ENERGY

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.

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.

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.

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.

See also Assessment of Nutritional Status; Body Composition; Hunting and Gathering; Inuit; Nutrition Transition: Worldwide Diet Change; Physical Activity and Nutrition.

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

ENERGY

Energy, from the Greek energeia (en, in; ergon, work), originally a technical term in Aristotelian philosophy denoting "actuality" or "existence in actuality," means, in general, activity or power of action. In the physical sciences it is defined as the capability to do work, as accumulated work or, in the words of Wilhelm Ostwald, as "that which is produced by work or which can be transformed into work." Energy is measured in terms of units of work, to overcome a resisting force of one dyne over a distance of one centimeter. (The joule = 10⁷ erg = the watt-second; the kilogram-meter = 9.81 × 10⁷ erg. In atomic physics the unit is the electron volt; ev = 1.6 × 10⁻¹² erg.

In physics, energy is either kinetic or potential. A body of mass m moving with a velocity v possesses, owing to its motion, the kinetic energy ½mv ², which is the work necessary to overcome the inertial resistance in accelerating the body from rest to its final velocity and which is again transformed into work if the body is brought to rest. The energy that a system of bodies possesses by virtue of the relative geometrical position of its constituent parts, if subjected to gravitational, elastic, electrostatic, or other forces, is its potential energy. If, for example, a stone is raised from the surface of the earth, the potential energy of the system stone-and-earth is increased; if an elastic spring is expanded, its potential energy increases with increase of length. The attribute "potential" thus merely characterizes the latency of temporarily stored energy and does not call into question the reality of this kind of energy. With the recognition of the principle of the conservation of energy, it became apparent that the concept of energy applies to all branches of physics and to all physical sciences. Because of the at least partial convertibility of any energy into mechanical work, the aforementioned units of work also serve as measures of such energies as thermal, electric, magnetic, acoustic, and optical. For thermal energy (heat) it proved practical also to retain as a separate unit the caloric unit of heat, the calorie (equal to 4.18 × 10⁷ erg).

History of the Concept

In spite of its universality, the general notion of energy as a basic concept in science is a relatively recent result of a long and intricate conceptual process. From the scientific point of view this process may conveniently be divided into five consecutive stages: (1) early conceptions of energy as a source of force, (2) the rise of the concept of mechanical work, (3) the recognition of different forms of energy, of their interconvertibility, and of the conservation of their sum total, (4) the emancipation of energy as an autonomous existent, and (5) the mathematization of energy as an integral invariant. From the philosophical point of view—that is, with respect to the ontological and epistemological status of the concept of energy—one may speak of (1) accidental, (2) substantial, (3) relational, (4) causal, and (5) formal conceptions of energy.

energy and force

Aristotle was the first to use energeia as a technical term in his conceptual scheme, where it often signified the progressive "actualization" of that which previously existed only in potentiality. He also seems to have formed, though in an implicit manner, the idea of energy in the sense of accumulated force or accumulation of force. Force, for him, was not only the cause of motion but also the factor determining the duration or extent of motion. In the Physics he formulated the fundamental law of his dynamics, which, in modern terminology, states that the velocity, D/T (distance divided by time), of a mobile is proportional to the ratio of the magnitude of the moving force, A, and the resistance, B, a relationship that he described by enumerating exhaustively all possibilities under which AT/BD remains constant (with the exception of doubling the distance, D, as well as the time, T ). He argued that a given finite force cannot move a mobile over an infinite distance or for an infinite time. Aristotle thus associated with every force a capacitative limitation, or, in modern terms, an energy content.

The implications of this statement for cosmology—in particular, for the motion of the celestial spheres, which derive their eternal motion ultimately from the "first mover" in accordance with the axiom "all things that are in motion must be moved by something else"—called for further clarifications. Thus, for example, Averroes, in his "Commentary on the Physics," distinguished between the primary motive force, the motor separatus, and the secondary forces, the motores coniuncti ; the latter, in direct contact with the spheres, corresponding to the medieval "intelligences," draw finite quotas of force from the inexhaustible supply of the former. By this process, according to which only finite amounts are subtracted from an infinite accumulation of force, Averroes thought he was able to explain both the eternity of celestial motion and the fact that this motion does not occur instantaneously (in instanti ), as motion under the effect of an infinite cause should do.

Considerations of this kind, which engaged Aristotelian commentators until the times of Thomas Aquinas, show clearly that the notion of force signified not only the immediate cause of motion or acceleration but also its cumulative determination, or energy content. Thomas considered the possibility of a finite and yet invariable moving force, which, being immutable, acts always in the same manner (vis infatigabilis ), and thus he conceived of force as a moving agent independent of and separated from a constantly rejuvenating source, a notion essential for the future conception of the universe as a clockwork in action without the need of a constant supply of additional energy. Early in the fourteenth century the nominalist Peter Aureoli, in Liber Sententiarum, distinguished explicitly between two different aspects of force: its velocity-determining property and its capacity of consumption, or measure of exhaustibility. His differentiation can rightfully be regarded as the first ontological distinction between force and energy.

This, of course, does not imply that allusions to particular forms of energy are not found in early scientific writings. In fact, already in the Mechanica, commonly ascribed to Aristotle, the notion of kinetic energy is clearly referred to when it is asked:

How is it that, if you place a heavy axe on a piece of wood and put a heavy weight on the top of it, it does not cleave the wood to any considerable extent, whereas, if you lift the axe and strike the wood with it, it does split it, although the axe when it strikes the blow has much less weight upon it than when it is placed on the wood and pressing on it? It is because the effect is produced entirely by movement, and that which is heavy gets more movement from its weight when it is in motion than when it is at rest.

mechanical work

The modern concept of energy, as the definition shows, is a generalization of the notion of work in mechanics. The concept of work can be traced back to the principle of virtual displacements, or virtual velocities, which, in turn, has its ultimate origin in Aristotelian dynamics. Aristotle's conclusions (in De Caelo ) concerning one single force (under whose action "the smaller, lighter body will be moved farther …; for as the greater body is to the less, so will be the speed of the lesser body to that of the greater") were soon generalized for the case of a force counteracting a load, as exemplified in simple machines such as the wheel and the axle. In particular, the study of the law of the lever, as mentioned in the Mechanica, in Archimedes' On the Equilibrium of Planes, in the writings of Hero of Alexandria, and in the Liber Karastonis, a Latin version of the ninth-century Arabic text by Thabit ibn Kurrah, contributed to the gradual establishment of the principle of virtual displacements for which finally, in the thirteenth century, Jordanus Nemorarius tried to give a theoretical proof. The Renaissance formulation of this law—namely, that the ratio between force and load is reciprocal to that of the spaces (distances) traversed within the same time—as pronounced by Guidobaldo del Monte (Mechanica, 1577), by Simon Stevin (Hypomnemata Mathematica, Leiden, 1608, Book 3), and by Galileo Galilei (Opere 2), formed the basis for the definition of work as force times distance traversed.

Pierre Varignon, in his Nouvelle Mécanique ou statique (Paris, 1725), reported a letter from Johann Bernoulli, dated January 26, 1717, in which the term energy appears in this connection, apparently for the first time in the modern period: "For all equilibrium of forces in whatever manner they are applied to each other, whether directly or indirectly, the sum of the positive energies will be equal to the sum of the negative energies taken positively." Although some historians, referring to this letter, have ascribed to Bernoulli the definition of energy as "force times distance," a critical study of the text shows undoubtedly that he still defined energy as "force times virtual velocity." In spite of the fact that this notion and its derivative, namely, the notion of work defined as "force times distance," played at least implicitly an important part in the establishment of classical mechanics—Joseph Louis Lagrange saw in the principle of virtual velocities the fundamental basis for his Mécanique analytique (1788), the highlight of classical mechanics—energy considerations were rarely found in theoretical or even practical mechanics prior to the middle of the nineteenth century. Before the development of the steam engine and the rise of thermodynamics, industry had little interest in energy calculations: Force, not its integrated form, counted in the use of simple machines. The primary object of theoretical mechanics, moreover, was still celestial dynamics, where, again, energetics was of little avail. This certainly is also one of the reasons why Isaac Newton's Principia contains practically no reference to the concept of energy or to any of its applications.

