Nature to us is an aggregate of particles in motion. We have to speak of massive particles, whether we call these visible material bodies, or molecules, or atoms, or electrons, in order that we may describe nature. We must employ the fiction of a substantia physica. We only know the substance or matter in terms of energy; it is really the latter that is known to us. It is the poverty of our language, or rather it is the legacy of a materialistic age, that compels us to speak of particles that move, rather than of motions as entities in themselves.
Considering, then, the idea of particles in motion as a fiction necessary for clear description, we can study energy. There is only one kind, or form, of energy which presents itself to our aided or unaided intuitions, that is kinetic energy. Bodies that move possess this energy represented by their motion: they can be made to do work, that is, their energy can be transformed into other forms of energy. All things are in motion. A gas consists of molecules incessantly moving with high velocity, and colliding and rebounding from each other. The energy of a gas is the sum of one-half of the masses of all the molecules, multiplied by the squares of the velocities of all the molecules, that is, Σ 1/2mv2. This is also the kinetic energy of a projectile, or of a planet revolving round the sun. Kinetic energy is that of the uniform, unchanging motion of some entity possessing mass, but we must extend our notion of mass so as to include immaterial, imponderable entities such as electrons.
This energy cannot be destroyed or created—the law of conservation of energy. This is a principle or mode of our thought. We are unable scientifically or philosophically to think of an entity ceasing to be. Dreams and phantoms show us entities which are real while they last, but which cease to exist. If we do attempt to think of entities that appear from, or disappear into, nothing, we surrender the notion of reality. The more we think of it the more clearly we shall see that the things which we call real are the things which are conserved.
Yet energy, to our immediate intuitions, seems to disappear. A flying bullet strikes against a target and becomes flattened out into a motionless piece of lead. A red-hot piece of iron cools down to the temperature of its surroundings. A golf-ball driven up the side of a hill comes to rest in the grass. A current of electricity passing through water is used up, that is, electricity of a higher potential is required to force the current through water than to force it through thick copper wire. In all these cases we might think that energy is lost, but we cannot believe this. The kinetic energy of the flying bullet becomes transformed into the increase of the kinetic energy of the molecules of the metal of which the bullet was composed; for the latter becomes greatly heated when its flight is arrested and this increased heat ought to be equal to the kinetic energy of the bullet in flight. The red-hot piece of iron cools, and the kinetic energy of its molecules becomes less and less, but this does not cease to exist, for the energy is simply transferred by radiation and conduction to the surrounding bodies, the temperature of which it raises. The golf-ball driven up the hill comes to rest and loses its kinetic energy. Some of this has been transferred to the air through which it passes, the latter being heated very slightly; some of it is expended by friction with the grass over which the ball rolls before coming to rest, and this energy is traceable in heat-effects, or in mechanical effects, but the rest of it apparently ceases to exist. But this would be contradictory to the principle of conservation, and so we say that the lost kinetic energy has become potential. The current of electricity may heat the water through which it passes, and some of the energy which seems to disappear is so to be traced, but the greater fraction is apparently lost. A quantity of free hydrogen and oxygen is, however, generated, and we say that the kinetic energy of the moving electrons has become transformed into the potential chemical energy of the gaseous mixture.
