold nights and then dried under the intense daytime sun. The resulting product, called chuño, can be stored for many months and has an energy content more than three times that of a fresh potato (330 kilocalories per 100 grams versus 90 kilocalories per 100 grams).

Human Variation in Energy Expenditure

Humans also show considerable variation in levels of energy expenditure. Recent work by Allison E. Black and colleagues indicates that daily energy expenditure in human groups typically ranges from 1.2 to 5.0 times BMR (i.e., PAL = 1.2–5.0). The lowest levels of physical activity, PALs of 1.20 to 1.25, are observed among hospitalized and nonambulatory populations. In contrast, the highest levels of physical activity (PALs of 2.5–5.0) have been observed among elite athletes and soldiers in combat training. Within this group, Tour de France cyclists have the highest recorded daily energy demands of 8,050 kcal/day (a PAL = 4.68)!

Table 5 presents data on body weight, total daily energy expenditure, and PALs of adult men and women from selected human groups. Men of the subsistence-level populations (that is, foragers, pastoralists, and agriculturalists) are, on average, 20 kilograms (45 pounds) lighter than their counterparts from the industrialized world, and yet have similar levels of daily energy expenditure (2,897 versus 2,859 kcal/day). The same pattern is true for women; those from subsistence-level populations are 12.5 kilograms (28 pounds) lighter than women of industrialized societies, but have higher levels of daily energy expenditure (2,227 versus 2,146 kcal/day).

Thus, daily energy needs are expressed relative to BMR; it is found that adults living a "modern" lifestyle in the industrialized world have significantly lower physical activity levels than those living more "traditional" lives. Among men, PALs in the industrialized societies average 1.67 (range = 1.53 to 1.84), as compared to 1.90 (range = 1.58 to 2.38) among the subsistence-level groups. Physical activity levels among women average 1.63 in the industrialized world (range = 1.48 to 1.69) and 1.78 (range = 1.56 to 2.03) among the subsistence-level societies.

The differences in daily energy demands between subsistence-level and industrialized populations are further highlighted in Figure 1, which shows daily energy expenditure (kilocalories/day) plotted relative to body weight (in kilograms). The two lines denote the best-fit regressions for both groups. These regressions show that at the same body weight, adults of the industrialized world have daily energy needs that are 600 to 1,000 kilocalories lower than those of people living in subsistence-level societies.

It is these declines in physical activity and daily energy expenditure associated with "modern" lifestyles that are largely responsible for the growing problem of obesity throughout the world. In the United States, rates of obesity have increased dramatically over the last twenty years, such that now over half of the adult American population is either overweight or obese. Equally disturbing has been the emergence of obesity as a problem in part of the developing world where it was virtually unknown less than a generation ago. In some sense, obesity and other chronic diseases of the modern world (diabetes and cardiovascular disease, for example) represent a continuation of trends that started early in man's evolutionary history. Humans have developed a diet that is extremely rich in calories while at the same time minimizing the amount of energy necessary for physical work and activity. Ongoing work in nutritional science is attempting to better understand the biological and environmental factors that influence patterns of energy consumption and expenditure to promote human health and well-being.

Table 5

Bibliography

Black, Allison E., W. Andrew Coward, Tim J. Cole, and Andrew M. Prentice. "Human Energy Expenditure in Affluent Societies: An Analysis of 574 Double-Labelled Water Measurements." European Journal of Clinical Nutrition 50 (1996): 72–92.

Consolazio, C. Frank, Robert E. Johnson, and Louis J. Pecora. Physiological Measurements of Metabolic Functions in Man. New York: McGraw-Hill, 1963.

Durnin, John V. G. A., and Reginald Passmore. Energy, Work and Leisure. London: Heineman, 1967.

Food and Agriculture Organization, World Health Organization, and United Nations University (FAO/WHO/UNU). Energy and Protein Requirements. Report of Joint FAO/ WHO/UNU Expert Consultation. WHO Technical Report Series No. 724. Geneva: World Health Organization, 1985.

Gibson, Rosalind S. Principles of Nutritional Assessment. Oxford: Oxford University Press, 1990.

James, William P. T., and E. Claire Schofield. Human Energy Requirements: A Manual for Planners and Nutritionists. Oxford: Oxford University Press, 1990.

Kleiber, Max. The Fire of Life: An Introduction to Animal Energetics, 2d ed. Huntington, N.Y.: Krieger, 1975.

Leonard, William R. "Human Nutritional Evolution." In Human Biology: A Biocultural and Evolutionary Approach, edited by Sara Stinson, Barry Bogin, Rebecca Huss-Ashmore, and Dennis O'Rourke, pp. 295–343. New York: Wiley-Liss, 2000.

Leonard, William R., and Marcia L. Robertson. "Comparative Primate Energetics and Hominid Evolution." American Journal of Physical Anthropology 102 (1997): 265–281.

McArdle, William D., Frank I. Katch, and Victor L. Katch. Exercise Physiology: Energy, Nutrition and Human Performance, 5th ed. Philadelphia: Lippincott Williams and Wilkins, 2001.

McLean, Jennifer A., and G. Tobin. Animal and Human Calorimetry. Cambridge: Cambridge University Press, 1987.

Ulijaszek, Stanley J. Human Energetics in Biological Anthropology. Cambridge: Cambridge University Press, 1995.