According to Ernst Mach, in Die Mechanik in ihrer Entwicklung (Leipzig, 1883; translated as The Science of Mechanics, La Salle, IL, 1942), the delay of the development of energetics as compared with that of general mechanics stemmed from what he called "trifling historical circumstances," namely, the fact that in Galileo's investigations of free fall, the relationship between velocity and time was established before the relationship between velocity and distance, so that, as multiplication with mass shows, the notions of quantity of motion or momentum and force gained priority and were regarded as more fundamental than the concept of energy, which thus appeared as a derived conception. Whatever the reason for energetics' lagging behind Newtonian mechanics, it is an indisputable fact that the concept of energy became a subject of discussion among philosophers rather than among physicists or mechanicians.

the measure of "force"

Foremost among the philosophical discussions was the controversy between the Cartesians and Gottfried Wilhelm Leibniz over whether the true measure of "force" (i.e., energy) is momentum (the product of mass and velocity) or vis viva (as defined by Leibniz, the product of mass and the square of velocity). René Descartes, having shown in his Principles of Philosophy that the (scalar) quantity of motion or momentum (the vectorial nature of this quantity was recognized only by Christian Huygens) is conserved, concluded that momentum is the measure of energy. Leibniz, in "A Short Demonstration of a Remarkable Error of Descartes" ("Brevis Demonstratio Erroris Memorabilis Cartesii," in Acta Eruditorum, 1689), opposed this view. Lifting a load of 1 pound, he claimed, to a height of 4 feet requires the same work as lifting 4 pounds to the height of 1 foot. Since, according to Galileo, the velocities (of free fall) are proportional to the square roots of the heights (of fall), the velocity of the first object is twice that of the second before reaching ground, or v ₁ = 2v ₂. Assuming that the "forces" (energies) are proportional to the masses (moles), Leibniz concluded that m ₁ · f (v ₁) = m ₂ · f (v ₂), where f (v ) is an as yet unknown function of the velocity, v. Substituting m ₂ = 4m ₁ and v ₁ = 2v ₂ yields f (2v ₂) = 4 · f (v ₂), which shows that the unknown function is quadratic in its argument, v. What is conserved and hence is the measure of "force," Leibniz concluded, is mv ².

This controversy between the Leibnizians, among them Johann Bernoulli, Willem Jakob Gravesande, Christian von Wolff, Georg Bilfinger, and Samuel König, and the Cartesians, among them Colin Maclaurin, James Stirling, and Samuel Clarke, was essentially only a battle of words, since the Leibnizians considered force acting on bodies traveling over equal distances and the Cartesians considered force acting on bodies during equal intervals of time, as Jean Le Rond d'Alembert in Traité de dynamique (1743) and Lagrange in Mécanique analytique (1788) made clear.

conservation of "force"

The interesting aspect of the Leibnizian-Cartesian controversy is the fact that both sides argued on the basis of the conservation of their respective "measures": for the Cartesians it was the conservation of momentum, for the Leibnizians that of "living force" (kinetic energy). Both contentions, as we know today, were correct, since both measures are integrals of the equations of motion. One of the most ardent supporters of Leibniz was his disciple Christian von Wolff, who in the Cosmologia Generalis (1731) declared: "In all the universe the same quantity of living force is always conserved." Johann Bernoulli, in the essay "De Vera Notione Virium Vivarum" (in Acta Eruditorum, 1735), was probably the first to treat this statement of the conservatio virium vivarum as a fundamental principle in mechanics. The apparent loss of "living force" in inelastic collisions was usually explained away by the hypothesis that the invisible small parts of matter gain in vis viva just as much as the macroscopic bodies seem to lose, a view Leibniz had already expressed in Essai de dynamique and reaffirmed in a letter to Samuel Clarke (Fifth Letter, August 18, 1716), where he stated that "active forces are preserved in the world" and continued: "'Tis true, their wholes (unelastic colliding bodies) lose it with respect to their total motion; but their parts receive it, being shaken by the force of the concourse. And therefore that loss of force is only in appearance. … the case here is the same, as when men change great money into small." Johann Bernoulli, in contrast, explained this apparent loss as an absorption of force required for the compression of the colliding bodies.

transformation of potential energy

What Bernoulli had in mind was obviously the so-called latent force, subsequently to be called potential energy, and his is the earliest description of transformation of kinetic energy into potential. The idea of such "latent force" was soon generalized to nonmechanical processes. Already in 1738 Daniel Bernoulli, in his Hydrodynamica, sive de Viribus et Motibus Fluidorum Commentarii, spoke of the "latent force" of combustible coal, which "if totally extracted from a cubic foot of coal and used for the motion of a machine, would be more efficient than the daily work of eight or ten men." But the measure of this "latent living force" was still mv ².

Strictly speaking, the notion of potential—that is, a function whose space derivatives yield the force components and which therefore equals the potential energy for a unit of mass, charge, etc.—preceded the idea of potential energy. For in 1777, Lagrange, in "Recherches sur l'attraction des spheroides homogènes" (Mémoire de l'Académie, Paris), calculated the potential for an arbitrary discrete distribution of mass particles, and in 1782, Pierre Simon de Laplace calculated the potential for a continuous distribution. Potentials were still spoken of as "force functions"; the term potential function was introduced for the first time in 1828 by George Green in his Essay of the Application of Mathematical Analysis and later (1840), independently, by Karl Gauss.

When, in 1788, Lagrange derived the principle of the conservation of mechanical energy, or what subsequently was generally called the "theorem of the living force," as an integral of the equation of motion, he asked himself how many such integrals exist and under what conditions. The question, however, whether a similar principle exists also for nonmechanical processes did not occur to him.

The first clear and consistent terminology of energy conceptions, still in the domain of mechanical processes, was used by the Paris school of practical mathematicians and mechanicians, not by the purely analytical school headed by Lagrange and Laplace. It was Lazare Carnot who, in his Essai sur les machines en général (1783; republished in 1803 in a revised and enlarged edition under the title Principes fondamentaux de l'équilibre et du mouvement ), declared that the "living force" can manifest itself either as mv ² or as Fd (force times distance), the second being a measure of the "latent living force." Jean V. Poncelet, in Mécanique industrielle (1829), finally introduced for this quantity the term mechanical work and stated distinctly that it is the inertia of masses that serves for the accumulation of work and thus enables the transformation of work into "living force" and vice versa. Poncelet also measured this quantity by the kilogrammeter, a unit of energy universally adopted since then.

We thus see how at the beginning of the nineteenth century the notions of work and living force and their transformability became firmly established within the confines of mechanics proper. Even the energy was used in this connection. In A Course of Lectures on Natural Philosophy (London, 1807), Thomas Young, though an adherent of the Cartesian measure of force, admitted that "in almost all cases of the forces employed in practical mechanics, the labour expended in producing any motion, is proportional not to the momentum, but to the energy which is obtained." But it took another fifty years until the term energy in its present meaning acquired full citizenship within the vocabulary of the physical sciences. This was brought about from quite a different quarter. It derived from the study of those phenomena where heat and chemical change are the characteristic features.

conversion processes

Although Francis Bacon, in his Novum Organum, had already stated that "the very essence of heat, or the substantial self of heat, is motion, and nothing else," and although similar statements had been made even before the seventeenth century, the late eighteenth century, in general, interpreted heat as a fluidum, in the spirit of the phlogiston theory. Still Jean B. J. Fourier, in his Théorie analytique de la chaleur (1822) declared: "Thermal processes are a special kind of phenomena which cannot be explained by the principle of motion and of equilibrium." Although Joseph Black's doctrine of latent heat accounted for the disappearance of heat on the basis of the fluidum theory, the appearance of heat, as Count Rumford's experiments, at Munich in 1796 and 1798, with the boring of cannon clearly showed, was incompatible with this theory. Having eliminated all sources from which the heat produced during the boring could have originated, Rumford concluded that "it appears to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner the heat was excited and communicated in those experiments, except it be motion."

At the same time (1799) Humphry Davy performed at the Royal Institution in London his famous experiment in which two pieces of ice were rubbed together by a clockwork mechanism in a vacuum, the whole apparatus being maintained at the freezing point of water. Davy concluded that heat was "a peculiar motion, probably a vibration of the corpuscles of bodies" (Essay on Heat, Light, and the Combinations of Light, London, 1799). Rumford's and Davy's experiments, though in their quantitative aspects not yet fully explored, suggested the interchangeability of heat and motion and thus led to the more general idea of an interconvertibility, or "correlation," of the forces of nature, previously regarded as disparate and incommensurable.

