It is especially important to be able to com pare the "natural" unit of heat accurately with the erg or the foot-poundal, and many elabo rate experimental researches have been con ducted for the purpose of improving our knowl edge of this relation. For lull particulars with regard to this topic the reader should refer to HEAT and THERMODYNAMICS; but it may be said, in this place, that Rowland found that one British thermal unit of heat is the equivalent of about 778 foot-pounds of mechanical work — the "pound" here being understood to signify the attraction of the earth for one pound of matter, at sea-level in the latitude of Baltimore.
Efficiency of It is not always possible to convert a given quantity of energy of one type wholly into energy of some other given type, or wholly into mechanical work. Heat, for example, cannot be wholly converted into me chanical energy— though the reverse process, of converting mechanical energy wholly into heat, is easily performed. This fact has led to the use of the expression ((available energy" to signify that part of the total energy of a body or system, which can be converted into mechanical energy. The distinction between available and unavail able energy is arbitrary, however, because the fraction of the total energy that is available de pends upon the completeness of our control over the conditions under which the transformation is attempted. Heat energy, for example, could be wholly converted into mechanical energy (so far as any theoretical limitation is concerned), if we could effect the transformation by means of a heat-engine having a condenser at the absolute zero of temperature, and in that case all the heat-energy would be "available." Similar limi tations and conditions apply to energy of other types. The fact that heat-energy is not fully convertible into mechanical energy under con ditions that we can realize, or which exist in nature, while the reverse transformation takes place quite readily and completely, leads to the recognition of the fact that in the processes of nature there must be, on the whole, a tendency toward the "degradation of energy," in the sense that there is a continuous diminution, in the uni verse, of the store of available energy. The supply of available energy, in other words, is tending continually to become dissipated, in the form of diffused, low-temperature heat.
For purposes of mathematical analysis, it is convenient to designate the condition of a body or system by representing, by means of algebraic symbols, its configuration, size, temperature, electric potential, and any other measurable at tributes that it may have — the particular at tributes or features that are selected being to a considerable extent arbitrary, though to serve the purpose of defining the condition of the body or system at every moment, they must be numer ous enough, and must be selected in such a way, so that no change, essential to the problem under consideration, can take place in the body without at least one of these symbols (or defining vari ables) changing its value. It may be that some
of the selected variables will be functionally de pendent upon the others; but there will always be a certain number (small in the cases usually considered) that will be independent, so that any one of them can vary without any of the others necessarily undergoing a simultaneous variation. Then if E represents the aggregate energy (in cluding all types) possessed by the body at a given moment, and if the body then undergoes an infinitesimal change of condition so that E increased by the theory of energetics teaches that a relation of the following form exists ; aE=X•ax+ Y-ay +Z.as+ . . .
where X, Y, Z, x, y, s, . . . are functions of the independent defining variables — some of them being perhus identical with certain of those variables. The symbols on the right-hand side may be so selected that each of the several expressions that are added together will repre sent the total quantity of energy of some one type that the body must take in, in order to un dergo the physical change corresponding to an increase of x, y, z, . . . by the respective amounts Aix ay, as, . . . The variables, more over, may be so chosen that X, Y, Z, will be analogous to intensities, in the sense that they do not depend in any way upon the mass or volume of the body, but only upon its physical state; and for this reason they are called the "intensity-factors." At the same time the in finitesimals ax, ay,az, . . . (since the dimen sions of every one of the added terms must be the same as the dimensions of energy) will be proportional to the volume of the body, or to its mass, or to some other quality or attribute that would necessarily vary if the size of the body should vary, without any change in X, Y, Z, . . The terms Ax, 4y, Az, are there fore called the of the terms on the right of the equation. Furthermore, the intensity-factor X will be of such a nature that its value within the body, as compared with its value in the environment immediately external to the body, determines whether the energy rep resented by X.Ax will enter the body or leave it.