Energy. The term energy as applied to a material system is used to denote the power of doing work which is possessed by that system. There is no manifestation of energy apart from matter. In consequence of this, matter is sometimes defined as the vehicle or receptacle of energy. A bullet projected vertically upwards possesses a great amount of energy; it can do work in overcoming obstacles to its motion. But the higher it rises the less resistance can it overcome; and at last, having reached the greatest height it can attain, it seems incapable of doing work. Yet it is not really incapable of doing work. It will gradually acquire speed in the downward direction, and will finally (the resistance of the air being neglected) reach the ground with the same speed as it had at first, and is thus capable of doing the same amount of work. Therefore, when at its highest position and seemingly incapable of doing work, it really possessed energy as at first. Hence we are led to recognise two leading types of energy—energy of motion and energy of position; or, as they are usually called, kinetic energy and potential energy. We have many examples in nature of both types. Currents of air or of water possess kinetic energy; a stone resting on the brow of a cliff, and water at the edge of a fall, possess potential energy.
But although energy may be classed under one or other of these two types, there are many forms in which it is manifested. There is energy of visible motion and energy of position in visible arrangements of bodies, as in the bullet moving upwards or downwards, or at rest at its highest position. A bent spring evidently possesses potential energy. An oscillating pendulum possesses alternately kinetic energy and potential energy. At the extremity of its swing the energy is entirely potential; at the middle of its range the energy is entirely kinetic; at intermediate positions it is partly of one kind, partly of the other. Heat is another form of energy. The particles of a hot body are in rapid motion, and the hotter the body the more rapid is the motion. The motion is on an invisibly small scale, but it can be communicated to other matter in such a way as to produce visible motion. Thus the invisible motions which constitute heat are applied in the steam-engine or air-engine to produce visible motion of a piston, and so to perform mechanical work. When Heat (q.v.) becomes latent in a body, part at least of the energy is spent in overcoming molecular forces, and the relative distances of the molecules of the body are altered; and so we have potential energy stored up in the molecules. Again we have the so-called radiant energy—energy propagated by means of undulations through the ether. This includes light as well as radiant heat, the two differing merely as regards wave-length. So also it includes the electro-magnetic undulations recently experimentally demonstrated by Hertz, the wave-length of which may be many feet instead of of an inch as in orange-coloured light. The vibrations of the particles of a hot or luminous body are communicated to the ether, and propagated by wave-motion through it at the rate of 186,000 miles per second. In the ether, therefore, the energy is partly potential, partly kinetic (see ETHER). There is also energy of chemical separation. Carbon and oxygen combine in the burning of ordinary fuel, and the energy which they contain in their separated state is used to produce mechanical work, as in the steam-engine; and in the explosion of gunpowder visible energy of motion is produced even more directly from the energy of chemical separation of the constituent substances. We have also potential energy of electrical separation, for if two conductors be charged with electricity, one positively and the other negatively, an attraction between them becomes apparent. In approaching each other the charged bodies can be made to do work. Again, when we have electricity in motion in a conductor, we have another means of producing work. The current of electricity produces heat and also tends to produce motion of other conductors in which electric currents flow. The attraction or repulsion between magnets can also be made to produce work, and so also we can get work from the mutual action between magnetised bodies and conductors in which electric currents flow.
Thus we see that energy may be manifested to us in a number of different forms; but as we do not yet know the ultimate nature of matter or of electricity, we cannot assert that the forms which we have just considered are all essentially distinct. It is not impossible that the energy of chemical separation is due to electrical separation, or that energy resulting from magnetisation is due to motion of electricity.
In the above remarks we have spoken not only of the production of work from energy, but of the production of one form of energy from another, and of the passage of potential energy into kinetic energy. This change of energy from one form to another is known as the Transformation of Energy, and distinguishes it from matter. While matter is passive or inert, energy is continually in process of transformation—indeed we are cognisant of energy only in virtue of its change. We should never know that a moving cannon-ball possessed energy if we did not see its destructive effects; we should never know that electrified clouds possessed energy did we not see damage done by lightning.
