Popular Science Monthly/Volume 17/June 1880/The Availability of Energy
By W. D. MILLER, B.A.
IT follows, as a direct consequence of the most usual definition of matter as "the vehicle of energy," and is also arrived at from experience, that energy never does and never can manifest itself except in connection with matter. And, although we could readily conceive of, and in fact see many instances of, matter without energy, yet no person of sound intelligence, or, as said Newton, "no one with a competent faculty of thinking," could for a moment entertain the idea of energy without matter; and we naturally suspect that anything which is so dependent upon another for its existence, as it were, will, in some way or other, mold itself to suit the form and convenience of the other. It thus becomes a question of primary importance as to how energy is connected with and dependent upon matter, and as to how its form and availability are influenced by its connections.
That the same amounts of different kinds of energy, or even of different forms of the same kind, are vastly different in their effects, is a thing of every-day experience. A mass raised above the earth's surface possesses in consequence a certain amount of energy, in virtue of which it can do work; but if it be allowed to fall to the ground under the influence of the earth's attraction, then, although the amount of energy on the earth is neither increased nor diminished, it may be absolutely impossible to gain any work from it. In this instance energy of position is at first transformed into energy of motion, but the moment the mass strikes the ground all motion, as far as we are able to discover, is gone; but we know that the motion of the mass as a whole has only been transformed into motion of the particles among each other, and of the particles of the body on which the mass impinges, constituting the phenomenon of matter commonly called heat. The first two states are available as sources of mechanical energy, but in the third state the energy is scattered into an infinite number of infinitely small energies, as it were, and, in the case of small masses at least, is lost forever as far as doing work is concerned; and so much energy is let down from a high to a low class, and the whole energy of the universe is rendered less available by a corresponding amount.
But not only do equal quantities of energies of different kinds manifest themselves so very differently, but the same is true as to equal amounts of the same kind. A boxer may receive a blow from his antagonist which may stagger him, and perhaps throw him off his balance, but yet do him no permanent injury; while a rifle-ball with half the energy, though it might not disturb his equilibrium, would in all probability inflict instant death. Any number of examples of this kind might be given to show to what an extent the form which a given amount of energy assumes and the constancy of its effects are dependent upon the matter with which it is associated.
Now, the transformability of energy is a measure of its availability, and, in fact, energy is of use to us only and solely because it may be and is constantly transformed (consequently, whatever terms determine its transformability, the same hold good for the determination of its availability).
Since all forms of energy are essentially kinetic or potential, or the energy of heat-motion, it is sufficient if we examine the laws with regard to these.
A body is said to possess potential energy when in virtue of its position it can do work. A raised weight possesses potential energy, which, by a simple contrivance, may be converted into work; a bent bow and a wound-up spring possess energy of position, because of the separation of their molecules, which we may avail ourselves of by allowing them to fall back into their natural positions.
If a body be allowed to fall, it necessarily loses the energy which it had in virtue of its position as it approaches the ground, but at the same rate it gains a different kind proportional in amount to the space passed through, and consequently to the square of the velocity. In the case of a projectile, or pendulum-bob, there is a gradual transformation from kinetic to potential energy during the ascent, and a retransformation during the descent. If we spend work in raising a weight, bending a bow, or winding up a spring, that work is spent in laying up stores of energy which we may avail ourselves of at any future time. But if in performing any of these actions we encounter resistance, as in the case of friction, part of the work is spent in overcoming it; and, when we endeavor to get back the energy we put forth, we find that we fail by as much as was spent in overcoming the friction. The energy so spent was long a puzzle to scientific minds, and was believed to be absolutely destroyed, until the experiments of Rumford and Davy fully demonstrated that the work spent in overcoming friction was transformed into heat—a form of kinetic energy, it is true, but of such an inferior class as to have entirely escaped the notice of the shrewdest observers. It is, in general, a very easy matter to transform the whole of the potential or kinetic energy of a body into heat; but it becomes quite a different undertaking when we propose to reconvert the heat into either of the other forms.
Carnot was the first who made any progress in the investigation of the subject of the transformation of heat into mechanical energy. His manner of operating was strikingly original and one of great merit, and has assisted wonderfully in the development of this part of science since his time. He established two new and distinct propositions in connection with his method:
1. That we have no right to reason on what has taken place in any series of operations till the working substance has been brought back to its initial state, nor to assign any relation between heat and work by such reasoning.
2. That a reversible engine is the most perfect engine possible. And, consequently, if we possessed a reversible engine, and a condenser absolutely deprived of heat, we could convert the whole of the heat from the boiler into mechanical energy. But since it is impossible to obtain an absolutely cold condenser, there is always a large fraction lost in attempting to convert heat into mechanical energy. Sir W. Thomson, working from the principle laid down by Carnot, found that the heat taken in by a perfect engine is to that given out as the absolute temperature of the boiler is to that of the condenser. He also, carrying the process further, devised a correct proof of Carnot's second proposition, based upon the axiom that "it is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter, by cooling it below the temperature of the coldest of the surrounding bodies."
