Energy

ENERGY, in physical science, a term which may be defined as accumulated mechanical work, which, however, may be only partially available for use (from the Gr. EvEpyeca: Ev, in, 'p-yov, work). A bent spring possesses energy, for it is capable of doing work in returning to its natural form ; a charge of gunpowder possesses energy, for it is capable of doing work in exploding; a Leyden jar charged with electricity possesses energy, for it is capable of doing work in being discharged ; a magnet is capable of attracting certain bodies (e.g., iron) and doing work during their approach. The motions of bodies, or of the ultimate parts of bodies, also involve energy, for stopping them would be a source of work.

Measurement.

All kinds of energy are ultimately measured in terms of work. If we raise 1 lb. of matter through a foot we do a certain amount of work against the earth's attraction; if we raise 2 lb. through the same height we do twice this amount of work, and so on. Also, the work done in raising 1 lb. through 2 ft. will be double of that done in raising it i ft. Thus we re cognize that the work done varies conjointly as the resistance over come and the distance through which it is overcome.

Now, we may select any definite quantity of work we please as our unit, as, for example, the work done in lifting a pound a foot high from the sea-level in the latitude of London, which is the unit of work generally adopted by British engineers, and is called the "foot-pound." The most appropriate unit for scientific pur poses is one which depends only on the fundamental units of length, mass and time, and is hence called an absolute unit. Such a unit is independent of gravity or of any other quantity which varies with the locality. Taking the centimetre, gramme and second as our fundamental units, the most convenient unit of force is that which, acting on a gramme for a second, produces in it a velocity of a centimetre per second; this is called a Dyne. The unit of work is that which is required to overcome a resistance of a dyne over a centimetre, and is called an Erg. In the latitude of Paris the dyne is equal to the weight of about of a gramme, and the erg is the amount of work required to raise of of a gramme vertically through one centimetre.

Energy is commonly defined as the capacity for doing work. Since, however, we cannot always bring about the change the term capacity is somewhat misleading; it is better to define energy as that which diminishes when work is done by an amount equal to the work so done. The unit of energy should therefore be the same as that of work, and the centimetre-gramme-second (C.G.S.) unit of energy is the erg.

It will be seen from that which has been stated that energy may become manifest in many ways ; or, in other words there are many forms of energy.

Forms.

The forms of energy which are most readily re cognized are of course those in which the energy can be most directly employed in doing mechanical work; and it is manifest that masses of matter which are large enough to be seen and handled are more readily dealt with mechanically than are smaller masses. Hence when useful work can be obtained from a system by simply connecting visible portions of it by a train of mechan ism, such energy is more readily recognized than is that which would compel us to control the behaviour of molecules before we could transform it into useful work. This leads up to the funda mental distinction, introduced by Lord Kelvin, between "available energy," which we can turn to mechanical effect, and "diffuse energy," which is useless for that purpose.

Potential Energy.

If a pound weight be suspended by a string passing over a pulley, in descending through i o f t. it is capable of raising nearly a pound weight attached to the other end of the string, through the same height, and thus can do nearly io foot-pounds of work. The smoother we make the pulley the more nearly does the amount of useful work which the weight is capable of doing approach 1 o foot-pounds, and if we take into account the work done against the friction of the pulley, we may say that the work done by the descending weight is 10 foot-pounds, and hence when the weight is in its elevated position we have at disposal 1 o foot-pounds more energy than when it is in the lower position. It should be noticed, however, that this energy is pos sessed by the system consisting of the earth and pound together, in virtue of their separation, and that neither could do work with out the other to attract it. The system consisting of the earth and the pound therefore possesses an amount of energy which de pends on the relative positions of its two parts, on account of the latent physical connection existing between them. In most me chanical systems the working stresses acting between the parts can be determined when the relative positions of all the parts are known; and the energy which a system possesses in virtue of the relative positions of its parts, or its configuration, is classified as "potential energy," to distinguish it from energy of motion which we shall presently consider. The word potential does not imply that this energy is not real ; it exists in potentiality only in the sense that it is stored away in some latent manner; but it can be drawn upon without limit for mechanical work.

Kinetic Energy.

It is a fundamental result in dynamics that, if a body be projected vertically upwards in vacuo, with a velocity of v centimetres per second, it will rise to a height of centi metres, where g represents the numerical value of the acceleration produced by gravity in centimetre-second units. Now, if in repre sent the mass of the body in grammes its weight will be mg dynes, for it will require a force of mg dynes to produce in it the accelera tion denoted by g. Hence the work done in raising the mass will be represented by that is, ergs. Now, whatever be the direction in which a body is moving, a frictionless constraint, like a string attached to the body, can cause its velocity to be changed into the vertical direction without any change taking place in the magnitude of the velocity. Thus it is merely in virtue of the velocity that the mass is capable of rising against the resistance of gravity, and hence we recognize that on account of its motion the body possessed units of energy. Energy of motion is usually called "kinetic energy." A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum. When at the limits of its swing, the pendulum is for an instant at rest, and all the energy of the oscillation is static or potential. When passing through its position of equilibrium, since gravity can do no more work upon it without changing its fixed point of support, all the energy of oscillation is kinetic. At intermediate positions the energy is partly kinetic and partly potential.

Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts. Since our conception of velocity is essentially relative, it is plain that any property possessed by a body in virtue of its motion can be effectively possessed by it only in relation to those bodies with respect to which it is moving. If a body whose mass is m grammes be moving with a velocity of v centimetres per second relative to the earth, the available kinetic energy possessed by the system is ergs if m be small relative to the earth. But if we consider two bodies each of mass m and one of them moving with velocity v relative to the other, only units of work is available from this system alone. Thus the estimation of kinetic energy is inti mately affected by the choice of our base of measurement.

Conservation of Energy.

When the stresses acting between the parts of a system depend only on the relative positions of those parts, the sum of the kinetic energy and potential energy of the system is always the same, provided the system be not acted upon by anything outside it. Such a system is called "con servative," and is well illustrated by the swinging pendulum above referred to. But there are stresses which depend on the relative motion of the visible bodies between which they appear to act. When work is done against these forces no full equivalent of potential energy may be produced ; this applies especially to fric tional forces, for if the motion of the system be reversed the forces will be also reversed and will still oppose the motion. It was long believed that work done against such forces was lost, and it was not till the 19th century that the energy thus trans formed was traced ; the conservation of energy has become the master-key to unlock the connections in inanimate nature.

The conception of work and of energy was originally derived from observation of purely mechanical phenomena, that is to say, phenomena in which the relative positions and motions of visible portions of matter were all that were taken into consideration. Hence it is not surprising that, in those more subtle forms in which energy cannot be readily or completely converted into work, the universality of the principle of energy, its conservation, as regards amount, should for a long while have escaped recognition after it had become familiar in pure dynamics.

It was pointed out by Thomson (Lord Kelvin) and P. G. Tait that Newton had divined the principle of the conservation of energy, so far as it belongs purely to mechanics. But what be came of the work done against friction and such non-conservative forces remained obscure, while the chemical doctrine that heat was an indestructible substance afterwards led to the idea that it was lost. There was, however, even before Newton's time, more than a suspicion that heat was due to the motions of the ultimate parts of which bodies are built up. Francis Bacon expressed his conviction that heat consists of a kind of motion or "brisk agitation" of the particles of matter. In the Novum Organum, after giving a long list of the sources of heat, he says: "From these examples, taken collectively as well as singly, the nature whose limit is heat appears to be motion. . . . It must not be thought that heat generates motion or motion heat (though in some respects this is true), but the very essence of heat, or the substantial self of heat, is motion, and nothing else." It must not be forgotten, however, that early writers make no distinction between heat and temperature. No definiteness therefore can be attributed to such anticipations as this. It was only when Joseph Black showed that heat was something (distinct from tempera ture) which could be measured that the ground was cleared for bringing it into the mechanical scheme.

Rumford's Investigations.

The first vigorous effort to restore the universality of the doctrine of energy was made by Benjamin Thompson, Count Rumford, and was published in the Phil. Trans. for 1798. Rumford was engaged in superintending the boring of cannon in the military arsenal at Munich, and was struck by the amount of heat produced by the action of the boring bar upon the brass castings. In order to see whether the heat came out of the chips he compared the capacity for heat of the chips abraded by the boring bar with that of an equal quantity of the metal cut from the block by a fine saw, and obtained the same result in the two cases, from which he concluded that "the heat produced could not possibly have been furnished at the expense of the latent heat of the metallic chips." Rumford then turned up a hollow cylinder which was cast in one piece with a brass six-pounder, and having reduced the con nection between the cylinder and cannon to a narrow neck of metal, he caused a blunt borer to press against the hollow of the cylinder with a force equal to the weight of about io,000 lb., while the casting was made to rotate in a lathe. By this means the mean temperature of the brass was raised through about 70° Fahr., while the amount of metal abraded was only 837 grains.

In order to be sure that the heat was not due to the action of the air upon the newly exposed metallic surface, the cylinder and the end of the boring bar were immersed in 18.77 lb. of water contained in an oak box. The temperature of the water at the commencement of the experiment was 6o° F and after two horses had turned the lathe for 21 hours the water boiled. Taking into account the heat absorbed by the box and the metal, Rumford calculated that the heat developed was sufficient to raise 26.58 lb. of water from the freezing to the boiling point, and in this calculation the heat lost by radiation and conduction was neg lected. Since one horse was capable of doing the work required, Rumford remarked that one horse can generate heat as rapidly as nine wax candles burning in the ordinary manner.