Of the transformation of energy a few examples must suffice. We cause carbon and oxygen to combine in the furnace of a steam-boiler, or hydrogen and oxygen to combine in the cylinder of a gas-engine. This produces invisible motion of molecules, which in turn produces visible mechanical motion of the piston and connected mechanism. This motion may be communicated to a 'dynamo,' causing conducting wires to move in a magnetic field. Thus electric currents are produced in the wires. These currents may produce heat in, and cause radiation from, a highly resisting carbon filament. Or they may produce magnetic effects, and finally mechanical motion, in a motor. Thus energy may be applied by means of the dynamo and motor to the production of mechanical work in a place where it would not be easy to use an engine directly.
In the case of the telephone, the condensations and rarefactions of the air (which produce sound when they impinge on the ear) cause vibrations of the telephone diaphragm. As this motion occurs in the near neighbourhood of the pole of a magnet, electric currents of varying intensity and direction are produced in a coil of wire surrounding the pole. These currents pass round the magnet of the receiving telephone, and produce magnetic effects similar to those occurring at the sending instrument. Therefore similar mechanical effects are caused, and so like sounds are heard.
In the voltaic battery energy of chemical separation is transformed into energy of current electricity. The electric current may be passed through slightly acidulated water. The water is thus broken up into its constituents, so that energy of chemical separation is again obtained.
Many other examples of the transformation of energy might be given, but it is sufficient to remark that any form can be directly or indirectly transformed into any other form. A matter of greatest importance to us is the determination of the sources or source from which ultimately we derive mechanical work. The work obtained from animal labour is derived from the chemical energy of the food supplied to the animal. This food is vegetable food either actually or ultimately; for, even if it be actually animal, the energy of such food is ultimately traceable to the vegetable world. Now all vegetables grow by means of solar radiation, which decomposes carbonic acid in their tissues, so that energy obtained from animal labour is obtained actually from the sun. And if we use fuel in an engine, the energy of the fuel is in the same way due to the sun. If we use wind-power to drive our machines, the energy is also solar, for it is the sun which causes the atmospheric currents. So also the work obtainable from moving water, except in the case of tidal currents, is due to the heat radiated from the sun. Thus the sun is the great source of our energy; and, if he ceased to supply us with it, we could no longer produce work, except indeed in so far as he has already supplied us with a store in potential forms.
We have already stated that the energy of a material system is sometimes exhibited in one form, sometimes in another, but this statement may be greatly extended. If no energy leaves the system, and if no new energy enters it, the quantity which disappears from one form reappears entirely in another. This is known as the principle of the Conservation of Energy. In the case of the bullet projected upwards, the potential energy in the highest position would be the exact equivalent of the original kinetic energy, if none were communicated to the air or other bodies. The same would hold in the case of the pendulum, if no energy were given from the system to the air or the supporting arrangement. [At one time the expression conservation of force was used instead of conservation of energy, but the word 'force' meant then what we now call 'energy.' The conservation of force, as we now use the word, means something totally different. See FORCE.]
The law of conservation of energy may be stated as follows: The total amount of energy in a material system cannot be varied, provided the system neither parts with energy to other bodies nor receives it from them. This law is merely a generalisation from observed facts; a single known exception would cause us to abandon or modify the statement. But the amount of positive proof in favour of the law is now exceedingly great, perhaps the strongest proof being afforded by the accuracy of scientific predictions founded upon the assumption of its truth. As an example, we may refer to the prediction of the lowering of the freezing-point of water by pressure. The assertion of the principle of conservation of energy is equivalent to a denial of the possibility of the 'Perpetual Motion' (q.v.).