Approaching this problem from a chemical and biological point of view, Justus von Liebig, one of the earliest investigators of the economy of living organisms, advanced the theory that the mechanical energy of animals, as well as the heat of their bodies, originated from the chemical energy of their food. Such physiological experiments as those carried out in Liebig's laboratory made possible the study of conversion processes and together with increased concern with engines and natural philosophical considerations, seem to have been responsible for the independent discoveries, between 1837 and 1847, of the principle of energy conservation. In fact, Liebig's pupil Friedrich Mohr, adopting the mechanistic view that all forms of energy are manifestations of mechanical force, wrote as early as 1837: "Besides the known fifty-four chemical elements there exists in nature only one agent more, and this is called 'Kraft' ['force']; it can under suitable conditions appear as motion, cohesion, electricity, light, heat, and magnetism."

energy conservation principle

Robert von Mayer, a physician from Heilbronn, Bavaria, who had served on a ship in the tropics, had noted that the venous blood of his patients there was redder than it had been in Europe. He explained this difference by an excess of oxygen due to a reduced combustion of the food that provided the heat of the body. He thus concluded that chemical energy, heat of the body, and muscular work are interconvertible, an idea that he pursued upon his return by a quantitative investigation of the mechanical equivalent of heat. The first enunciation of the energy conservation principle, combined with the determination of the mechanical equivalent of heat, is found in Mayer's article "Bemerkungen über die Kräfte der unbelebten Natur" (in Liebig, ed., Annalen der Chemie und Pharmacie, 1842, Vol. XLII, pp. 233–240). His calculations, as explained in greater detail in his Die organische Bewegung (1845) were based on the difference of the specific heats of air at constant volume and at constant pressure, as measured by F. Delaroche and others, yielding, in modern units, 3.65 joule per calorie; had Mayer employed Henri Regnault's more accurate results he would have arrived at 4.2 joule per calorie, the currently accepted value. The amount of heat liberated by the expenditure of mechanical or electrical work was systematically measured by James Prescott Joule, a Manchester brewer and amateur scientist. In heating liquids by the rotation of paddle wheels, forcing water through narrow tubes, or compressing masses of air, Joule demonstrated that the expenditure of the same amount of work, irrespective of the manner in which this work was done, resulted in the development of the same amount of heat. His measurements of such conversion processes gave a firm quantitative support for the conservation principle.

The discovery of the physical principle of the conservation of energy was soon found to be in full agreement with the principal tenets of the prevailing natural philosophy, the German Naturphilosophie, whose early proponent, Friedrich Wilhelm Joseph von Schelling, had declared in 1799, in Einleitung zu dem Entwurf eines Systems der Naturphilosophie, "that magnetic, electrical, chemical, and finally even organic phenomena would be interwoven into one great association … [which] extends over the whole of nature." Mayer supported his own conclusions by the metaphysical argumentation that forces are essentially causes and "causes equal effects"; since causes are indestructible and convertible into effects, forces must likewise be indestructible and interconvertible. Even the experimentalist Joule, in an article "On the Calorific Effects of Magneto-electricity, and on the Mechanical Value of Heat" (Philosophical Magazine, series 3, 23 [1843]: 442), declared: "I shall lose no time in repeating and extending these experiments, being satisfied that the grand agents of nature are by the Creator's fiat indestructible." In another paper (in Philosophical Magazine, series 3, 26 [1845]: 382) he stated: "Believing that the power to destroy belongs to the Creator alone, I entirely coincide with Roget and Faraday in the opinion, that any theory which, when carried out, demands the annihilation of force, is necessarily erroneous." The conduciveness of the philosophical climate toward the enunciation of the energy principle can most clearly be recognized from the arguments of A. Colding, who arrived at the principle independently of Mohr, Mayer, and Joule:

The first idea I conceived on the relationship between the forces of nature was the following. As the forces of nature are something spiritual and immaterial, entities whereof we are cognizant only by their mastery over nature, these entities must of course be very superior to everything material in the world; and as it is obvious that it is through them only that the wisdom we perceive and admire in nature expresses itself, these powers must evidently be in relationship to the spiritual, immaterial, and intellectual power itself that guides nature in its progress; but if such is the case, it is consequently quite impossible to conceive of these forces as anything naturally mortal or perishable. Surely, therefore, the forces ought to be regarded as absolutely imperishable. ("Nogle Soetninger om Kraefterne," 1843, in Philosophical Magazine, series 4, 27 [1864]: 56–64).

Even the classic paper of Hermann von Helmholtz, the physiologist turned physicist, "On the Conservation of Force" (Über die Erhaltung der Kraft, Berlin, 1847), shows clearly the impact of contemporaneous philosophy, with its renunciation of Hegelianism and its reversion to an idealistic rationalism, when it declares:

The final aim of the theoretic natural sciences is to discover the ultimate and unchangeable causes of natural phenomena. Whether all the processes of nature be actually referrible to such—whether changes occur which are not subject to the laws of necessary causation, but spring from spontaneity or freedom, this is not the place to decide; it is at all events clear that the science whose object it is to comprehend nature must proceed from the assumption that it is comprehensible.

The requirement of referring the phenomena of nature back to unchangeable final causes was interpreted by Helmholtz as reducing physical processes to motions of material particles possessing unchangeable moving forces that are dependent on conditions of space alone. Thus, Helmholtz, starting with the eighteenth-century dynamics of bodies acting under mutual attraction, generalized the Newtonian conception of motion to the case of a large number of bodies and showed that the sum of force and tension (what we now call kinetic and potential energies) remain constant during the process of motion. Applying conventional analytical mathematics, Helmholtz proved that the principle of the conservation of living force not only can be derived from Newtonian dynamics but may also serve as an equivalent point of departure for the deduction of theoretical mechanics.

This fundamental assumption may be formulated as the principle of the impossibility of a perpetuum mobile. When a system of particles acting under central forces passes from one configuration to another, the velocities acquired can be used to perform some work; in order to draw the same amount of work a second time from the system, one would have to restore its initial conditions by expending on it forces or energy from outside the system. The principle now requires that the amount of work gained by the transition from the first position to the second and the amount of work lost by the passage of the system from the second configuration to the first be equal, no matter in what way or at what velocity the change has been effected; otherwise a perpetuum mobile could be constructed on the basis of this cycle, contrary to the principle. So far Helmholtz's reasoning is but a paraphrase of the arguments used by Sadi Carnot and Benoît Clapeyron in their foundations of the thermodynamics of heat engines. By replacing the concept of work by that of "tensions" (verbrauchte Spannkräfte ), which are equal but of opposite sign to the work performed, Helmholtz transformed the equation between living force (kinetic energy) and work into the statement that the sum of living force and tension is a constant, the tension being a function of the instantaneous state of the system. Although prima facie an insignificant change, this reformulation of the mechanical principle of the conservation of living force through the introduction of "tensions" opened up incalculable perspectives in that it could be applied to all branches of physics, not only to mechanics proper. Moreover, the new formulation was strikingly analogous to that of the principle of the conservation of matter, or mass, an accepted axiom in physical science since the times of Antoine Lavoisier. Exploiting the adaptability of the concept of "tension" to nonmechanical phenomena, Helmholtz not only reconciled the new doctrine of heat with the theory of mechanics, heat explicitly being treated as a form of energy, but also demonstrated the validity of the conservation principle for electrodynamics and other departments of physics. The recognition that mechanical work, heat, and electricity were only different forms of one and the same physical substratum—a result that can rightfully be considered the greatest physical discovery of the nineteenth century—found its analytical vindication in Helmholtz's paper.