—William R. Leonard

Laws and regulations concerning the production and distribution of energy have existed for over one hundred years in the United States. Energy law became recognized as a specialty following the energy crises of the 1970s. It focuses on the production, distribution, conservation, and development of energy resources like coal, oil, natural gas, nuclear power, and hydroelectric power.

In 1876, the U.S. Supreme Court, in Munn v. Illinois, 94 U.S. (Otto) 113, 24 L. Ed. 77, held that "natural monopolies" could be regulated by the government. Munn concerned grain elevators but stood more generally for the principle that the public must be allowed to control private property committed to a use in which the public has an interest. This legal recognition of natural monopolies provides the basis for much of the legal and regulatory control the government exercises over utility companies.

The regulation of energy in the late 1800s was on a local and regional level, and was primarily market driven. The transition from using wood as a primary source of energy to using coal was almost complete, and a second transition from coal to natural gas and oil was beginning.

In 1900, Standard Oil Company controlled 90 percent of the oil market; within a few years, antitrust litigation had reduced its market share to 64 percent. Aside from antitrust enforcement, the federal government was content to let the market control the energy industry. Oil, coal, and natural gas found their greatest structural impediment in the "bottleneck" of distribution — pipelines for oil and natural gas, and railways for coal. The dominant model of energy policy that emerged from this period and existed unchanged until the 1970s was one of support for conventional resources and regulation of industries whose natural monopolies required some government oversight to ensure that their public purpose served a public interest.

On October 17, 1973, the Organization of Petroleum Exporting Countries (OPEC) announced an embargo of oil exports to all countries, including the United States, that were supporting Israel in the Yom Kippur War. Only approximately 10 percent of the United States' oil imports were affected, but the perception of a major oil shortage motivated the next three presidential administrations to exert a strong federal influence over energy.

President Richard M. Nixon created the Federal Energy Office (Exec. Order No. 11,930, 41 Fed. Reg. 32, 399) and appointed an "energy czar" to oversee oil supplies. President Gerald R. Ford's administration saw the passage of the Strategic Petroleum Reserve (42 U.S.C.A. § 6234) and the promulgation of minimum efficiency regulations for automobiles. In 1977, Jimmy Carter's administration created the Department of Energy (42 U.S.C.A. § 7101), which was the framework for the coordination, administration, and execution of a comprehensive national energy program.

The goal of a comprehensive national energy program was achieved with the passage of the National Energy Act of 1978, which consisted of five distinct pieces of legislation. The National Energy Conservation Policy Act (42 U.S.C.A. § 8201 et seq.) set standards and provided financing for conservation in buildings. The Powerplant and Industrial Fuel Use Act (42 U.S.C.A. § 8301 et seq.) encouraged the transition from oil and gas to coal in boilers. The Public Utilities Regulatory Policies Act (15 U.S.C.A. § 2601) granted Congress authority over the interstate transmission of electric power. The Natural Gas Policy Act (15 U.S.C.A. § 3301) unified the gas market and promoted the deregulation of the natural gas industry. The Energy Tax Act (26 U.S.C.A. § 1 et seq.) approved tax credits to promote conservation.

The administration of Ronald Reagan set policies that marked a significant change in the national energy policy, away from the Carter administration's centralized, governmentally regulated energy plan, which set ambitious goals for market stabilization and energy conservation through government intervention. The Reagan administration favored a more market-driven approach to achieve these goals. Although unsuccessful in its goal to abolish the Department of Energy, the Reagan administration was able to deregulate the natural gas industry through administrative initiatives (under the Federal Energy Regulatory Commission) and the Wellhead Decontrol Act of 1989 (15 U.S.C.A. § 3301).

The administration of George Bush also favored a market-driven approach to the regulation of energy, but the Persian Gulf War against Iraq in 1991 required Congress to respond to volatile conditions in the oil-exporting Middle East. The National Energy Policy Act of 1992 (42 U.S.C.A. § 13201) addressed issues such as competition among electric power generators and tax credits for wind and biomass energy production systems.

The National Energy Policy Plan, issued in 1995 during Bill Clinton's administration, continued the market-focused approach of the Reagan and Bush administrations. Citing as its primary goal a "sustainable energy policy," the plan states that the "administration's energy policy supports and reinforces the dominant role of the private sector" in achieving this goal.

The mid-1990s focus of market-driven, private sector regulation of energy development, conservation, and distribution may have to change in the years ahead. The energy needs of industrialized nations are intensifying, and the developing countries of the world are increasing their energy demands at a rate of 4.5 percent a year. Oil demand in Asia alone grew 50 percent from 1985 to 1995.

Energy policies in the future are likely to include emphasis on the development of more efficient, sustainable sources of energy. Many countries are already exploring the energy potential of biomass, wind, hydroelectric, and solar power.

See: Electricity; Energy Department; Environmental Law; Mine and Mineral Law; Public Utilities.

