52 REPRESENTATION BY SURFACES OF THE 



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 dissi- 

 pated 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 if. 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 



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 Warmetheorie, 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 

 difference in the form of the thermodynamic surface, nor in any of our geometrical 

 constructions, if only we suppose the direction in which entropy is measured to be 

 reversed. It would only make it necessary to substitute -77 for 77 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. 