At first, however, Helmholtz's memoir was hardly recognized, since its argumentation was based on mathematical reasoning, which at this time was accessible to but a small number of specialists. Another fundamental obstacle in the way of a just assessment of the new truth was the indiscriminate homonymous usage of the term force in both its Newtonian and its Leibnizian significations. Once the semantic difficulties had been removed, the principle of the conservation of energy found general acceptance and even popularity, owing to the writings of William Thomson (Lord Kelvin). In a discourse before the Royal Institution in 1856, Thomson distinguished carefully the significance of the Newtonian notion of force from what he called "energy." The term energy —apart from its early usage by Bernoulli and Young—had already been used three years earlier by William Rankine in his "On the General Law of the Transformation of Energy" (Philosophical Magazine, series 4, 5 [1853]: 106), but only Thomson's application led to its universal acceptance. "Any piece of matter or any group of bodies, however connected, which either is in motion, or can get into motion without external assistance, has what is called mechanical energy. The energy of motion may be called either 'dynamical energy' or 'actual energy.' The energy of a material system at rest in virtue of which it can get into motion, is called 'potential energy'" (On the Origin and Transformation of Motive Power, 1856). In 1893, in a footnote to a reprint of his 1856 lecture (in Popular Lectures and Addresses, London, 1894, Vol. II), Thomson wrote: "Shortly after the date of this lecture I gave the name 'kinetic energy' which is now in general use. It is substituted for 'actual' and for 'dynamical.'" Thus Helmholtz's "tension" was renamed "potential energy," and the sum total of kinetic and potential energies, the total energy of the system, was shown to be a constant that is characteristic of the system.

These innovations, however, had still to overcome some opposition. The Rankine-Thomson designation "potential energy" was rejected by John F. W. Herschel ("On the Origin of Force," in Fortnightly Review and Familiar Lectures, 1857) as "unfortunate," being too common a name for such a "great truth." Even the term conservation of force or energy was subjected to severe criticisms, particularly by T. H. Huxley and by Herbert Spencer in his First Principles (1862), on the ground that "conservation" implies a conserver and an act of conserving and therefore the assumption that without such an act, force (energy) would disappear—an idea at variance with the conception to be conveyed. But in addition to the terminology, the conception itself, particularly that of potential energy, was still a matter of debate. An interesting testimony to these difficulties is Michael Faraday's paper "On the Conservation of Force" (Philosophical Magazine, series 4, 13 [1857]: 225–239), in which the following problem is raised: Is there creation or annihilation of force if the distance between two gravitating bodies is changed and the attractive force varies inversely with the square of the distance? "Gravitation," Faraday continued, "has not yet been connected by any degree of convertibility with the other forms of force…. That there should be a power of gravitation existing by itself having no relation to the other natural powers, and no respect to the law of the conservation of force, is as little likely as that there should be a principle of levity as well as of gravity." Rankine's answer to Faraday's objection (Philosophical Magazine, series 4, 17 [1859]: 250) seems to have had little effect, for as late as 1876, James Croll, in his paper "On the Transformation of Gravity" (Philosophical Magazine, series 5, 2 [1876]: 242–254), attempted to solve Faraday's query with the assumption that "a stone when in the act of falling [may] be acted upon by gravity with less force at any given moment than it would be were the stone at rest at that instant."

the emancipation of energy

Although Croll's paper is full of misconceptions, which, interestingly, were clarified in an answer by the Viennese physiologist Ernst von Brücke, "On Gravitation and the Conservation of Force" (Philosophical Magazine, series 4, 15 [1858]: 81–90), it was of great importance for the subsequent development of the concept of energy. It connected the notion of energy for the first time with that of space. That space and change of position are necessary conditions for energy transformations Croll tried to demonstrate by the following consideration: four possibilities of energy transformations are conceivable—a change of potential energy into kinetic, of kinetic into potential, of kinetic into kinetic, and of potential into potential. Since, however, there "is evidently no such thing in nature, so far as is yet known, as one form of potential passing directly into another form" of potential energy and the existence of kinetic energy always implies change of position, the point is proved. Having thus associated energy with space, Croll went on to dissociate it from the material medium. "Our inability to conceive how force can exist without a material medium has its foundation in a metaphysical misconception," an idea he explained in greater detail in his book Philosophy of Theism (London, 1857). Croll's almost casual remarks, though scientifically rather objectionable and philosophically highly speculative, may be regarded as the earliest objection to the prevailing view, which still conceived of energy as an attribute, so to speak, of the dynamic system.

Meanwhile, James Clerk Maxwell's Treatise on Electricity and Magnetism (1873) appeared, opening the way for a field-theory treatment of electromagnetic phenomena. It showed, in particular, that the work necessary to build up an electromagnetic field can be regarded as equivalent to the energy produced in space with a certain density that depends on the squares of the magnitudes of the electric and magnetic fields. In the case of nonstatic fields these calculations lead to the conclusion, as was shown by J. H. Poynting in "On the Transfer of Energy in the Electromagnetic Field" (Philosophical Transactions of the Royal Society 175 [1885]: 343–361), that energy has to flow from one place in space to another in order to compensate for changes that occur in a particular region of space. A transfer of energy, it is true, had been associated with electricity before Poynting, but the energy flow was always considered as being confined to the conducting wires.

But the existence of induced currents and of electromagnetic actions at a distance from a primary circuit from which they draw their energy, has led us, under the guidance of Faraday and Maxwell, to look upon the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, that is, if we believe that when it disappears at one point and reappears at another it must have passed through the intervening space, we are forced to conclude that the surrounding medium contains at least a part of the energy, and that it is capable of transferring it from point to point.

Thus the surrounding medium or empty space became the arena in which energy moves, and energy, disjoined from matter, was raised in its ontological status from a mere accident of a mechanical or physical system to the autonomous rank of independent existence: matter ceased to be the indispensable vehicle for its transport. Mechanics, with its restricted conception of transfer of energy by matter, could proceed only as far as Gaspard de Coriolis's notion of "energy currents," described in his Traité de la mécanique (1844). The complete emancipation or reification of energy could be achieved only by a theory of action-at-a-distance, such as Maxwell's theory of electromagnetism. Here energy could be labeled and traced in its motion or change of form just as a piece of matter is ticketed so that it can be identified in other places under other conditions.

The recognition of the new ontological status of energy led to a result of great philosophical importance: It strengthened the position of those who opposed the prevailing kinetic-corpuscular theory of nature, according to which all processes are reduced to motions of particles and motion is the fundamental concept for physical explanation. Referring to the demonstrated equivalence of all forms of energy, the opponents claimed that kinetic energy is only one of the forms in which this quantity appears. In their view, energy was a much more general conception than motion, a conception that should not be narrowed down to mean only energy of attraction and repulsion of gravitational or electrostatic nature or energy of various forms of motion. One of the earliest exponents of this school of "energetics" was G. Helm, who, in a treatise, Die Lehre von der Energie (Leipzig, 1887), revived the term energetics, originally coined by Rankine, to characterize his position, according to which energy is the basic physical reality responsible for all natural phenomena. Helm referred to Gustav Zeuner, Ernst Mach, Josiah Gibbs, James Clerk Maxwell, A. J. von Oettingen, and Joseph Popper as advocating similar ideas. In particular, he claimed, energy can always be broken down into two factors, an intensity and an extensity factor, which characterize the quantity of energy as well as the direction in which changes of energy take place (the intensity factor always decreases).

In spite of further expositions, Helm's ideas did not attract much attention until Wilhelm Ostwald incorporated Helm's "factorization of energy" into the second edition of his treatise on physical chemistry, Lehrbuch der allgemeinen Chemie (1893), as the foundation of his theory of chemical affinity. In the period between the first and second editions of his treatise Ostwald embraced the new doctrine of energetics, and with his address in 1895 to the German Congress of Naturalists at Lübeck, "The Conquest of Scientific Materialism" (Die Überwindung des wissenschaftlichen Materialismus ), he became the principal speaker of the new movement. In his view, not only was energy the universal currency of physics, but all phenomena of nature were merely manifestations of energy and of its manifold transformations.

In "Lectures on Natural Philosophy" (Vorlesungen über Naturphilosophie, Leipzig, 1901) Ostwald contended that since substance is by definition that which persists under transformations or changes, energy is substance. Methodological as well as epistemological considerations, he claimed, force us to see in energy the only substance—methodologically because the alternative view, scientific materialism, has failed to give an exhaustive explanation in even a single case of natural phenomena; epistemologically because "what we hear originates in work done on the ear drum and the middle ear by the vibrations of the air. What we see is only radiant energy which does chemical work on the retina that is perceived as light…. From this point of view the totality of nature appears as a series of spatially and temporally changing energies, of which we obtain knowledge in proportion as they impinge on the body, and especially upon the sense organs fashioned for the reception of the appropriate energies." Ostwald's conception of a physical object in terms of energy, of its volume in terms of compressibility, and of its shape in terms of elasticity is one of the final stages in a development that began with John Locke's sensationalistic conception and eventually put an end to the substantial conception of matter.