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Quotes:

"Controlled deep breathing helps the body to transform the air we breathe into energy. The stream of energized air produced by properly executed and controlled deep breathing produces a current of inner energy which radiates throughout the entire body and can be channeled to the body areas that need it the most, on demand." - Nancy Zi

"The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine." - Ernest Rutherford

"Is it a fact -- or have I dreamt it -- that, by means of electricity, the world of matter has become a great nerve, vibrating thousands of miles in a breathless point of time?" - Nathaniel Hawthorne

"Energy and persistence alter all things." - Benjamin Franklin

"Coal is a portable climate. It carries the heat of the tropics to Labrador and the polar circle; and it is the means of transporting itself whithersoever it is wanted. Watt and Stephenson whispered in the ear of mankind their secret, that a half-ounce of coal will draw two tons a mile, and coal carries coal, by rail and by boat, to make Canada as warm as Calcutta, and with its comfort brings its industrial power." - Ralph Waldo Emerson

"If your energy is as boundless as your ambition, total commitment may be a way of life you should seriously consider." - Dr. Joyce Brothers

See more famous quotes about Energy

In physics, the ability to do work. Objects can have energy by virtue of their motion (kinetic energy), by virtue of their position (potential energy), or by virtue of their mass (see E = mc²).

Power that may be translated into motion, overcoming resistance, or effecting physical change; the ability to do work. Energy assumes several forms; it may be thermal (in the form of heat), electrical, mechanical, chemical, radiant or kinetic. In doing work, the energy is changed from one form to another or to several forms. In these changes some of the energy is ‘lost’ in the sense that it cannot be recaptured and used again. Usually there is loss in the form of heat, which escapes or is dissipated unused. All energy changes give off a certain amount of the energy as heat.
All activities of the body require energy, and all needs are met by the consumption of food containing energy in chemical form. The animal diet comprises three main sources of energy: carbohydrates, proteins and fats. Of these three, carbohydrates most readily provide the kind of energy needed to activate muscles. Proteins work to build and restore body tissues. The body transforms chemical energy derived from food by the process of metabolism, an activity that takes place in the individual cell. Molecules of the food substances providing energy pass through the cell membrane. Inside the cell, chemical reactions occur that produce the new forms of energy and yield by-products such as water and waste materials. See also adenosine.

• dietary e. — the total energy intake in the diet is the gross energy. Digestible energy is gross energy less fecal energy. Metabolizable energy is digestible energy less that lost in fermentation in the gut, energy lost in urine. Net energy is metabolizable energy less energy used in specific dynamic action response. Expressed as joules, calories or occasionally therms (1 calorie=4.18 joule).
• e. density — see caloric density.
• e. feeds — feeds with a high carbohydrate content and therefore low fiber (<18%) and protein (<20%) contents.
• free e. — the energy equal to the maximum amount of work that can be obtained from a process occurring under conditions of fixed temperature and pressure.
• nuclear e. — energy that can be liberated by changes in the nucleus of an atom (as by fission of a heavy nucleus or by fusion of light nuclei into heavier ones with accompanying loss of mass).
• nutritional e. deficiency — causes loss of body weight, milk, egg and wool production. Continued for long periods or severe restriction causes particular metabolic upsets in pregnant and lactating ewes and cows—see pregnancy toxemia, acetonemia (2); in neonates, hypoglycemia. In others causes emaciation, inanition, starvation.
• e. production — production of ATP through oxidative phosphorylation or anaerobic glycolysis.
• e. requirements — generally vary between species and particularly between individuals. They are determined by many factors, especially age, level of activity, physiological status and body size, specifically body surface area. The basal energy requirement (BER) is the level required by a healthy animal at complete rest in a neutral environmental temperature. It can be calculated by using several formulae, based on body weight or body surface area, which is then used in the further calculation of the maintenance energy requirement (MER) which takes into account the individual animal's level of activity or disease status.
• e. reserves — any reduced carbon stored in compounds such as fatty acids in triacylglycerols of adipose tissue, glucose in glycogen, and amino acids in protein releases energy, ultimately in the form of ATP on oxidation of the carbon.
• e. transfer — conversion of energy from one form usually chemical in the form of ATP to another usually chemical, but can be electrical, mechanical or heat energy.

The capacity for doing work.

• Principles of Mechanics, Waves, and Measurement - energy: capacity to do work
• Physical Properties and Changes - energy: capacity to do work, which diminishes in a system when work is done by an amount equal to work so done

This article is about the scalar physical quantity. For an overview of and topical guide to energy, see Outline of energy. For other uses, see Energy (disambiguation).

"Energetic" redirects here. For other uses, see Energetic (disambiguation).

Lightning is the electric breakdown of air by strong electric fields, which produce a force on charges. When these charges move through a distance, a flow of energy occurs. The electric potential energy in the atmosphere then is transformed into thermal energy, light, and sound, which are other forms of energy.

In physics, energy (Ancient Greek: ἐνέργεια energeia "activity, operation"^[1]) is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems.^[2][3] Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.

The total energy contained in an object is identified with its mass, and energy (like mass), cannot be created or destroyed. When matter (ordinary material particles) is changed into energy (such as energy of motion, or into radiation), the mass of the system does not change through the transformation process. However, there may be mechanistic limits as to how much of the matter in an object may be changed into other types of energy and thus into work, on other systems. Energy, like mass, is a scalar physical quantity. In the International System of Units (SI), energy is measured in joules, but in many fields other units, such as kilowatt-hours and kilocalories, are customary. All of these units translate to units of work, which is always defined in terms of forces and the distances that the forces act through.

