The reverse is also impossible. For then we need merely couple the engines in the reverse way in order to obtain the same effect. Therefore, since B can do neither less nor more work than A, the two must do the same amount of work—which was to be proved.
It is obvious that this process of proof is similar to that by which the law of conservation was established. Because the arbitrary creation of energy from nothing is impossible there must be definite and immutable relations of change between the forms of energy. Because energy at rest does not spontaneously pass into conditions in which it can do work, the efficiencies of the machines must have definite and unchangeable values. If, for example, we could cause heat of its own accord to rise to a higher temperature, we could also construct a perpetual motion machine which would always yield work at no expense. But this perpetual motion would not be one that creates work out of nothing, but one that extracts it from energy at rest. A perpetual motion machine of this nature, too, is, according to our experience, impossible, and this impossibility forms the content of the second fundamental principle.
On the face of it this apparently "self-evident" proposition does not reveal how fruitful of results it is when applied to the discovery of simple but not obvious relations. It can only be said here that the deductions from this principle form the chief content of the extensive science of thermodynamics, which deals with the changes of heat into other forms of energy. We must only emphasize the fact that the application of this law, as was already observed in stating it, is not confined to the changes of heat alone. It is a law rather which finds application in all the forms of energy. For in every form of energy there is a property which corresponds to temperature in heat, and upon the equality or the inequality of which depends whether the energy in question is at rest or ready for transformations. This property is called the intensity of the energy. In work, for instance, it is force, in volume-energy it is pressure. If once the intensity in a body is equal, its energy is at rest, and it never again moves of its own accord.
Another form in which to present these relations is to make a distinction between free energy and energy at rest. If we have a heat quantity the temperature of which is higher than that of the surrounding objects, it can be used to do work only until its temperature has dropped to that of the surrounding objects. Although energy in abundance is still present, there is no longer any energy capable of change, or free energy. Since differences of temperature, like other differences of intensity, have a constant tendency to diminish, the amount of free energy on earth is constantly decreasing, and yet it is only this free energy that has value. For since all phenomena depend upon change of energy, and change of energy is possible only through free energy, free energy is the condition of all phenomena.
51. Electricity and Magnetism.
While the knowledge of heat energy goes back to the most ancient periods of civilization, electrical and magnetic energies are relatively young acquisitions. The highly developed technical application of both with the rich harvests they have yielded belongs exclusively to most recent times.
Both these forms of energy, like those discussed above, are connected in the main with ponderable "matter," but in a much slighter and less regular measure. While it is not possible as yet to render any given body free of heat (although lately the absolute zero point has been considerably approximated), freedom from electrical and magnetic energy is the normal condition of most bodies. This is connected with the peculiarity that electrical and magnetic properties are decidedly bi-symmetrical or polar. This property is not found in any other form of energy, and can serve as the special scientific characteristic of electricity and magnetism. This peculiarity shows itself in the concepts of positive and negative magnetism, and positive and negative electricity, and is due to the fact that two equal opposite quantities of electricity or magnetism, when added together, do not produce double their value, but nullify each other.[G]
The fact that electrical and magnetic energies generally exist only in a transitory state (with the notable exception of the magnetic condition of the earth) is probably the cause of our not having developed a sense organ for them, especially since their phenomena as they occur in nature have only occasionally and in very rare instances (thunderstorms) an influence upon us. On the other hand, the modern development of electrotechnics is based upon that property of electrical energy by virtue of which large quantities of it can be conducted along a thin wire over great distances without any considerable loss, and at the point desired can be easily changed into any other forms of energy. But since the collection and conservation of large quantities of electrical energy is hardly possible technically, the electrical apparatus must be so constructed that the quantities each time required should be produced at the moment they are used. The chief source of electricity is the chemical energy of coal, which is first transformed into heat, then into mechanical energy, and finally into electrical energy. This extremely roundabout process is necessary because a method technically practicable of transforming the chemical energy of coal directly into electrical energy has not yet been invented. On the other hand, mechanical energy can be easily and completely changed into electrical energy. Upon this is based the exploitation of much "water power," the energy of which could not be utilized but for the great capacity for change of the electrical form.
52. Light.
The case of light in our day seems to be similar to that of sound, which, although it has its special sense organ in man, is yet no particular form of energy, but has been found to be a combination of mechanical energies in an oscillatory or mutually changing state. It seems highly probable that light, too, is not a special form of energy, but a peculiar oscillatory combination of electrical and magnetic energies. It is true that the circle of proof is not yet quite closed, but the gaps have become so small that the above conclusion may at any rate be accepted as highly probable.