The "dissolution of matter" into energy was particularly welcomed by the adherents of the monistic school of thought in their search for a unified conception of the universe. Gustave Le Bon, for instance, in his L'evolution de la matière (Paris, 1905), spoke of the "dematerialization of matter into energy," a philosophical conclusion that in the same year found a far-reaching and profound scientific foundation. For in a paper titled "Does the Inertia of a Body Depend upon Its Energy Content?" ("Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" in Annalen der Physik 18 [1905]: 639–641), Albert Einstein showed, on the basis of the Maxwell-Hertz equations of the electromagnetic field, that "if a body gives off the energy E in the form of radiation, its mass diminishes by E/c ²," where c denotes the velocity of light. Since then the mass-energy relation, E = mc ², has been of fundamental importance, particularly in nuclear physics, where P. M. S. Blackett, G. P. S. Occhialini, O. Klemperer, and others showed that the total mass of a particle can be transformed into energy.

Whereas in classical mechanics differences of energy alone were of physical significance, so that energy could be determined only up to an additive constant, in modern physics energy lost this indeterminateness and became a physical quantity of absolute magnitude. Moreover, in the theory of relativity the principles of the conservation of energy, or mass, and momentum, the latter being the basis of the Cartesian measure of "force," revealed themselves only as different aspects of one and the same conservation law, the conservation of the momentum-energy four-vector. On the basis of the Einstein equation E = mc ² the problem of the source of solar (or stellar) energy could be solved, the "packing effect" in nuclear physics could be explained, and the release of nuclear energy could be predicted. Energy was released mass, and mass was frozen energy, or as Bertrand Russell, in Human Knowledge: Its Scopes and Limits (New York, 1948), summarized the situation: "Mass is only a form of energy, and there is no reason why matter should not be dissolved into other forms of energy. It is energy, not matter, that is fundamental in physics."

conservation and invariance

Although the theory of relativity threw new light on the conservational aspects of energy, or mass, the relationship between conservation and invariance found its final elucidation in Emmy Noether's article "Invariant Variational Problems" ("Invariante Variationsprobleme," in Göttinger Nachricten [1918], pp. 235–257), which demonstrates the conservation of certain quantities (for example, the canonical energy-momentum tensor) for dynamic systems that are invariant under continuous transformations of the coordinates or, more generally, of the field functions involved. Conservation thus appeared as a consequence of symmetry properties, a fact that was in part known already from the Hamiltonian formulation of classical mechanics. In particular, if homogeneity of space and time is assumed, that is, if it is postulated that the system is invariant under translational transformations of the origins of space-coordinates and time-coordinates, then the conservation of momenta and of energy is but a mathematical consequence. The principle of the conservation of energy of a given dynamic system is therefore ultimately a consequence of the invariance (or symmetry) of the system under changes in the zero-point of the time scale, that is, a consequence of the homogeneity of time.

See also Alembert, Jean Le Rond d'; Aristotle; Averroes; Bacon, Francis; Bilfinger, Georg Bernhard; Clarke, Samuel; Descartes, René; Einstein, Albert; Faraday, Michael; Force; Galileo Galilei; Gibbs, Josiah; Helmholtz, Hermann Ludwig von; Huxley, Thomas Henry; Lavoisier, Antoine; Leibniz, Gottfried Wilhelm; Mach, Ernst; Maxwell, James Clerk; Newton, Isaac; Ostwald, Wilhelm; Peter Aureol; Philosophy of Physics; Russell, Bertrand Arthur William; Schelling, Friedrich Wilhelm Joseph von; Thomas Aquinas, St.; Wolff, Christian.

Bibliography

Duhem, P. L'évolution de la mécanique. Paris, 1903.

Haas, A. E. "Die Begründung der Energetik durch Leibniz." Annalen der Naturphilosophie 7 (1908): 373–386.

Haas, A. E. Die Entwicklungsgeschichte des Satzes von der Erhaltung der Kraft. Vienna, 1909.

Helm, G. Die Energetik nach ihrer geschichtlichen Entwicklung. Leipzig, 1898.

Hiebert, Erwin N. Historical Roots of the Principle of Conservation of Energy. Madison: State Historical Society of Wisconsin for the Dept. of History, University of Wisconsin, 1962.

Jammer, M. "The Factorization of Energy." British Journal for the Philosophy of Science 14 (1963): 160–166.

Kuhn, T. S. "Energy Conservation as an Example of Simultaneous Discovery." In Critical Problems in the History of Science, edited by M. Clagett. Madison: University of Wisconsin Press, 1959.

Mach, E. Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit. Prague, 1872.

Planck, M. Das Prinzip der Erhaltung der Kraft. Leipzig: Teubner, 1st ed., 1887; 2nd ed., 1908.

M. Jammer (1967)

ENERGY

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 mv ². 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_f ² = v₀ ² + 2as, where v _f² is the final speed of the object, v ₀² its initial speed, a acceleration and s distance. By substituting values within these equations, one arrives at the formula of ½ mv ² 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 mv ² 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 = mc ² 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 = mc ², 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 = mc ². 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.

KEY TERMS

CONSERVATION OF ENERGY:

A law of physics which holds that 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.

COSINE:

For an acute (less than 90°) in a right triangle, the cosine (abbreviated cos) is the ratio between the adjacent legand the hypotenuse. Regardless of the size of the triangle, this figure is a constant for any particular angle.

ENERGY:

The ability of an object (or in some cases a non-object, such as a magnetic force field) to accomplish work.

FRICTION:

The force that resists motion when the surface of one object comes into contact with the surface of another.

HORSEPOWER:

The British unit of power, equal to 550 foot-pounds per second.

HYPOTENUSE:

In a right triangle, the side opposite the right angle.

JOULE:

The SI measure of work. One joule (1 J) is equal to the work required to accelerate 1 kilogram of mass by 1 meter per second squared (1 m/s²) over a distance of 1 meter. Due to the small size of the joule, however, it is often replaced by the kilowatt-hour, equal to 3.6 million(3.6 · 106) J.

KINETIC ENERGY:

The energy that an object possesses by virtue of its motion.

MATTER:

Physical substance that occupies space, has mass, is composed of atoms (or in the case of subatomic particles, is part of an atom), and is convertible into energy.

MECHANICAL ENERGY:

The sum of potential energy and kinetic energy within a system.

POTENTIAL ENERGY:

The energy that an object possesses by virtue of its position.

POWER:

The rate at which work is accomplished over time, a figure rendered mathematically as work divided by time. The SI unit of power is the watt, while the British unit is the foot-pound per second. The latter, because it is small, is usually reckoned in terms of horsepower.

REST ENERGY:

The energy an object possesses by virtue of its mass.

RIGHT TRIANGLE:

A triangle that includes a right (90°) angle. The other two angles are, by definition, acute or less than 90°.

SCALAR:

A quantity that possesses only magnitude, with no specific direction.

SI:

An abbreviation of the French Système International d'Unités, which means "International System of Units." This is the term within the scientific community for the entire metric system, as applied to a wide variety of quantities ranging from length, weight and volume to work and power, as well as electromagnetic units.

SYSTEM:

In discussions of energy, the term "system" refers to a closed set of interactions free from interference by outside factors. An example is the baseball dropped from a height to illustrate potential energy and kinetic energy the ball, the space through which it falls, and the ground below together form a system.

VECTOR:

A quantity that possesses both magnitude and direction.

WATT:

The metric unit of power, equal to 1 joule per second. Because this is such a small unit, scientists and engineers typically speak in terms of kilowatts, or units of 1,000 watts.

WORK:

The exertion of force over a given distance. Work is the product of force and distance, where force and distance are exerted in the same direction. Hence the actual formula for work is F · cos θ · s, where F = force, s = distance, and cos θ is equal to the cosine of the angle θ (the Greek letter theta) between F and s. In the metric or SI system, work is measured by the joule (J), and in the British system by the foot-pound.