A system can transfer energy to another system by simply transferring matter to it (since matter is equivalent to energy, in accordance with its mass). However, when energy is transferred by means other than matter-transfer, the transfer produces changes in the second system, as a result of work done on it. This work manifests itself as the effect of force(s) applied through distances within the target system. For example, a system can emit energy to another by transferring (radiating) electromagnetic energy, but this creates forces upon the particles that absorb the radiation. Similarly, a system may transfer energy to another by physically impacting it, but in that case the energy of motion in an object, called kinetic energy, results in forces acting over distances (new energy) to appear in another object that is struck. Transfer of thermal energy by heat occurs by both of these mechanisms: heat can be transferred by electromagnetic radiation, or by physical contact in which direct particle-particle impacts transfer kinetic energy.

Energy may be stored in systems without being present as matter, or as kinetic or electromagnetic energy. Stored energy is created whenever a particle has been moved through a field it interacts with (requiring a force to do so), but the energy to accomplish this is stored as a new position of the particles in the field—a configuration that must be "held" or fixed by a different type of force (otherwise, the new configuration would resolve itself by the field pushing or pulling the particle back toward its previous position). This type of energy "stored" by force-fields and particles that have been forced into a new physical configuration in the field by doing work on them by another system, is referred to as potential energy. A simple example of potential energy is the work needed to lift an object in a gravity field, up to a support. Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appears as system mass, whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it.

Any form of energy may be transformed into another form. For example, all types of potential energy are converted into kinetic energy when the objects are given freedom to move to different position (as for example, when an object falls off a support). When energy is in a form other than thermal energy, it may be transformed with good or even perfect efficiency, to any other type of energy, including electricity or production of new particles of matter. With thermal energy, however, there are often limits to the efficiency of the conversion to other forms of energy, as described by the second law of thermodynamics.

In all such energy transformation processes, the total energy remains the same, and a transfer of energy from one system to another, results in a loss to compensate for any gain. This principle, the conservation of energy, was first postulated in the early 19th century, and applies to any isolated system. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.^[4]

Although the total energy of a system does not change with time, its value may depend on the frame of reference. For example, a seated passenger in a moving airplane has zero kinetic energy relative to the airplane, but non-zero kinetic energy (and higher total energy) relative to the Earth.

Contents 1 History 2 Energy in various contexts 2.1 Distinction between energy and power 3 Conservation of energy 4 Applications of the concept of energy 4.1 Energy transfer 4.2 Energy and the laws of motion 4.2.1 The Hamiltonian 4.2.2 The Lagrangian 4.2.3 Noether's Theorem 4.3 Energy and thermodynamics 4.3.1 Internal energy 4.3.2 The first law of thermodynamics 4.4 Equipartition of energy 4.5 Oscillators, phonons, and photons 4.6 Work and virtual work 4.7 Quantum mechanics 4.8 Relativity 4.9 Energy and life 5 Measurement 5.1 Methods 5.2 Units 5.3 Energy density 6 Forms of energy 7 Transformations of energy 8 See also 9 Notes and references 10 Further reading 11 External links

History

Main articles: History of energy and timeline of thermodynamics, statistical mechanics, and random processes

The word energy derives from the Greek ἐνέργεια energeia, which possibly appears for the first time in the work of Aristotle in the 4th century BCE.

Thomas Young – the first to use the term "energy" in the modern sense.

The concept of energy emerged out of the idea of vis viva (living force), which Gottfried Leibniz defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, a view shared by Isaac Newton, although it would be more than a century until this was generally accepted. In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its modern sense.^[5] Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy". It was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum.

William Thomson (Lord Kelvin) amalgamated all of these laws into the laws of thermodynamics, which aided in the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. It also led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan.

During a 1961 lecture^[6] for undergraduate students at the California Institute of Technology, Richard Feynman, a celebrated physics teacher and Nobel Laureate, said this about the concept of energy:

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

—The Feynman Lectures on Physics

Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. That is, energy is conserved because the laws of physics do not distinguish between different instants of time (see Noether's theorem).

Energy in various contexts

The concept of energy and its transformations is useful in explaining and predicting most natural phenomena. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often described by entropy (equal energy spread among all available degrees of freedom) considerations, as in practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

The concept of energy is widespread in all sciences.

• In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved. Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thus the products of a reaction may have more or less energy than the reactants. A reaction is said to be exergonic if the final state is lower on the energy scale than the initial state; in the case of endergonic reactions the situation is the reverse. Chemical reactions are invariably not possible unless the reactants surmount an energy barrier known as the activation energy. The speed of a chemical reaction (at given temperature T) is related to the activation energy E, by the Boltzmann's population factor e^−E/kT – that is the probability of molecule to have energy greater than or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation.The activation energy necessary for a chemical reaction can be in the form of thermal energy.
• In biology, energy is an attribute of all biological systems from the biosphere to the smallest living organism. Within an organism it is responsible for growth and development of a biological cell or an organelle of a biological organism. Energy is thus often said to be stored by cells in the structures of molecules of substances such as carbohydrates (including sugars), lipids, and proteins, which release energy when reacted with oxygen in respiration. In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human metabolism, assuming an average human energy expenditure of 12,500kJ per day and a basal metabolic rate of 80 watts. For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts is about the maximum.^[7] The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a “feel” for the use of a given amount of energy^[8]
• In geology, continental drift, mountain ranges, volcanoes, and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior.,^[9] while meteorological phenomena like wind, rain, hail, snow, lightning, tornadoes and hurricanes, are all a result of energy transformations brought about by solar energy on the atmosphere of the planet Earth.
• In cosmology and astronomy the phenomena of stars, nova, supernova, quasars and gamma ray bursts are the universe's highest-output energy transformations of matter. All stellar phenomena (including solar activity) are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter (usually molecular hydrogen) into various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter elements, primarily hydrogen).