With the present physical constitution of matter this is true, so far as we are yet able to penetrate at least; but since its constitution might have been such as to render such an axiom null, we purpose to inquire into the physical properties of matter which admit of such an enunciation, and the results which in consequence must be predicted for the present universe.
Let us consider a hot spherical body, whose energy we wish to communicate to another equal sphere, absolutely cold, and suppose for a moment that they have a thin outside crust absolutely impermeable to heat, and that the mass of each sphere is concentrated in a single little ball, to whose motion the heat is due, the ball in the cold sphere will of course lie still at the bottom, while the other is flying about at an inconceivable rate; if, now, the two spheres be brought into contact, and an opening be made between them, in a very short time the ball will undoubtedly pass from the hot to the cold sphere, and thus all the energy will be transferred at once, and, if a movable partition were inserted in the passage, all the heat-energy might be transformed into mechanical energy.
If we suppose two balls, instead of one, in each sphere, as soon as one passes from the hot to the cold, it will share its motion with the two already there, and one or more of them may pass back before the second has escaped, and thus at once the relations are rendered more complex, and the chance for availing ourselves of all the energy is diminished. If, now, the number of balls becomes infinite, or if we reduce our imaginary spheres to two real spheres, and substitute molecules for balls, then 1: is not an exaggeration of the chance of all the energy being in one of the spheres at any time in the future; on the other hand, the continual tendency is to, and the ultimate result is, absolute equality in temperature.
Clerk Maxwell has made the supposition of a vessel full of air, divided into two portions, A and B, by a division in which there is a small hole; and a being, who can see the molecules, opens and closes this hole so as to allow only the swifter molecules to pass from A to B, and only the slower ones from B to A. He will thus, without the expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermo-dynamics.
By the above mode of reasoning, together with the conclusions drawn from our experience of bodies consisting of an immense number of molecules, the result has been arrived at that the availability of a given amount of energy is determined on a physical basis, and is dependent on the infinite number of particles of which every tangible mass must be composed.
The instance cited by Professor Maxwell is only "applicable to the more delicate observations and experiments, which we may suppose made by one who can perceive and handle the individual molecules which we deal with only in large masses."
In the theory of dynamics we say that action and reaction are equal; and if a body be arrested in the course of any motion, and sent back on its path with exactly the same velocity, it will retrace its path, and at any point of that path it will have exactly the same velocity and the same energy as when it passed through it in the opposite direction. But, practically, we are unable to realize such a law, because of the resistances we meet with in friction, electric induction, etc., so that any series of actions taking place in nature is not a reversible one, or the mechanical energy spent can never be wholly restored to its primitive condition. But as a reversible process is the only one which can maintain itself for all time, it follows that our earth is gradually lowering its energy from high to lower classes; the ultimate form to which all must be reduced being that which has its source not in the position or motion of masses, but of molecules.
If this process of transformation were not continually going on, our fires would cease to burn, our machines stop working, and all animal and vegetable life would perish. "The whole of active life is simply transformations of energy." Wherever two particles of matter fall together, whenever a drop of rain falls to the earth, whenever an atom of carbon combines with an atom of oxygen in the furnace, we must look upon it as so much energy let down, the greater part of which is dissipated and lost to human good. But it may easily be seen that this degradation of energy is not restricted to the earth alone, for among natural forces we recognize—
1. The energy of fuel, under which we include the energy of food, as being simply the fuel of an animated machine.
But, not content with what we receive, we dig down into the bowels of the earth and exhaust our own. There can be no doubt as to the final result to which this universal tendency points. Long after the earth has become uninhabitable, it may be, the kinetic energy of every planet of our system being frittered away into heat by friction on the ethereal medium, they shall find their way, one by one, into the sun's mass, thus giving him the energy by which he will work on for long ages after they are defunct; while he, in his turn, with all his accumulated mass, will precipitate himself into the center of some larger system: and this process will go on till, after various oscillations throughout, perhaps, infinite ages, the whole material universe is accumulated in a single mass, which will then go on radiating its heat into space till it becomes a black, cold, and lifeless mass.
This universal tendency of energy to concentrate, or rather to scatter itself into the least available form, is simply what has been called "the dissipation of energy," and may be said to be the complement of the availability of energy, and, like it, finds its basis and explanation in that molecular constitution of the material universe which renders it impossible for any amount of energy, which has once distributed itself among the immense number of molecules in any body, ever, of itself, to rise again to a more tangible and available condition.