of the Thermodynamic Properties of Substances. 403 



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 sur- 

 face 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 extei'nal bodies, nor any heat to pass to or from 

 them, except a certain body of given constant tem]i)erature 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 tem- 

 perature, and also the greatest amount of heat which can be taken 

 from it, under the su|)posed conditions. It through the point of the 

 initial state a straiglit line be drawn in the plane perpendicular to 

 the axis of v, so that the tangent of the angle which it makes with 

 the direction of the axis of // shall be equal to the given tempera- 

 ture t' , it may easily be shown that the vertical projections of the 

 two segments of this line made by the point of the initial state and 

 the surface of dissipated energy represent the two quantities required.* 



These problems may be modified so as to make them approach 

 more nearly the economical problems which actually present them- 

 selves, if we suppose the body to be surrounded by a medium of con- 

 stant pressure and temperature, and let the body and the medium 

 together take the place of tlie body in the preceding problems. The 

 results would be as follows : 



If we suppose a plane representing the constant pressure and tem- 

 perature of the medium to be tangent to the surface of dissipated 

 energy of the body, the distance of the j^oint representing the initial 

 state of the body from this plane measured parallel to the axis of e 

 will represent the available energy of the body and medium, the dis- 

 tance of the point to the plane measured parallel to the axis of // will 

 represent the capacity for entropy of the body and medium, the dis- 

 tance of the point to the plane measured parallel to the axis of v will 

 represent the magnitude of the greatest vacuum which can be pro- 

 duced in the body or medium (all the power used being derived from 



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. 



* Thus, in figure 3, if the straight line MAN be drawn so that tan NAC = t', MR 

 will be the greatest amount of heat which can be given to tlie body of constant tem- 

 perature and NS will be the greatest amount which can be taken from it. 



Trans. Connecticdt Academy, Vol. II. 3J Dec, 1873. 