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang, later being "released" (transformed to more active types of energy such as kinetic or radiant energy), when a triggering mechanism is available.

Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs. In a slower process, radioactive decay of these atoms in the core of the Earth releases heat. This thermal energy drives plate tectonics and may lift mountains, via orogenesis. This slow lifting represents a kind of gravitational potential energy storage of the thermal energy, which may be later released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars created these atoms.

In another similar chain of transformations beginning at the dawn of the universe, nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang. At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight. Such sunlight from our Sun may again be stored as gravitational potential energy after it strikes the Earth, as (for example) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbines or generators to produce electricity). Sunlight also drives many weather phenomena, save those generated by volcanic events. An example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddenly to power a few days of violent air movement. Sunlight is also captured by plants as chemical potential energy in photosynthesis, when carbon dioxide and water (two low-energy compounds) are converted into the high-energy compounds carbohydrates, lipids, and proteins. Plants also release oxygen during photosynthesis, which is utilized by living organisms as an electron acceptor, to release the energy of carbohydrates, lipids, and proteins. Release of the energy stored during photosynthesis as heat or light may be triggered suddenly by a spark, in a forest fire, or it may be made available more slowly for animal or human metabolism, when these molecules are ingested, and catabolism is triggered by enzyme action.

Through all of these transformation chains, potential energy stored at the time of the Big Bang is later released by intermediate events, sometimes being stored in a number of ways over time between releases, as more active energy. In all these events, one kind of energy is converted to other types of energy, including heat.

Distinction between energy and power

Although in everyday usage the terms energy and power are essentially synonyms, scientists and engineers distinguish between them. In its technical sense, power is not at all the same as energy, but is the rate at which energy is converted (or, equivalently, at which work is performed). Thus a hydroelectric plant, by allowing the water above the dam to pass through turbines, converts the water's potential energy into kinetic energy and ultimately into electric energy, whereas the amount of electric energy that is generated per unit of time is the electric power generated. The same amount of energy converted through a shorter period of time is more power over that shorter time.

Conservation of energy

Main article: Conservation of energy

Energy is subject to the law of conservation of energy. According to this law, energy can neither be created (produced) nor destroyed by itself. It can only be transformed.

Most kinds of energy (with gravitational energy being a notable exception)^[10] are subject to strict local conservation laws as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.^[6][11] Conservation of energy is the mathematical consequence of translational symmetry of time (that is, the indistinguishability of time intervals taken at different time)^[12] - see Noether's theorem.

According to Conservation of energy the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system.

This law is a fundamental principle of physics. It follows from the translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable.

This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by

which is similar in form to the Heisenberg uncertainty principle (but not really mathematically equivalent thereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

In particle physics, this inequality permits a qualitative understanding of virtual particles which carry momentum, exchange by which and with real particles, is responsible for the creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanical energy state of photons) are also responsible for electrostatic interaction between electric charges (which results in Coulomb law), for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, for van der Waals bond forces and some other observable phenomena.

Applications of the concept of energy

Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.^[13]

• The total energy of a system can be subdivided and classified in various ways. For example, it is sometimes convenient to distinguish potential energy (which is a function of coordinates only) from kinetic energy (which is a function of coordinate time derivatives only). It may also be convenient to distinguish gravitational energy, electric energy, thermal energy, and other forms. These classifications overlap; for instance, thermal energy usually consists partly of kinetic and partly of potential energy.
• The transfer of energy can take various forms; familiar examples include work, heat flow, and advection, as discussed below.
• The word "energy" is also used outside of physics in many ways, which can lead to ambiguity and inconsistency. The vernacular terminology is not consistent with technical terminology. For example, while energy is always conserved (in the sense that the total energy does not change despite energy transformations), energy can be converted into a form, e.g., thermal energy, that cannot be utilized to perform work. When one talks about "conserving energy by driving less," one talks about conserving fossil fuels and preventing useful energy from being lost as heat. This usage of "conserve" differs from that of the law of conservation of energy.^[11]

In classical physics energy is considered a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy-momentum 4-vector).^[14] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts).

Energy transfer

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by the definition of energy the transfer of energy between the "system" and adjacent regions is work. A familiar example is mechanical work. In simple cases this is written as the following equation:

(1)

if there are no other energy-transfer processes involved. Here is the amount of energy transferred, and   represents the work done on the system.

More generally, the energy transfer can be split into two categories:

(2)

where represents the heat flow into the system.

There are other ways in which an open system can gain or lose energy. In chemical systems, energy can be added to a system by means of adding substances with different chemical potentials, which potentials are then extracted (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). Winding a clock would be adding energy to a mechanical system. These terms may be added to the above equation, or they can generally be subsumed into a quantity called "energy addition term " which refers to any type of energy carried over the surface of a control volume or system volume. Examples may be seen above, and many others can be imagined (for example, the kinetic energy of a stream of particles entering a system, or energy from a laser beam adds to system energy, without either being either work-done or heat-added, in the classic senses).

