Page:Scientific Papers of Josiah Willard Gibbs.djvu/88

52 few words on the terminology of this subject. If Professor Clausius had defined entropy so that its value should be determined by the equation instead of his equation (Mechanische Wärmetheorie, Abhand. ix. § 14; Pogg. Ann. July, 1865)  where $$S$$ denotes the entropy and $$T$$ the temperature of a body and $$dQ$$ the element of heat imparted to it, that which is here called capacity for entropy would naturally be called available entropy, a term the more convenient on account of its analogy with the term available energy. Such a difference in the definition of entropy would involve no constructions, if only we suppose the direction in which entropy is measured to be reversed. It would only make it necessary to substitute $$- \eta$$ for $$\eta$$ in our equations, and to make the corresponding change in the verbal enunciation of propositions. Professor Tait has proposed to use the word entropy "in the opposite sense to that in which Clausius has employed it" (Thermodynamics, § 48. See also § 178), which appears to mean that he would determine its value by the first of the above equations. He nevertheless appears subsequently to use the word to denote available energy (§ 182, 2d theorem). Professor Maxwell uses the word entropy as synonymous with available energy, with the erroneous statement that Clausius uses the word to denote the part of the energy which is not available (Theory of Heat, pp. 186 and 188). The term entropy, however, as used by Clausius does not denote a quantity of the same kind (i.e., one which can be measured by the same unit) as energy, as is evident from his equation, cited above, in which $$Q$$ (heat) denotes a quantity measured by the unit of energy, and as the unit in which $$T$$ (temperature) is measured is arbitrary, $$S$$ and $$Q$$ are evidently measured by different units. It may be added that entropy as defined by Clausius is synonymous with the thermodynamic function as defined by Rankine.

Thirdly. A certain initial condition of the body is given as before. No work is allowed to be done upon or by external bodies, nor any heat to pass to or from them; from which conditions bodies may be excepted, as before, in which no permanent changes are produced. It is required to find the amount by which the volume of the body can be diminished, using for that purpose, according to the conditions, only the force derived from the body itself. The conditions require that the energy of the body shall not be altered nor its entropy diminished. Hence the quantity sought is represented by the distance of the point representing the initial state from the surface of dissipated energy, measured parallel to the axis of volume.

Fourthly. An initial condition of the body is given as before. Its volume is not allowed to be increased. No work is allowed to be done upon or by external bodies, nor any heat to pass to or from them, except a certain body of given constant temperature $$t'$$. From the latter conditions may be excepted as before bodies in which no permanent changes are produced. It is required to find the greatest amount of heat which can be imparted to the body of constant temperature, and also the greatest amount of heat which can be taken from it, under the supposed conditions. If through the point of the