Finally, Rumford reviewed all the sources from which the heat might have been supposed to be derived, and concluded that it was simply produced by the friction, and that the supply was in exhaustible. "It is hardly necessary to add," he remarks, "that anything which any insulated body or system of bodies can con tinue to furnish without limitation cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner that heat was excited and communicated in these experiments, except it be motion." Transformation of Energy.—About the same time Davy showed that two pieces of ice could be melted by rubbing them together in a vacuum, although everything surrounding them was at a temperature below the freezing point. He did not, however, infer that since the heat could not have been supplied by the ice, for ice absorbs heat in melting, this experiment afforded con clusive proof against the substantial nature of heat.

Though we may allow that the results obtained by Rumford and Davy demonstrate satisfactorily that heat is in some way due to motion, yet they do not tell us to what particular dynamical quantity heat corresponds. For example, does the heat generated by friction vary as the friction and the time during which it acts, or is it proportional to the friction and the distance through which the rubbing bodies are displaced—that is, to the work done against friction—or does it involve any other conditions? If it can be shown that, however the duration and all other conditions of the experiment may be varied, the same amount of heat can in the end be always produced when the same amount of energy is ex pended, then, and only then, can we infer that heat is a form of energy, and that the energy consumed has been really transformed into heat. This was left for J. P. Joule to achieve ; his experiments conclusively prove that heat and energy are of the same nature, and that all other forms of energy can be transformed into an equivalent amount of heat.

Mechanical Equivalent of Heat.—The quantity of energy which, if entirely converted into heat, is capable of raising the temperature of the unit mass of water from o° C to I° C is called the mechanical equivalent of heat.

In 1842 R. Mayer, a physician at Heilbronn, published an attempt to determine the mechanical equivalent of heat from the heat produced when air is compressed. Mayer made an assumption that the whole of the work done in compressing the air was converted into heat, and neglecting the possibility of heat being consumed in doing work within the air itself or being pro duced by the transformation of internal potential energy. Joule afterwards proved (see below) that Mayer's assumption was nearly in accordance with fact, so that his method was a sound one as far as experiment was concerned; and it was only on account of the values of the specific heats of air at constant. pressure and at constant volume employed by him being very inexact that the value of the mechanical equivalent of heat ob tained by Mayer was very far from the truth.

Joule's Researches.—Passing over L. A. Colding, who in presented to the Royal Society of Copenhagen a paper entitled Theses concerning Force, we come to Dr. James Prescott Joule of Manchester, to whom we are indebted more than to any other for the establishment of the principle of the conservation of energy on the broad basis on which it has since stood. The best known of Joule's experiments was that in which a brass paddle consisting of eight arms rotated in a cylindrical vessel of water containing four fixed vanes, which allowed the passage of the arms of the paddle but prevented the water from rotating as a whole. The paddle was driven by weights, and the temperature of the water was observed by thermometers which could indicate of a degree Fahrenheit. Special experiments were made to determine the work done against resistances outside the vessel of water, which amounted to about .006 of the whole, and corrections were made for the loss of heat by radiation, the buoyancy of the air affecting the descending weights, and the energy dissipated, i.e., converted into heat, when the weights struck the floor with a finite velocity. From these experiments Joule obtained 772.692 foot-pounds in the latitude of Manchester as equivalent to the amount of heat required to raise 1 lb. of water through I° Fahr., from the freezing point. Adopting the centigrade scale, this gives I,390.846 foot-pounds.

With an apparatus similar to the above, but smaller, made of iron and filled with mercury, Joule obtained results varying from 772.814 foot-pounds when driving weights of about 58 lb. were employed to 775.352 foot-pounds when the driving weights were only about 191 lb. By causing two conical surfaces of cast-iron immersed in mercury and contained in an iron vessel to rub against one another when pressed together by a lever, Joule ob tained 776.045 foot-pounds for the mechanical equivalent of heat when the heavy weights were used, and 774.93 foot-pounds with the small driving weights. In this experiment a great noise was produced, corresponding to a loss of energy, and Joule en deavoured to determine the amount of energy necessary to pro duce an equal amount of sound from the string of a violoncello and to apply a corresponding correction.

The close agreement between the results at least indicated that "the amount of heat produced by friction is proportional to the work done and independent of the nature of the rubbing surfaces." Joule inferred from them that the mechanical equivalent of heat is probably about 772 foot-pounds, or, employing the centigrade scale, about 1,390 foot-pounds.