(3)

Where E in this general equation represents other additional advected energy terms not covered by work done on a system, or heat added to it.

Energy is also transferred from potential energy () to kinetic energy () and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

(4)

The equation can then be simplified further since (mass times acceleration due to gravity times the height) and (half mass times velocity squared). Then the total amount of energy can be found by adding .

Energy and the laws of motion

In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity. Several formulations of mechanics have been developed using energy as a core concept.

The Hamiltonian

The total energy of a system is sometimes called the Hamiltonian, after William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.^[15]

The Lagrangian

Another energy-related concept is called the Lagrangian, after Joseph Louis Lagrange. This is even more fundamental than the Hamiltonian, and can be used to derive the equations of motion. It was invented in the context of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy.

Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction).

Noether's Theorem

Noether's (first) theorem (1918) states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.

Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.

Energy and thermodynamics

Internal energy

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.^[16]

The first law of thermodynamics

The first law of thermodynamics asserts that energy is conserved^[17] and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a commonly used corollary of the first law is that, for a system subject only to pressure forces and heat transfer (e.g., a cylinder-full of gas), the differential change in the internal energy of the system (with a gain in energy signified by a positive quantity) is given as

,

where the first term on the right is the heat transfered into the system, expressed in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated), and the last term on the right hand side is identified as work done on the system, where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system).

This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat and pV-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a closed system is expressed in a general form by

where is the heat supplied to the system and is the work applied to the system.

Equipartition of energy

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential. At two points in the oscillation cycle it is entirely kinetic, and alternatively at two other points it is entirely potential. Over the whole cycle, or over many cycles, net energy is thus equally split between kinetic and potential. This is called equipartition principle; total energy of a system with many degrees of freedom is equally split among all available degrees of freedom.

This principle is vitally important to understanding the behavior of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available energy states that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is called the second law of thermodynamics.

Oscillators, phonons, and photons

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In an ensemble (connected collection) of unsynchronized oscillators, the average energy is spread equally between kinetic and potential types.

In a solid, thermal energy (often referred to loosely as heat content) can be accurately described by an ensemble of thermal phonons that act as mechanical oscillators. In this model, thermal energy is equally kinetic and potential.

In an ideal gas, the interaction potential between particles is essentially the delta function which stores no energy: thus, all of the thermal energy is kinetic.

Because an electric oscillator (LC circuit) is analogous to a mechanical oscillator, its energy must be, on average, equally kinetic and potential. It is entirely arbitrary whether the magnetic energy is considered kinetic and whether the electric energy is considered potential, or vice versa. That is, either the inductor is analogous to the mass while the capacitor is analogous to the spring, or vice versa.

1. By extension of the previous line of thought, in free space the electromagnetic field can be considered an ensemble of oscillators, meaning that radiation energy can be considered equally potential and kinetic. This model is useful, for example, when the electromagnetic Lagrangian is of primary interest and is interpreted in terms of potential and kinetic energy.

2. On the other hand, in the key equation , the contribution is called the rest energy, and all other contributions to the energy are called kinetic energy. For a particle that has mass, this implies that the kinetic energy is at speeds much smaller than c, as can be proved by writing  √ and expanding the square root to lowest order. By this line of reasoning, the energy of a photon is entirely kinetic, because the photon is massless and has no rest energy. This expression is useful, for example, when the energy-versus-momentum relationship is of primary interest.

The two analyses are entirely consistent. The electric and magnetic degrees of freedom in item 1 are transverse to the direction of motion, while the speed in item 2 is along the direction of motion. For non-relativistic particles these two notions of potential versus kinetic energy are numerically equal, so the ambiguity is harmless, but not so for relativistic particles.

Work and virtual work

Main articles: Mechanics, Mechanical work, Thermodynamics, and Quantum mechanics

Work, a form of energy, is force times distance.

This says that the work () is equal to the line integral of the force F along a path C; for details see the mechanical work article.

Work and thus energy is frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball.

Quantum mechanics

Main article: Energy operator

In quantum mechanics energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. In results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of slow changing (non-relativistic) wave function of quantum systems. The solution of this equation for bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by the Planck equation (where is the Planck's constant and the frequency). In the case of electromagnetic wave these energy states are called quanta of light or photons.

Relativity

When calculating kinetic energy (work to accelerate a mass from zero speed to some finite speed) relativistically - using Lorentz transformations instead of Newtonian mechanics, Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it rest mass energy - energy which every mass must possess even when being at rest. The amount of energy is directly proportional to the mass of body:

,

where

m is the mass,

c is the speed of light in vacuum,

E is the rest mass energy.

For example, consider electron-positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process - the inverse process is called pair creation - in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

In general relativity, the stress-energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.^[14]

It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurate to state that every energy has an inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it.

Energy and life

Main article: Bioenergetics

Basic overview of energy and human life.