In a scholium to his third law of motion, Newton asserts that 'if the action of an external agent is estimated by the product of its force into its velocity, and the reaction of the resistance in the same way by the product of the velocity of each part of the system into the resisting force, arising from friction, cohesion, weight, and acceleration, the action and reaction will be equal to each other, whatever be the nature and motion of the system.' Now the product of a force into the velocity produced by it is simply the rate at which the force does work. Hence, as was first pointed out by Thomson and Tait in their work on Natural Philosophy, this statement of Newton's is almost a complete statement of the principle of conservation of energy. Newton did not know what becomes of work spent in overcoming friction; he believed that it disappeared from the system. Had he known that it was converted into an exact equivalent in the form of heat, his statement would have been complete. It was not until long after Newton's time that Heat (q.v.) was recognised to be a form of energy. The experiments of Rumford and Davy first led to this result. Rumford's experiments were made in 1798 and 1799, on the work done, and the heat produced, in the boring of cannon. He concluded that heat must be due to motion. Davy's experiments on the melting of ice by friction were also made about the same time, but it was not until 1812 that he came to the conclusion that 'the immediate cause of the phenomenon of heat is motion, and the laws of its communication are precisely the same as the laws of the communication of motion.' From data given by Rumford, it may be calculated that 940 foot-pounds of work are necessary to produce heat sufficient to raise the temperature of one pound of water by 1° F.—the foot-pound being the work done in raising a pound through one foot against gravity. The researches of Colding and Joule, however, have given a far better determination of the mechanical equivalent of heat; and Joule's experiments, especially, extend to all forms of energy, and prove their exact equivalence. His experiments on the heating of water by friction gave results varying from 770 to 774 foot-pounds as the mechanical equivalent of heat. His final result was 772, the possible error being much less than 1 per cent. Many indirect methods have also been used by Joule and others. Thus, the mechanical equivalent may be directly determined by observing the quantity of heat developed during the passage of an electric current of known intensity through a conducting wire of known resistance. The result for heat being assumed, it is easy to find the work-equivalent of other forms of energy. Thus, we can determine the equivalent in work of the energy of chemical separation—e.g. by dissolving zinc in sulphuric acid, and observing the heat developed. If the zinc be dissolved in a voltaic cell which is producing a current, heat is evolved in the various parts of the circuit in proportion to their resistance. Thus, by placing in the circuit a wire of great resistance, almost all the heat will be developed in the wire, and so may readily be measured. Again, by making the current produce work through the agency of an electro-magnetic engine, the work may be directly measured, care being had to take account of energy lost in the process by friction or otherwise. Less heat is developed in the circuit in proportion as the work done is greater, the total energy being constant. So, by expending work in driving a magneto-electric machine, we may find the work-equivalent of electric energy. As the electric energy ultimately becomes heat, Joule used this method in one of his determinations of the quantity of heat produced from a known amount of work.
We have seen that we can neither increase nor diminish the total quantity of energy in the universe, while any one form of it may be changed into any other; but we have made no inquiry as to whether or not all forms are equally transformable. The question is obviously of vital importance to us; for, if one form be less transformable than the rest, when we change any other kind into this one, we shall not be able completely to re-transform it. Thus there will be a tendency for all forms to be reduced to this more permanent form, and we shall not be able so readily to obtain mechanical work from it. Sir W. Thomson first pointed out that there is in nature a universal tendency to this Dissipation (or, as it has since, and perhaps preferably, been called Degradation) of Energy. The final form which all energy tends to take is that of heat. But heat tends continually to diffuse so as to equalise temperature; and, when there is no difference of temperature between the source and condenser of a heat-engine, no work can be obtained from it, for the amount of work which can be obtained from a given quantity, , of heat (see HEAT) is , and being the absolute temperatures of the source and condenser respectively, while is the mechanical equivalent of heat. Obviously is the quantity of energy lost for useful purposes so far as this engine is concerned. This shows that all the amount of heat supplied cannot be transformed into work, unless the condenser be at the absolute zero of temperature. If we take as our source of heat in one case a cubic foot of some metal at a given absolute temperature, and in another case two cubic feet of the same metal containing together the same quantity of heat as the one cubic foot formerly contained, and therefore at half the temperature provided the specific heat be constant, it is obvious, from the above expression, that twice as much heat will be lost in the second case as in the first. Hence, we see that heat at low temperature is much less use- ful than the same quantity of heat at high temperature. And a corresponding statement is true for other forms of energy. Thus, if we have two Leyden jars alike in every respect, and charge one with a certain quantity of electricity, we can get a certain amount of work from the arrangement, which is made evident by the loudness of the sound and the brightness of the flash on discharge. But if we first divide the original charge between the two jars, and then discharge them, we can only get half the amount of energy. The reason is that the potential is only one-half of what it was in the first case; and the higher the potential of a given quantity of electricity is, the greater is the amount of work it can do, just as the usefulness of heat depends upon temperature. In fact, if be the potential of the charge in the first case, is the energy; but in the second case the charge of each jar is , and the potential of each is , so that the energy in each is , the total amount being therefore , or only half of the original energy. The remaining half is accounted for by the energy spent in dividing the charge—light, sound, and heat being produced. Again, work may be obtained by letting compressed gas expand; and the amount of work depends upon the pressure. The gas may be allowed to expand without doing work, but energy will be dissipated, for the expanded gas, being at less pressure, cannot do so much work as it could do before expansion.