In 1840 he further showed that when an electric current was produced by means of a dynamo-magneto-electric machine the heat generated in the conductor, when no external work was done by the current, was the same as if the energy employed in pro ducing the current had been converted into heat by friction, thus showing that electric currents conform to the principle of the conservation of energy, since energy can neither be created nor destroyed by them. He also determined a roughly approximate value for the mechanical equivalent of heat from the results of these experiments. He also extended his investigations to the currents produced by batteries.

In 1844 and 1845 Joule published a series of researches on the compression and expansion of air. A metal vessel was placed in a calorimeter and air forced into it, the amount of energy ex pended in compressing the air being measured. Assuming that the whole of the energy was converted into heat, when the air was subjected to a pressure of 21.5 atmospheres Joule obtained for the mechanical equivalent of heat about 824.8 foot-pounds, and when a pressure of only 10.5 atmospheres was employed the result was 796.9 foot-pounds.

In the next experiment the air was compressed as before, and then allowed to escape through a long lead tube immersed in the water of a calorimeter, and finally collected in a bell jar. The amount of heat absorbed by the air could thus be measured, while the work done by it in expanding could be readily calculated. In allowing the air to expand from a pressure of 21 atmospheres to that of 1 atmosphere the value of the mechanical equivalent of heat obtained was 821.89 foot-pounds. Between 1 o atmospheres and 1 it was 815.875 foot-pounds, and between 23 and 14 atmos pheres 761.74 foot-pounds.

But, unlike Mayer, Joule was not content with assuming that when air is compressed or allowed to expand the heat generated or absorbed is the equivalent of the work done and of that only, no change being made in the internal energy of the air itself when the temperature is kept constant. To test this two vessels similar to that used in the last experiment were placed in the same calorimeter and connected by a tube with a stop-cock. One contained air at a pressure of 22 atmospheres, while the other was exhausted. On opening the stop-cock no work was done by the expanding air against external forces, since it expanded into a vacuum, and it was found that no heat was generated or ab sorbed. This showed that Mayer's assumption was practically true. The subsequent researches of Dr. Joule and Lord Kelvin (Phil. Trans., P. 357, P. 321, and 1862, p. 579) showed that the statement that no internal work is done when a gas expands or contracts is not quite true, but the amount is very small in the cases of those gases which, like oxygen, hydrogen and nitrogen, can only be liquefied by intense cold and pressure. (See LIQUEFAC TION OF GASES.) Subsequent Determinations.—For a long time the final result deduced by Joule by these varied and careful investigations was accepted as the standard value of the mechanical equivalent of heat. Recent determinations by H. A. Rowland and others, necessitated by modern requirements, have shown that it is in error, but by less than 1 %. The writings of Joule, which thus occupy the place of honour in the practical establishment of the conservation of energy, have been collected into two volumes published by the Physical Society of London. On the theoretical side the greatest stimulus came from the publication in 1847, with out knowledge of Mayer or Joule, of Helmholtz's great memoir, tiber die Erhaltung der Kraft, followed immediately (1848-1852) by the establishment of the science of thermodynamics (q.v.), mainly by R. Clausius and Lord Kelvin on the basis of "Carnot's principle" (1824), modified in expression so as to be consistent with the conservation of energy.

The general equation of thermodynamics consistent with

the above investigations may be written : Heat entering a system = Increase of energy of the system plus the external work done by the system during the entry. It is clear from this that it is erroneous to speak of the heat in a body. Heat can pass inwards or outwards but the amount so passing is not a measure of the change of energy of the body for some of it passes out simul taneously as external work. The language in common use is an inheritance from the old caloric theory according to which heat was regarded as a substance. When heat passes into a solid or liquid very little external work is done and the usual nomenclature is fairly satisfactory. But it is essential to an understanding of thermodynamics to realize that it is not satisfactory in general. This subject is further considered in THERMODYNAMICS (q.v.).

Tendency of Transformations.

It may, however, be added here that in all cases there is a general tendency for other forms of energy to be transformed into heat on account of the friction of rough surfaces, the resistance of conductors, or similar causes, and thus to lose availability. In some cases, as when heat is con verted into the kinetic energy of moving machinery or the poten tial energy of raised weights, there is an ascent of energy from the less available form of heat to the more available form of mechan ical energy, but in all cases this is accompanied by the transfer of other heat from a body at a high temperature to one at a lower temperature, thus losing availability to an extent that more than compensates for the rise.

Recent theoretical developments in physics have given rise to the presumption that the law of conservation of energy as usually understood is valid only for small motions such as are met with in engineering problems. For the modifications necessary to ob tain a general theory applicable to all cases reference must be made to the article on RELATIVITY (q.v.). t W. GAR.; J. LA.)