Any living organism relies on an external source of energy—radiation from the Sun in the case of green plants; chemical energy in some form in the case of animals—to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and food molecules, the latter mostly carbohydrates and fats, of which glucose (C₆H₁₂O₆) and stearin (C₅₇H₁₁₀O₆) are convenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O

C₅₇H₁₁₀O₆ + 81.5O₂ → 57CO₂ + 55H₂O

and some of the energy is used to convert ADP into ATP

ADP + HPO₄²⁻ → ATP + H₂O

The rest of the chemical energy in the carbohydrate or fat is converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains when split and reacted with water, is used for other metabolism (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for work:^[18]

gain in kinetic energy of a sprinter during a 100 m race: 4 kJ

gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3kJ

Daily food intake of a normal adult: 6–8 MJ

It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the energy they receive (chemical energy or radiation), and it is true that most real machines manage higher efficiencies. In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to the molecules it is built from. The second law of thermodynamics states that energy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across the remainder of the universe ("the surroundings").^[19] Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy ecological niches that are not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology: to take just the first step in the food chain, of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis, 64.3 Pg/a (52%) are used for the metabolism of green plants,^[20] i.e. reconverted into carbon dioxide and heat.

Measurement

A schematic diagram of a Calorimeter - An instrument used by physicists to measure energy

Because energy is defined as the ability to do work on objects, there is no absolute measure of energy. Only the transition of a system from one state into another can be defined and thus energy is measured in relative terms. The choice of a baseline or zero point is often arbitrary and can be made in whatever way is most convenient for a problem.

Methods

The methods for the measurement of energy often deploy methods for the measurement of still more fundamental concepts of science, namely mass, distance, radiation, temperature, time, electric charge and electric current.

Conventionally the technique most often employed is calorimetry, a thermodynamic technique that relies on the measurement of temperature using a thermometer or of intensity of radiation using a bolometer.

Units

Main article: Units of energy

Throughout the history of science, energy has been expressed in several different units such as ergs and calories. At present, the accepted unit of measurement for energy is the SI unit of energy, the joule. In addition to the joule, other units of energy include the kilowatt hour (kWh) and the British thermal unit (Btu). These are both larger units of energy. One kWh is equivalent to exactly 3.6 million joules, and one Btu is equivalent to about 1055 joules.^[21]

Energy density

Main article: Energy density

Energy density is a term used for the amount of useful energy stored in a given system or region of space per unit volume.

For fuels, the energy per unit volume is sometimes a useful parameter. In a few applications, comparing, for example, the effectiveness of hydrogen fuel to gasoline it turns out that hydrogen has a higher specific energy than does gasoline, but, even in liquid form, a much lower energy density.

Forms of energy

Main article: Forms of energy

Heat, a form of energy, is partly potential energy and partly kinetic energy.

In the context of physical sciences, several forms of energy have been defined. These include:

• Thermal energy, thermal energy in transit is called heat
• Chemical energy
• Electric energy
• Radiant energy, the energy of electromagnetic radiation
• Nuclear energy
• Magnetic energy
• Elastic energy
• Sound energy
• Mechanical energy
• Luminous energy
• Mass (E=mc²)

These forms of energy may be divided into two main groups; kinetic energy and potential energy. Other familiar types of energy are a varying mix of both potential and kinetic energy.

Energy may be transformed between these forms, some with 100% energy conversion efficiency and others with less. Items that transform between these forms are called transducers.

The above list of the known possible forms of energy is not necessarily complete. Whenever physical scientists discover that a certain phenomenon appears to violate the law of energy conservation, new forms may be added, as is the case with dark energy, a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe.

Classical mechanics distinguishes between potential energy, which is a function of the position of an object, and kinetic energy, which is a function of its movement. Both position and movement are relative to a frame of reference, which must be specified: this is often (and originally) an arbitrary fixed point on the surface of the Earth, the terrestrial frame of reference. It has been attempted to categorize all forms of energy as either kinetic or potential: this is not incorrect, but neither is it clear that it is a real simplification, as Feynman points out:

These notions of potential and kinetic energy depend on a notion of length scale. For example, one can speak of macroscopic potential and kinetic energy, which do not include thermal potential and kinetic energy. Also what is called chemical potential energy is a macroscopic notion, and closer examination shows that it is really the sum of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy and most other forms of energy. This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.

Transformations of energy

Main article: Energy transformation

One form of energy can often be readily transformed into another with the help of a device- for instance, a battery, from chemical energy to electric energy; a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) and ultimately to electric energy through an electric generator. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction, the conversion of energy between these processes is perfect, and the pendulum will continue swinging forever.

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Matter may be destroyed and converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

Transformation of energy into useful work is a core topic of thermodynamics. In nature, transformations of energy can be fundamentally classed into two kinds: those that are thermodynamically reversible, and those that are thermodynamically irreversible. A reversible process in thermodynamics is one in which no energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomization in a crystal).

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

See also

	Energy portal
	Physics portal

	Book: Energy
Wikipedia books are collections of articles that can be downloaded or ordered in print.