Energy

Latin America is rich in energy resources, but these resources are unevenly distributed among the region's countries. Petroleum dominates commercial energy production and consumption at every level throughout Latin America. The region is also richly endowed with natural gas and hydroelectric power potential, and Colombia and Venezuela have begun to develop their coal reserves for export.

Development of Latin American energy resources has come at great expense. Brazil is a prime example, with over 40 percent of public investment in the early 1980s accounted for by domestic energy investment. Foreign debt mounted during the 1970s and 1980s as the World Bank, Inter-American Development Bank, and other lenders injected much-needed capital into grandiose petroleum, gasohol, nuclear, and hydroelectric projects. Oil price fluctuations eroded the ability to repay these debts, causing many to rethink the approach to development of Latin American energy resources.

ENERGY CONSUMPTION

Latin America and the Caribbean are dependent on oil for a disproportionate share of their energy needs—almost 52 percent in 2004. The degree of dependence on oil among the smaller countries is more pronounced. For the Caribbean islands, oil represents 90 percent of the commercial energy requirements. From 2002 to 2006 Venezuelan oil exports to the United States slowed as relations between the two countries soured. However, Venezuela increased its oil exports to Latin America, with 36.7 percent going there in 2006.

Total primary energy consumption for Latin America and the Caribbean in 2004 equalled 28.45 quadrillion Btu, of which oil consumption represented 14.8 quadrillion Btu. Natural gas and hydropower contribute approximately 21 percent each, whereas coal represents 4 percent.

Most of the region's energy is consumed in Brazil (30 percent) and Mexico (22 percent). Mexico is the region's largest consumer of petroleum, using 29 percent of the petroleum available in 2004. Brazil also relies more on hydropower as a commercial source of energy than does any other major country in Latin America.

The primary determinants of increased energy consumption in developing countries are population growth, income growth, industrialization, and urbanization, each of which requires more energy services. Increases in energy prices tend to reduce the rate of growth in energy demand; this occurred during the early 1980s. Latin American energy demand surged in the late 1980s, increasing at an annual rate of 2.9 percent. Most of the growth was in hydroelectric, natural gas, and coal demand.

COMMERCIAL ENERGY PRODUCTION

Latin America produced surplus energy throughout the twentieth century. The region will likely remain a net exporter into the twenty-first century despite the fact that the rate of growth in energy production has fallen below that of energy consumption. Venezuela is a member of OPEC and must abide by its production quotas. (Ecuador withdrew from OPEC in 1992.)

Most Latin American countries exercise strong, monopolistic control over energy development. The lack of competition has negative effects on energy resource management. In Mexico and Venezuela, state control of oil and gas exploration and production sectors is absolute. In other countries, private sector participation is strictly controlled. Brazil in the 1990s began to let its oil company operate more independently and allowed foreign investors to buy shares.

Oil and Gas

In 2004 Latin America produced 36.144 quadrillion Btu of primary energy (petroleum, natural gas, coal, hydropower, and nuclear) while consuming only 28.45 quadrillion Btu. Petroleum production of 21.4 quadrillion Btu represented 59 percent of total energy production.

Latin America had 116 million barrels of conventional crude oil reserves in 2006. Venezuela and Mexico together accounted for 79.25 percent of that total. Venezuelan reserves are the sixth-highest in the world, and in 2006 Venezuela was also the world's sixth-largest oil exporter; Mexico was the tenth-largest. Nine other countries (Bolivia, Brazil, Chile, Colombia, Argentina, Ecuador, Guatemala, Peru, and Trinidad and Tobago) have oil reserves of varying sizes that are not considered significant by world standards.

Natural gas reserves are also dominated by Venezuela, which in 2006 accounted for 60 percent of the 250.8 trillion cubic feet in Latin America. Nearly all current gas production is associated gas, and production levels have been restrained by oil production levels. Brazil has a huge natural gas resource that is being underutilized. In 2007, natural gas met only 2 percent of the country's energy requirements, mainly due to lack of infrastructure.

Intraregional oil and gas trade has become common in Latin America. Petroleum dominates intraregional trade in northern Latin America, whereas natural gas is more popular in the south. Argentina renewed a twenty-year agreement to import 2.19 billion cubic meters of natural gas annually from Bolivia. Brazil signed a deal with Bolivia whereby 1.28 billion cubic meters of gas will be burned annually in the thermal power plant to be built at the Bolivian border town of Puerto Suárez, and the electricity will be sent to the Brazilian state of Mato Grosso do Sul.

Bolivia and Argentina have turned to Chile, which also is in need of gas. Argentine-Chilean negotiations over routing, volume, price, and pipeline construction delayed bidding until November 1991. Bolivia entered the Chilean scene, offering alternative supply to mining complexes in northern Chile. However, any deal may founder due to the lack of diplomatic relations between Bolivia and Chile.

Coal

Recoverable coal reserves in Latin America were estimated to be 23,263 million short tons in 2006. Brazil's reserves represent 62 percent of Latin American reserves, and the country produced 47.9 percent of the region's total. Colombia has the largest export coal mine in the world, the opencast El Cerrejón. The mine has been exporting one million tons of coal per month since the mid-1980s.

Brazil, Chile, Mexico, and Venezuela are investing to spur bituminous coal production. Coal use in Brazil is very low despite substantial resources, due to its poor quality. Mexico has offered to invest in the mining of Colombian coal, which would be used in Mexican power generation.

Hydropower

Hydropower represents the largest single supply source for electricity in Latin America. In 2004, 55.7 percent of all electricity supplied came from hydropower. Several Latin American nations have pursued development of hydro resources as a means of reducing their dependence on oil imports. Brazil, Argentina, Colombia, Venezuela, and Paraguay all have large shares of hydropower in their electricity generation. Hydro incurs high capital costs long before electricity begins flowing, and these projects accounted for sizable proportions of these countries' foreign and domestic debts.

The Itaipú plant on the Paraná River along the Paraguay-Brazil border has the largest hydro capacity in the world, at 11.7 megawatts. Brazil underwrote all the construction costs and purchases all electricity generated. Despite supplying 24 percent of current primary energy needs and nearly 90 percent of its electricity, Brazil has exploited less than 20 percent of the country's estimated hydro potential. Another 12 percent is under construction or planned through 2000.

Nuclear

Nuclear-generated electricity provides less than 1 percent of Latin America's primary energy. Argentina has the longest experience with nuclear power; its 344-megawatt Atucha 1 heavy-water reactor has been operational since 1974, but by 1984, Atucha 1 was operating at half capacity, unable to compete with cheaper hydroelectricity. Work on Atucha 2 was delayed. Brazil brought its 626-megawatt Angra dos Reis 1 plant into operation in 1981. Angra 2 came online in 2000.

Construction on Mexico's first reactor, the 650-megawatt Laguna Verde, began in 1970, but it never went into operation, and Uramex, the state-run mining company that had begun exploiting uranium reserves, closed in 1985. Mexico's nuclear program calling for twenty reactors by the year 2000 was canceled during the 1980s after it was estimated that the program accounted for more than half of the public-sector debt attributable to the energy sector. Nuclear power in Latin America was not anticipated to have much of a future.

Traditional Fuels

Wood and agricultural-animal wastes are used in the rural sectors and account for an estimated 800,000 barrels per day of oil equivalent. Firewood provided as much as half of the region's energy in 1945. It continues to be used by rural populations in residential applications.

Sugarcane waste (bagasse) has become a significant source of energy for sugar mills producing their own electricity and steam. Bagasse is used in independent facilities, isolated from electricity grids, in Belize, Brazil, Mexico, Cuba, the Dominican Republic, Jamaica, and other Caribbean islands.

Renewables

The island nations of the Caribbean face pronounced isolation problems. Regional solutions such as electricity interconnections or cross-border road networks are not viable. Caribbean islands are ideal candidates for smaller-scale renewable energy applications. Geothermal, wind, biomass, and photovoltaic technologies have been demonstrated with the assistance of international agencies.

The tectonic regions of Mexico, Central America, and the Caribbean offer ample geothermal resources. El Salvador has exploited geothermal resources since 1975. Mexico is operating geothermal wells in Baja California, exporting half the output to southern California utilities. Guatemala is planning to build a 15-megawatt geothermal plant.