POTENTIAL ENERGY
Therefore, if energy disappears or appears, we do not say that it is destroyed or is created: we invent potential energies, into which we suppose that the energies in question have become transformed, in order that we may still think of them as being subject to an a priori principle of conservation. Although a particle of radium continually generates heat, we do not therefore think of the first principle of energetics as being invalidated, for we suppose that the energy which thus appears was really potential in the atoms of radium. But it was contrary to all our former experience of atoms that they should contain any other energy than that of their own motion, and so the further assumption was made that the atom, at least the atom of the radio-active substance, is really complex, and not simple, as chemical theory demands. It is made up of smaller particles, and possesses a definite structure. In certain circumstances the atom may disintegrate, and the energy which held together its particles, whether these were simpler corpuscles or electrons, is given off as the heat which the radio-active substance apparently generates. The potential energy of the chemical atom is therefore a hypothesis which has been devised in order to preserve the validity of the law of conservation, and the reality of this hypothesis is being tested by investigation. If we accept it as true, are the deductions made from it justified in our experience? That is the test which must be satisfied in all the hypotheses where potential energies are invented, and the potentials are only real if the test is satisfactory. The golf ball at rest at the top of the hill is a different entity from the golf ball at rest at the bottom of the hill: it is capable of developing energy, for a touch may cause it to roll down the hill, when most of the energy which was expended in order to drive it to the top of the hill will reappear in the form of the kinetic energy of motion of the ball. The atoms of hydrogen and oxygen which were dissociated by the energy of the electric current are different things from the atoms of hydrogen and oxygen which are combined together to form the molecules of water. Their state when the gases are in the elementary condition, or are “free,” is that of molecules moving rapidly and incessantly, rebounding from each other after colliding with each other: they possess energy of position—potential energy—because they are separate from each other. If they “combine,” as when a minute electric spark explodes the mixture of gases, they tractate together, and remain in proximity to each other, becoming molecules of water. The energy which became potential in the gaseous mixture, when the electric energy of the current seemed to disappear, now appears as the heat generated by the combustion, that is, as the greatly increased kinetic energy of the molecules of the gas (steam) which takes the place of the mixture of hydrogen and oxygen. Previous to the explosion this gas was a mixture of molecules of hydrogen and oxygen (2H2+2O) at the ordinary temperature, but after the explosion it consists of a smaller number of molecules at a very much higher temperature.
What is “energy of position”? The golf ball at the bottom of the hill was at a distance of R feet from the centre of the earth, but at the top of the hill it is at a distance of R + 100 feet from the centre of the earth. In the first case it was free to fall R feet, but in the second case it is free to fall R + 100 feet. The atoms of the constituent molecules of water occupy the position H−O−H, the bonds (−) indicating that the atoms are very close together; but when the water is decomposed by an electric current, the atoms occupy the positions O−O + H−H + H−H, the (+) indicating that the atoms are relatively far apart from each other. Now the golf ball and the earth, or the atoms of hydrogen and oxygen, are physically the same material entities, whether they are close together or far apart, yet when the earth and the ball, or the atoms of oxygen and hydrogen, are separated from each other, their “properties” are different from what they are when they are close together. What is it that makes the difference? It is that which is between them. Is it, in the last case, “the potential energy of chemical affinity”? This dreadful phrase is actually used in a recent book on biology: “In the elements carbon and oxygen, so long as they remain separate, a certain amount of energy remains latent. When the carbon and oxygen atoms are allowed to come together and unite, this potential energy of chemical affinity is liberated as kinetic energy.” What is changed by the tractation and pellation (the terms suggested by Soddy in place of the anthropomorphic ones, “attraction” and “repulsion”)? It is the ether which has become changed in some way. Potential energy resides therefore in the ether of space.
ISOTHERMAL AND ADIABATIC CHANGES
Let us consider the changes which occur in a gas under the influence of changes in temperature and pressure, premising that the remarks which we have to make can be applied to bodies in the liquid and solid conditions, with some necessary modifications. A gas, then, consists of a very great number of particles, or molecules, in motion. These molecules move in straight lines at very high velocities, and if the envelope in which the gas is contained is a restricted one, the molecules collide with each other, and with the walls of the envelope; and, being assumed perfectly elastic, they rebound from each other, and from the walls of the vessel, with the same velocity which they had when they collided. The pressure of the gas (say that of steam at a temperature of 110° C., and a pressure of 120 lbs. to the square inch in a steam boiler) is the sum of the impacts of the molecules on the walls of the containing vessel. When the temperature is high the molecules are moving at a higher mean velocity than when the temperature is lower, and their mean free path tends to become greater. The volume of a certain mass of gas, that is, the volume occupied by a certain very great number of molecules, is greater the higher is the temperature, provided the envelope is one capable of yielding. If we reduce the capacity of the envelope in which the gas is contained, the pressure will rise, for the intrinsic energy of the gas is still the same; but we have done work on it, and by the law of conservation this work, or at least the energy represented by it, must still exist. It is represented by the decreased length of free path of the molecules, and this means that the impacts on the walls of the vessel will be greater than they were. There is, therefore, a certain relation between the volume of a gas and its pressure, and this relation can be represented by an equation involving the temperature, the pressure, and the volume.