• Index of energy articles
• Index of wave articles

Notes and references

1. ^ Harper, Douglas. "Energy". Online Etymology Dictionary. http://www.etymonline.com/index.php?term=energy. Retrieved May 1, 2007. 
2. ^ "Retrieved on 2010-Dec-05". Faculty.clintoncc.suny.edu. http://faculty.clintoncc.suny.edu/faculty/michael.gregory/files/bio%20101/bio%20101%20lectures/chemistry/chemistr.htm. Retrieved 2010-12-12. 
3. ^ "Retrieved on 2010-Dec-05" (PDF). http://www.geo.cornell.edu/geology/classes/Chapters/Chapter02.pdf. Retrieved 2010-12-12. 
4. ^ Lofts, G; O'Keeffe D; et al. (2004). "11 — Mechanical Interactions". Jacaranda Physics 1 (2 ed.). Milton, Queensland, Australia: John Willey & Sons Australia Ltd.. p. 286. ISBN 0-7016-3777-3. 
5. ^ Smith, Crosbie (1998). The Science of Energy – a Cultural History of Energy Physics in Victorian Britain. The University of Chicago Press. ISBN 0-226-76420-6. 
6. ^ ^{a b} Feynman, Richard (1964). The Feynman Lectures on Physics; Volume 1. U.S.A: Addison Wesley. ISBN 0-201-02115-3. 
7. ^ "Retrieved on May-29-09". Uic.edu. http://www.uic.edu/aa/college/gallery400/notions/human%20energy.htm. Retrieved 2010-12-12. 
8. ^ Bicycle calculator - speed, weight, wattage etc. [1].
9. ^ "Earth's Energy Budget". Okfirst.ocs.ou.edu. http://okfirst.ocs.ou.edu/train/meteorology/EnergyBudget.html. Retrieved 2010-12-12. 
10. ^ "E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws". Physics.ucla.edu. 1918-07-16. http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html. Retrieved 2010-12-12. 
11. ^ ^{a b} The Laws of Thermodynamics including careful definitions of energy, free energy, et cetera.
12. ^ "Time Invariance". Ptolemy.eecs.berkeley.edu. http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html. Retrieved 2010-12-12. 
13. ^ Berkeley Physics Course Volume 1. Charles Kittel, Walter D Knight and Malvin A Ruderman
14. ^ ^{a b} Misner, Thorne, Wheeler (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0. 
15. ^ The Hamiltonian MIT OpenCourseWare website 18.013A Chapter 16.3 Accessed February 2007
16. ^ I. Klotz, R. Rosenberg, Chemical Thermodynamics - Basic Concepts and Methods, 7th ed., Wiley (2008), p.39
17. ^ Kittel and Kroemer (1980). Thermal Physics. New York: W. H. Freeman. ISBN 0-7167-1088-9. 
18. ^ These examples are solely for illustration, as it is not the energy available for work which limits the performance of the athlete but the power output of the sprinter and the force of the weightlifter. A worker stacking shelves in a supermarket does more work (in the physical sense) than either of the athletes, but does it more slowly.
19. ^ Crystals are another example of highly ordered systems that exist in nature: in this case too, the order is associated with the transfer of a large amount of heat (known as the lattice energy) to the surroundings.
20. ^ Ito, Akihito; Oikawa, Takehisa (2004). "Global Mapping of Terrestrial Primary Productivity and Light-Use Efficiency with a Process-Based Model." in Shiyomi, M. et al. (Eds.) Global Environmental Change in the Ocean and on Land. pp. 343–58.
21. ^ Ristinen, Robert A., and Kraushaar, Jack J. Energy and the Environment. New York: John Wiley & Sons, Inc., 2006.

Further reading

• Alekseev, G. N. (1986). Energy and Entropy. Moscow: Mir Publishers. 
• Crowell, Benjamin (2011) [2003]. Light and Matter. Fullerton, CA: Light and Matter. http://www.lightandmatter.com/html_books/lm/ch11/ch11.html. 
• Ross, John S. (23 April 2002). "Work, Power, Kinetic Energy". Project PHYSNET. Michigan State University. http://www.physnet.org/modules/pdf_modules/m20.pdf. 
• Smil, Vaclav (2008). Energy in nature and society: general energetics of complex systems. Cambridge, USA: MIT Press. ISBN 0-262-19565-8. 
• Walding, Richard,  Rapkins, Greg,  Rossiter, Glenn (1999-11-01). New Century Senior Physics. Melbourne, Australia: Oxford University Press. ISBN 0-19-551084-4. 

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Dansk (Danish)
n. - energi, handlekraft, overskud, ressourcer

Nederlands (Dutch)
kracht, energie, (arbeids)vermogen, fut, inspanning, voortvarendheid, kernenergie

Français (French)
n. - énergie, vigueur, (Phys) énergie

Deutsch (German)
n. - Kraft, Energie

Ελληνική (Greek)
n. - (φυσ.) ενέργεια, (μτφ.) ενεργητικότητα, ζωτικότητα, σωματική αντοχή, κουράγιο

Italiano (Italian)
energia, vigore, risolutezza, energia nucleare

Português (Portuguese)
n. - energia (f), potência (f), firmeza (f)

Русский (Russian)
энергия, сила, усилия, деятельность

Español (Spanish)
n. - fuerza, fortaleza, vigor, energía, determinación, energía nuclear

Svenska (Swedish)
n. - energi, kraft

中文（简体）(Chinese (Simplified))
精力, 活力, 精神

中文（繁體）(Chinese (Traditional))
n. - 精力, 活力, 精神

한국어 (Korean)
n. - 정력, 활동

日本語 (Japanese)
n. - 精力, 活力, 活動力, エネルギー

العربيه (Arabic)
‏(الاسم) طاقه, مقدرة, نشاط‏

עברית (Hebrew)
n. - ‮מרץ, אנרגיה‬

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