Examples of the degradation of energy are everywhere seen in nature. The fact that the optical image of a body is less distinct than the object itself is due to the fact that some of the so-called radiant energy is absorbed by the reflector, and takes the form of heat. The vibrations of a tuning-fork die down because the energy is communicated to the surrounding air, but they also diminish because of the production of heat from molecular friction in the vibrating body. The stilling of storms is accompanied by dissipation of energy. Possibly starlight is weakened in its passage through the ether. Indeed, no instance of transformation of energy can be pointed out in which there is not also dissipation of energy.
As we have already remarked, since all forms of energy tend to take the form of heat, and since heat is constantly tending by conduction and otherwise to equality of temperature, it follows that, unless the universe be infinite, energy will ultimately become useless for the production of work. The total amount of energy will, in accordance with the principle of conservation, be the same as at first, but any transformation of it will be impossible. There are two ways in which we may regard the energy of a given system; we may regard it from without the system, or from within. When we speak of the total energy of a system, we regard it from the outside. Thus, if we consider a thermal system, the total energy is the work which could be done by the heat in passing from the system to its surroundings, these being supposed to be constantly at the absolute zero of temperature. But the available energy (called in this case the thermo-dynamic motivity) is usually regarded as the greatest amount of work which can be obtained by equalising the temperatures of its various parts amongst themselves. [The motivity might, of course, also be regarded from without. In this case it would be the quantity of work obtainable by reducing all the parts of the system to some definite temperature.] The available energy of the universe, supposed finite, will therefore ultimately be zero. The energy of relative motion of its parts tends, in virtue of friction, to take the form of heat. Though we have no direct confirmation of the statement, yet we may conclude from analogy that the relative motion of the planets and of all heavenly bodies tends to cease. Thus, ultimately, potential energy of gravitating matter must become kinetic energy of visible motion, and then heat; so that the universe will at last contain only one huge material body rotating about its centre of inertia, and the rotation too must cease in time. And even the molecular motions must largely cease, being communicated to the ether. All this is, of course, pure speculation. We might even, if we considered it profitable, speculate further with Rankine and others as to the possibility of the restoration of the availability of energy. If the universe be finite we may have reflection of radiant energy from its boundaries. A material body coming into a focus might be instantly vaporised, the radiant energy becoming again high-temperature heat.
The second law of thermo-dynamics (see HEAT) is essentially a statement, for the case of heat and mechanical work, of the principle of the dissipation of energy. Its proof, as given by Sir W. Thomson, depends upon the assumption that we cannot produce work from heat which is entirely derived from the colder of two bodies used as the source and condenser of a heat-engine. On an excessively small scale heat does pass in nature from a cold part of a body to a hot part, so as to increase the difference of temperature. In an excessively small portion of a gas, the quicker moving particles may be found in one part and the slower moving particles in another, even although the motion was uniform at first. Similarly, by moving in portions of the sides of a vessel containing gas when no particles were impinging upon them, we could increase the motivity of the system without doing work. As this is practically impossible, we see that the truth of the second law of thermo-dynamics depends essentially upon the extreme smallness and the great number of the particles of a body; so that, in the case of the gas, the motivity is increased only because work is done in compressing the gas which takes the form of heat, and is then removed from the system. Thus, while there is increase of motivity of the energy of the system, there is degradation of external energy.
If at any instant the motion of every particle of matter in the physical universe were reversed, the dissipation of energy would cease. Available energy would increase, for everything would occur over again exactly as in past time, but in the reverse order. This increase of availability would, however, only last until the configuration which existed at the commencement of the present order of things was reached, when dissipation of energy would again occur. This reversal of motion might occur in a system containing a very few particles, but we must regard it as an impossibility in the physical universe as a whole.
See the articles in the present work on HEAT, LIGHT, ELECTRICITY, &c., as also FUEL, &c., and for Muscular Energy, see DIETETICS. On the subject of the preceding article, Tait's Recent Advances in Physical Science (1876) may be consulted, and the same author's Thermo-dynamics (1877); Balfour Stewart's Conservation of Energy (1880); and the relevant portions of Clerk Maxwell's Heat (1875).