§ 8 Carnot’s Principle. Its Generality
The second fundamental principle is that of the transformations of equilibrium, or of the conditions of reversibility, or again, Carnot’s principle. This principle, which first assumed a concrete form in thermodynamics, has been very widely extended. It has reached a degree of generality such that contemporary theoretical physicists such as Lord Kelvin, Le Châtelier, etc., consider it the universal law of physical, mechanical, and chemical equilibrium.
Carnot’s principle contains, as was shown by G. Robin, d’Alembert’s principle of virtual velocities, and according to physicists of to-day, as we have just remarked, it contains the laws peculiar to physico-chemical equilibrium. The application of this principle gives us the differential equations from which are derived numerical relations between the different energies, or the different modalities of universal energy.
Its Character.—It is very remarkable that we cannot give a general enunciation of this principle which by its revealing power has changed the face of physics. This is because it is less a law, properly so called, than a method or manner of interpreting the relations of the different forms of energy, and particularly the relations of heat and mechanical energy.
Conversion of Work into Heat and Vice-versâ.—The conversion of work into heat is accomplished without difficulty. For example, the hammering of a piece of iron on an anvil may bring it to a red heat. A shell which passes through an armour plate is heated, and melts and volatilizes the metal all round the hole it has made. By utilizing mechanical action under the form of friction all energy can be converted into heat.
The inverse transformation of heat into work, on the contrary, cannot be complete. The best motor that we can think of, and à fortiori the best we can realize, can only transform a third or a fourth of the heat with which it is supplied.
This is an extremely important fact. It is of incalculable importance to natural philosophy, and may be ranked among the greatest discoveries.
Higher and Degraded Forms of Energy.—Of these we may give an account by distinguishing among the forms of universal energy higher forms, and lower or degraded forms. Here we have the principle of the degradation of energy on its trial, and it may be regarded as a particular aspect of the second principle of energetics, or Carnot’s principle. Mechanical energy is a higher form. Thermal energy is a lower form, a degraded form, and one which has degrees in its degradation. Higher energy, in general, may be completely converted into lower energy; for example, work into heat: the slope is easy to descend, but it is difficult to retrace our steps; lower energy can be only partially transformed into higher energy, and the fraction thus utilizable depends upon certain conditions on which Carnot’s principle has thrown considerable light.
Thus, although in theory the thermal energy of a body may have its equivalent in mechanical energy, the complete transformation is only realizable from the latter to the former, and not from the former to the latter. This is due to a condition of thermal energy which is called temperature. The same quantity of thermal energy, of heat, may be stored in the same thermal body at different temperatures. If this quantity of thermal energy is in a very hot body we can utilize a large portion of it; if it is in a relatively cold body we can only convert a small portion of it into mechanical work. Thus the value of energy,—i.e., its capacity of being converted into a higher and more useful form,—depends on temperature.
The Capacity of Conversion depends on Temperature.—The conversion of heat into work assumes two bodies of different temperatures, the one warm and the other cold; a boiler and a condenser. Every thermal machine conveys a certain amount of heat from the boiler to the condenser, and what is not thus carried is changed into work. This residue is only a small fraction, a quarter, or at most a third of the heat employed, and that, too, in the theoretically perfect machine, in the ideal machine.
This output, this utilizable fraction depends on the fall of temperature from the higher to the lower level, just as the work of a turbine depends on the height of the waterfall which passes through it. But it also depends on the conditions of this fall, on the accessory losses from radiation and conduction. However, Carnot has shown that the output is the same, and a maximum for the same fall of temperature, whatever be the working agent (steam, hot air, etc.), and whatever be the machine—provided that this agent, this substance which works is not exposed to accessory losses, that it is never in contact with a body having temperature different to its own—or again, that it is connected only with bodies impermeable to heat.
This is Carnot’s principle in one of its concrete forms.
A machine which realizes this condition, that the agent (steam, alcohol, ether) is in relation, at all phases of its function, with bodies which can neither take heat from it nor give heat to it, is a reversible machine. Such a machine is perfect. The fraction of heat that it transforms into motion is constant; it is a maximum; it is independent of the motor, of its organs, of the agent: it accurately expresses the transformability of the heat agent into a mechanical agent under the given conditions.
The Degradation and Restoration of Energy.—The fraction not utilized, that which is carried to the condenser at a lower temperature, is degraded. It can only be used by a new agent, in a new machine in which the boiler has exactly the same temperature as the condenser in the first machine, and the new condenser has a lower temperature, and so on. The proportion of utilizable energy thus goes on diminishing. Its utilization requires conditions more and more difficult to realize. The thermal energy loses its potential and its value, and is further and further degraded as its temperature approaches that of the surrounding medium.
The degraded energy, theoretically, has kept its equivalent value but, practically, it is incapable of conversion. However, it is shown in physics that it can be raised and re-established at its initial level. But for that purpose another energy must be utilized and degraded for its benefit.
The End of the Universe.—What we have just seen with respect to heat and motion is to some degree true of all other forms of energy, as Lord Kelvin has shown. The principle of the degradation of energy is very general. Every manifestation of nature is an energetic transformation. In each of these transformations there is a degradation of energy—i.e., a certain fraction is lowered and becomes less easily transformable. So that the energy of the universe is more and more degraded; the higher forms are lowered to the thermal form, the latter increasing at temperatures which become more and more uniform. The end of the universe, from this point of view, would then be unity of (thermal) energy in uniformity of temperature.
Importance of the Idea of Energy in Physiology.—I have said that the application of Carnot’s principle furnished numerical relations between the different energetic transformations.
The science of living beings has not yet reached that point of development at which it is possible for us to obtain its numerical relations. However, the consideration of energy and the principle of conservation has altered the outlook of physiology on many questions which are of the highest importance.
The determination of the sources from which plants and animals draw their vital energies; the mediate transformation of chemical energy into animal heat in nutrition, or into motion in muscular contraction; the chemical evolution of foods; the study of soluble ferments—all these questions are of considerable importance when we wish to understand the mechanisms of life. They are therefore departments of physiological energetics in which great advances have already been made.