In addition to funding geothermal development in Central America, the Inter-American Development Bank has financed wind power in Barbados, bagasse cogeneration studies in Guyana, biogas from chicken manure in Guatemala, microhydro in Brazil, and photovoltaic cell production in Mexico.

Alcohol Fuels

The alcohol fuel program, seen at one time as the savior of Brazil, was moribund by August 1990. Heavy subsidies on alcohol cost Brazil $7 billion since the fuel was introduced fifteen years earlier in an effort to reduce the country's heavy dependence on imported oil. Removal of sub-sidies would mean that the 4.5 million owners of alcohol-fueled cars would be grounded. Production of alcohol fuel costs twice as much as gasoline. Excessive production costs are blamed on bureaucratic bungling, greedy sugarcane producers, corruption, and the vested interest of Petrobrás, the monopoly distributor of alcohol fuel.

Sales of alcohol-fueled vehicles in Brazil fell from 85 percent of total vehicle sales in 1985 to less than 5 percent in July 1990. Fuel production was not expected to meet demand, and imports will be required if rationing is to be avoided. In 1989, 29 distilleries closed down, and ten more closed during the first half of 1990. However, there was renewed interest in the ethanol program due to the high oil prices in the early twenty-first century. Guatemala also has a small alcohol fuel program.

DEVELOPMENT AND COOPERATION

In order to develop an energy infrastructure that will sustain economic growth, the countries of Latin America will have to attract new investment. World Bank lending for energy projects in 1990 totaled $3 billion. Of that, $1 billion went to Latin America. Two-thirds of the bank's lending goes directly to utilities to reinforce internal electric transmission systems. The balance goes to coal and oil-gas projects.

The U.S. Trade and Development Program has been operating in the private and public sectors of Latin America since the 1980s. Energy funding has been almost exclusively for oil and gas. The U.S. Agency for International Development energy programs are limited and small, except for Central America. Their period of active involvement in large thermal and hydroelectric projects was in the 1960s and 1970s, particularly in Brazil. The Inter-American Development Bank allocated an average of 27.6 percent of its loans ($10.97 billion) to energy projects from 1961 through 1987. In 1988, $405 million was lent for energy, of which 88 percent was for electric projects. A small portion of the Caribbean Development Bank's loans are for energy.

Under President Hugo Chávez, the petroleum-rich nation of Venezuela has promoted alternatives for energy development. In 2005 Chávez's new energy policy focused on six new projects, including refining, infrastructure, and integration in the Magna Reserve, and the Orinoco and Delta-Caribbean regions. In 2007 he announced the nationalization of the oil industry, and the state took over holdings by foreign multinational companies such as ExxonMobil, which had failed to give majority control of hydrocarbons to Venezuela.

Regional cooperation was promoted as the best way to develop Latin American energy resources. In the past, the joint energy option was for costly, controversial, and time-consuming hydroelectric projects. Cross-border hydro projects account for 25 percent of Latin America's generating capacity and much of its crippling debt. Grandiose schemes financed by the World Bank, the Inter-American Development Bank, and the United Nations fell out of favor. For example, Argentine president Carlos Saúl Menem shelved the Yacireta Dam on the Paraná River between Paraguay and Argentina after receiving approval for an Inter-American Development Bank loan of $250 million.

Latin America was anticipated to look to its own regional organizations specifically established to assist in energy development: the Organization of Latin American States for Energy Cooperation, the Regional Electrical Intergration Commission, and the Latin American State Oil Company Assistance Organization.

See alsoChávez, Hugo; Electrification; Industrialization; Inter-American Development Bank (IDB); Mining: Modern; United Nations; World Bank.

BIBLIOGRAPHY

Bamber, Derek. "Brazil: Coping with the Conflict." Petroleum Economist 57 (October 1990): 13-17.

Campodónico, Humberto. Reformas e inversión en la industria de hidrocarburos de América Latina. Santiago de Chile: Naciones Unidas, Comisión Económica para América Latina y el Caribe, División de Recursos Naturales e Infraestructura, 2004.

De la Pedraja, René. Energy Politics in Colombia. Boulder, CO: Westview Press, 1989.

García Dodero, Vicente, and Fernando Sánchez Albavera. Fundamento y anteproyecto de la ley para promover la eficencia energética en Venezuela. Santiago de Chile: Naciones Unidas, Comisión Económica para América Latina y el Caribe, División de Recursos Naturales Infraestructura, 2001.

González, Alejandro, and Lisa Pearl. Venezuela's Natural Gas—Why the Lack of Interest? Cambridge, MA: Cambridge Energy Research Associates, 2001.

Imran, Mudassar, and Phillip Barnes. "Energy Demand in the Developing Countries." World Bank Staff Commodity Working Paper. Washington, DC, 1990.

Imran, Mudassar, and Phillip Barnes. "Latin America: Governments Eyeing Gas and Oil Deals." Petroleum Economist 57 (May 1990): 142.

Latin American Energy Organization. The Foreign Debt and the Energy Sector of Latin America. Quito, Ecuador: Author, 1989.

Leonard, H. Jeffrey. Natural Resources and Economic Development in Central America. New Brunswick, NJ: Transaction Books, 1987.

Smith-Perera, Roberto. Energy and the Economy in Venezuela. Cambridge, MA: Harvard University Press, 1988.

U.S. Department of Energy. Report on the Western Hemisphere Energy Cooperation Study. Washington, DC: Author, 1990.

U.S. Department of Energy. 1989 International Energy Annual. Washington, DC: Author, 1991.

U.S. Department of Energy. "South America: International Gas Deals as Far Away as Ever." Petroleum Economist 58 (March 1991): 18-50.

                                        Mindi J. Farber

Energy

Potential and kinetic energy

Conservation of energy

Forms of energy

Electrical energy

Magnetic energy

Sound, chemical, and nuclear energy

Energy is commonly defined as the capacity to do work. Since work is defined as the action of a force through a distance, energy can also be described as the ability to make a force act through a distance. For example, a rocket motor exerts force against a rocket, accelerating it through space. In doing so, the rocket expends energy. A rocket can move through space at any velocity without expending energy, as long as its motor is not firing. Likewise, lifting a stone requires energy, because a force equal to or greater than the weight of the stone must be exerted through the height the stone is moved; but a falling stone expends no energy.

Unlike matter, energy can not be taken hold of or placed on a laboratory bench for study. We know the nature and characteristics of energy best because of the effect it has on objects around it, as in the case of the bar magnet and iron filings mentioned above.

Energy is described in many forms, including mechanical, heat, electrical, magnetic, sound, chemical, and nuclear. Although these forms appear to be very different from each other, they often have much in common and can generally be transformed into one another.

Over time, a number of different units have been used to measure energy. In the British system, for example, the fundamental unit of energy is the foot-pound. One foot-pound is the amount of energy that can move a weight of one pound a distance of one foot. In the metric system, the fundamental unit of energy is the joule (abbreviation: J), named after the English scientist James Prescott Joule (1818-1889). A joule is the amount of energy that can move a weight of one newton a distance of one meter.

Potential and kinetic energy

Every object has energy as a consequence of its position in space and/or its motion. For example, a baseball poised on a railing at the top of the observation deck on the Empire State Building has potential energy because of its ability to fall off the railing and come crashing down onto the street. The potential energy of the baseball—as well as that of any other object—is dependent on two factors, its mass and its height above the ground. The formula for potential energy is p.e. = m× g× h, where m stands for mass, h for height above the ground, and g for the gravitational constant (9.8 m per second per second).

Potential energy of position is a manifestation of the gravitational attraction of two bodies for each other. The baseball on top of the Empire State Building has potential energy because of the gravitational force that tends to bring the ball and Earth together. When the ball falls, both Earth and ball are actually moving toward each other. Since Earth is so many times more massive than the ball, however, we do not see its very minute motion.

When an object falls, at least part of its potential energy is converted to kinetic energy, the energy due to an object’s motion. The amount of kinetic energy possessed by an object is a function of two variables, its mass and its velocity. The formula for kinetic energy is k.e. = 1/2m× v², where m is the mass of the object and v is its velocity. This formula shows that an object can have a lot of kinetic energy for two reasons. It can either be very heavy or it can be moving very fast. For that reason, a fairly light baseball falling over a very great distance and traveling at a very great speed can do as much damage as a much more massive object falling at a slower speed.

