III. THE PRINCIPLE OF ENERGY IN PHYSICS.
We can know only from experience that mechanical processes produce other physical transformations, or vice versa. The attention was first directed to the connexion of mechanical processes, especially the performance of work, with changes of thermal conditions by the invention of the steam-engine, and by its great technical importance. Technical interests and the need of scientific lucidity meeting in the mind of S. Carnot led to the remarkable development from which thermodynamics flowed. It is simply an accident of history that the development in question was not connected with the practical applications of electricity.
In the determination of the maximum quantity of work that, generally, a heat-machine, or, to take a special case, a steam-engine, can perform with the expenditure of a given amount of heat of combustion, Carnot is guided by mechanical analogies. A body can do work on being heated, by expanding under pressure. But to do this the body must receive heat from a hotter body. Heat, therefore, to do work, must pass from a hotter body to a colder body, just as water must fall from a higher level to a lower level to put a mill-wheel in motion. Differences of temperature, accordingly, represent forces able to do work exactly as do differences of height in heavy bodies. Carnot pictures to himself an ideal process in which no heat flows away unused, that is, without doing work. With a given expenditure of heat, accordingly, this process furnishes the maximum of work. An analogue of the process would be a mill-wheel which scooping its water out of a higher level would slowly carry it to a lower level without the loss of a drop. A peculiar property of the process is, that with the expenditure of the same work the water can be raised again exactly to its original level. This property of reversibility is also shared by the process of Carnot. His process also can be reversed by the expenditure of the same amount of work, and the heat again brought back to its original temperature level.
Suppose, now, we had two different reversible processes A, B, such that in A a quantity of heat, Q, flowing off from the temperature t1 to the lower temperature t2 should perform the work W, but in B under the same circumstances it should perform a greater quantity of work W + W'; then, we could join B in the sense assigned and A in the reverse sense into a single process. Here A would reverse the transformation of heat produced by B and would leave a surplus of work W', produced, so to speak, from nothing. The combination would present a perpetual motion.
With the feeling, now, that it makes little difference whether the mechanical laws are broken directly or indirectly (by processes of heat), and convinced of the existence of a universal law-ruled connexion of nature, Carnot here excludes for the first time from the province of general physics the possibility of a perpetual motion. But it follows, then, that the quantity of work W, produced by the passage of a quantity of heat Q from a temperature t1 to a temperature t2, is independent of the nature of the substances as also of the character of the process, so far as that is unaccompanied by loss, but is wholly dependent upon the temperature t1, t2.
This important principle has been fully confirmed by the special researches of Carnot himself (1824), of Clapeyron (1834), and of Sir William Thomson (1849), now Lord Kelvin. The principle was reached without any assumption whatever concerning the nature of heat, simply by the exclusion of a perpetual motion. Carnot, it is true, was an adherent of the theory of Black, according to which the sum-total of the quantity of heat in the world is constant, but so far as his investigations have been hitherto considered the decision on this point is of no consequence. Carnot's principle led to the most remarkable results. W. Thomson (1848) founded upon it the ingenious idea of an "absolute" scale of temperature. James Thomson (1849) conceived a Carnot process to take place with water freezing under pressure and, therefore, performing work. He discovered, thus, that the freezing point is lowered 0·0075° Celsius by every additional atmosphere of pressure. This is mentioned merely as an example.
About twenty years after the publication of Carnot's book a further advance was made by J. R. Mayer and J. P. Joule. Mayer, while engaged as a physician in the service of the Dutch, observed, during a process of bleeding in Java, an unusual redness of the venous blood. In agreement with Liebig's theory of animal heat he connected this fact with the diminished loss of heat in warmer climates, and with the diminished expenditure of organic combustibles. The total expenditure of heat of a man at rest must be equal to the total heat of combustion. But since all organic actions, even the mechanical actions, must be set down to the credit of the heat of combustion, some connexion must exist between mechanical work and expenditure of heat.
Joule started from quite similar convictions concerning the galvanic battery. A heat of association equivalent to the consumption of the zinc can be made to appear in the galvanic cell. If a current is set up, a part of this heat appears in the conductor of the current. The interposition of an apparatus for the decomposition of water causes a part of this heat to disappear, which on the burning of the explosive gas formed, is reproduced. If the current runs an electromotor, a portion of the heat again disappears, which, on the consumption of the work by friction, again makes its appearance. Accordingly, both the heat produced and the work produced, appeared to Joule also as connected with the consumption of material. The thought was therefore present, both to Mayer and to Joule, of regarding heat and work as equivalent quantities, so connected with each other that what is lost in one form universally appears in another. The result of this was a substantial conception of heat and of work, and ultimately a substantial conception of energy. Here every physical change of condition is regarded as energy, the destruction of which generates work or equivalent heat. An electric charge, for example, is energy.
In 1842 Mayer had calculated from the physical constants then universally accepted that by the disappearance of one kilogramme-calorie 365 kilogramme-metres of work could be performed, and vice versa. Joule, on the other hand, by a long series of delicate and varied experiments beginning in 1843 ultimately determined the mechanical equivalent of the kilogramme-calorie, more exactly, as 425 kilogramme-metres.
If we estimate every change of physical condition by the mechanical work which can be performed upon the disappearance of that condition, and call this measure energy, then we can measure all physical changes of condition, no matter how different they may be, with the same common measure, and say: the sum-total of all energy remains constant. This is the form that the principle of excluded perpetual motion received at the hands of Mayer, Joule, Helmholtz, and W. Thomson in its extension to the whole domain of physics.