Natural Philosophy

by Wilhelm Ostwald

50. The Second Fundamental Principle.

Another fundamental discovery has been made in connection with the heat form of energy, which, like the law of conservation, relates to all forms of energy, but has found its first and most important application in heat. While the law of conservation answers the question, how much of the new form of energy is developed if a given quantity of energy changes, but gives no clue as to when such a change occurs, this second law asserts the condition under which such changes arise, and is therefore called the second fundamental principle.

The discovery of this law antedates Mayer's discovery of the law of conservation by about twenty years, and was made by a French military engineer, Sadi Carnot, who died soon afterward without having lived to see the recognition his great work obtained. Carnot asked himself the question, Upon what does the action of the steam engine, which had just then come into use, depend? This led him first to the more general question of the action of heat engines in general. He found that no heat engine could work unless the heat dropped from a higher to a lower temperature, just as no water wheel can work unless the water flows from a higher to a lower level, and he determined the conditions which an ideal heat engine must fulfil, that is, a machine in which the greatest possible value in work is obtained from heat. However, an ideal machine of this nature can be constructed in very different ways, and Carnot's discovery consists in the recognition of the fact that the quantity of work obtained from the heat unit does not at all depend upon the peculiar construction of the ideal machine, but is determined solely by the temperature between which the heat transition takes place. This follows from the following considerations:

In the first place an ideal engine must be reversible, that is, it must be capable of working both ways, changing heat into work and work back into heat. Now, if we have two ideal engines between the same temperatures, and if we assume that engine A produces more work from the same quantity of heat than engine B, then let A move one way and let B move the other way with the work obtained from A. Since B produces less work from a given amount of heat, hence more heat from an equal amount of work, there will in the end be more heat at the higher temperature than was originally there. But experience teaches that there is no means in nature by which heat in the absence of concomitant change could be caused to rise to a higher temperature. Therefore an engine so constructed as to produce this result is impossible, And B cannot be of such a nature as to produce less work from the same quantity of heat than A.

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.