Conservation of energy

The sum total of an object’s potential and kinetic energy is known as its mechanical energy. The total amount of mechanical energy possessed by a body is a constant. The baseball described above has a maximum potential energy and minimum kinetic energy (actually a zero kinetic energy) while at rest. In the fraction of a second before the ball has struck the ground, its kinetic energy has become a maximum and its potential energy has reached almost zero.

The case of the falling baseball described above is a special interest of a more general rule known as the law of conservation of energy. According to this law, energy can never be created or destroyed. In other words, the total amount of energy available in the universe remains constant and can never increase or decrease.

Although energy can never be created or destroyed, it can be transformed into new forms. In an electric iron, for example, an electrical current flows through metallic coils within the iron. As it does so, the current experiences resistance from the metallic coils and is converted into a different form, heat. A television set is another device that operates by the transformation of energy. An electrical beam from the back of the television tube strikes a thin layer of chemicals on the television screen, causing them to glow. In this case, electrical energy is converted into light. All of the modern appliances that we use transform of energy from one form to another.

In the early 1900s, Albert Einstein announced perhaps the most surprising energy transformation of all. Einstein showed by mathematical reasoning that energy can be converted into matter and vice versa. He expressed the equivalence of matter and energy in a now famous equation, E = mc ², where E is energy, m is mass, and c is a constant, the speed of light.

Forms of energy

The operation of a steam engine is an example of heat being used as a source of energy. Hot steam is pumped into a cylinder, forcing a piston to move within the cylinder. When the steam cools off and changes back to water, the piston returns to its original position. The cycle is then repeated. The up-and-down motion of the piston is used to turn a wheel or do some other kind of work. In this example, the heat of the hot steam is used to do work on the wheel or some other object.

The source of heat energy is the motion of molecules within a substance. In the example above, steam is said to be “hot” because the particles of which it is made are moving very rapidly. When those particles slow down, the steam has less energy. The total amount of energy contained within any body as a consequence of particle motion is called the body’s thermal energy.

One measure of the amount of particle motion within a body is temperature. Temperature is a measure of the average kinetic energy of the particles within the body. An object in which particles are moving very rapidly on average has a high temperature. One in which particles are moving slowly on average has a low temperature.

Temperature and thermal energy are different concepts, however, because temperature measures only the average kinetic energy of particles, while thermal energy measures the total amount of energy in an object. A thimbleful of water and a swimming pool of water might both have the same temperature, that is, the average kinetic energy of water molecules in both might be the same. But there is a great deal more water in the swimming pool, so the total thermal energy in it is much greater than the thermal energy of water in the thimble.

Electrical energy

Suppose that two ping pong balls, each carrying an electrical charge, are placed near to each other. If free to move, the two balls have a tendency either to roll toward each other or away from each other, depending on the charges. If the charges they carry are the same (both positive or both negative), the two balls will repel each other and roll away from each other. If they charges are opposite, the balls will attract each other and roll toward each other. The force of attraction or repulsion of the two balls is a manifestation of the electrical potential energy existing between the two balls.

Electrical potential energy is analogous to gravitational energy. In the case of the latter, any two bodies in the universe exert a force of attraction on each other that depends on the masses of the two bodies and the distance between them. Any two charged bodies in the universe, on the other hand, experience a force of attraction or repulsion (depending on their signs) that depends on the magnitude of their charges and the distance separating them. A lightning bolt traveling from the ground to a cloud is an example of electrical potential energy that has suddenly been converted to it “kinetic” form, an electrical current.

An electrical current consists of moving electrical charges and flows any time three conditions are met. First, there must be a source of electrical charges. A battery is a familiar source of electrical charges. Second, there must be a pathway through which the electric charges can flow. The pathway is known as a circuit. Third, there must usually be an electric field to cause the charges to move.

An electric current is useful, however, only if a third condition is met—the presence of some kind of device that can be operated by it. For example, one might insert a radio into the circuit through which electrical charges are flowing. When that happens, the electrical charges flow through the radio and make it produce sounds. That is, electrical energy is transformed into sound energy within the radio.

Magnetic energy

A magnet is a piece of metal that has the ability to attract iron, nickel, cobalt, or certain specific other kinds of metal. Every magnet contains two distinct regions, one known as the north pole and one, the south pole. As with electrical charges, unlike poles attract each other and like poles repel each other.

Masses set up gravitational fields, charges set up electric fields, and magnets set up magnetic fields. A field is physical influence in a region in space that can cause a magnetic, electrical, or other kind of force to be experienced. For example, imagine that a piece of iron is placed at a distance of 2 in (5 cm) from a bar magnet. If the magnet is strong enough, it may pull on the iron strongly enough to cause it to move. The piece of iron is said to be within the magnetic field of the bar magnet.

The concept of a field was, at one time, a difficult one for scientists to accept. How could one object exert a force on another object if the two were not in contact with each other?

One of the great discoveries in the history of physics was made by the English physicist James Clerk Maxwell (1831–1879) in the late nineteenth century. Maxwell found that the two major forms of energy known as electricity and magnetism are not really different from each other, but are instead closely associated with each other. That is, every electrical current has associated with it a magnetic field and every changing magnetic field creates its own electrical current.

As a result of Maxwell’s work, it is often more correct to speak of electromagnetic energy, a form of energy that has both electrical and magnetic components. Scientists now know that a number of seemingly different types of energy are all actually forms of electromagnetic energy. These include x rays, gamma rays, ultraviolet light, visible light, infrared radiation, radio waves, and microwaves. These forms of electromagnetic energy differ from each other in terms of the wavelength and frequency of the energy wave on which they travel. The waves associated with x rays, for example, have very short wavelengths and very high frequencies, while the waves associated with microwaves have much longer wavelengths and much lower frequencies.

Sound, chemical, and nuclear energy

When sound is created, sound waves travel through space, creating compressions (areas of higher pressure) in some regions and rarefactions (areas of lower pressure) in other regions. When these sound waves strike the human eardrum, they cause the drum to vibrate, creating the sensation of sound in the brain. Similar kinds of sound waves are responsible for the destruction caused by explosions. The sound waves collide with building, trees, people, and other objects, causing damage to them.

Chemical energy is a form of energy that results from the forces of attraction that hold atoms and other particles together in molecules. In water, for example, hydrogen atoms are joined to oxygen atoms by means of strong forces known as chemical bonds. If those are broken, the forces are released in the form of chemical energy. When a substance is burned, chemical energy is released. Burning (combustion or oxidation) is the process by which chemical bonds in a fuel and in oxygen molecules are broken and new chemical bonds are formed. The total energy in the new chemical bonds is less than it was in the original chemical bonds, and the difference is released in the form of chemical energy.

Nuclear energy is similar to chemical energy except that the bonds involved are those that hold together the particles of a nucleus, protons and neutrons. The fact that most atomic nuclei are stable is proof that some very strong nuclear forces exist. Protons are positively charged and one would expect that they would repel each other, blowing apart a nucleus. Since that does not happen, some kinds of force must exist to hold the nucleus together.

One such force is known as the strong force. If something happens to cause a nucleus to break apart, the strong force holding two protons together is released in the form of nuclear energy. That is what happens in an atomic (fission) bomb. A uranium nucleus breaks apart into two roughly equal pieces,

KEY TERMS

Conservation of energy— A law of physics that says that energy can be transformed from one form to another, but can be neither created nor destroyed.

Field— A region in space in which a magnetic, electrical, or some other kind of force can be experienced.

Joule— The unit of measurement for energy in the metric system.

Kinetic energy— The energy possessed by a body as a result of its motion.

Magnetic pole— The region of a magnetic in which magnetic force appears to be concentrated.

Potential energy— The energy possessed by a body as a result of its position.

Temperature— A measure of the average kinetic energy of all the elementary particles in a sample of matter.

Thermal energy— The total amount of energy contained within any body as a consequence of the motion of its particles.

and some of the strong force holding protons together is released as nuclear energy. The resulting fragments weigh slightly less than the original atom, and the mass lost is equal to the energy released.

David E. Newton