Thermodj/iKimics of Flidds. 339 



ARRANGEMENT OF THE ISOMETRIC, ISOPIESTIC, ISOTHERJIAL AND ISENTROPIC 

 ABOUT A POINT. 



The arvangement of tlie isometric, the isopiestic, the isothermal and 

 the isentropic drawn through any same point, in respect to the order 

 in which they succeed one another around that point, and in respect 

 to the sides of these lines toward which the volume, pressui'e, tem- 

 perature and entropy increase, is not altered by any deformation of 

 the surface on which the diagram is drawn, and is therefore indepen- 

 dent of the method by which the diagram is formed.* This arrange- 

 ment is determined by certain of the most characteristic thermody- 

 namic properties of the body in the state in question, and serves in 

 turn to indicate these jiroperties. It is determined, namely, hy the 



value of (y-j as positive, negative, or zero, i. e,, by the eifect of heat 



as increasing or diminishing the pressure when the volume is main- 

 tained constant, and by the nature of the • internal thermodynamic 

 equilibrium of the body as stable or neutral, — an unstable equilib- 

 rium, except as a matter of speculation, is of course out of the 

 question. 



Let us first examine the case in which \i—] is positive and the 



equilibrium is stable. As (y-) does not vanish at the point in ques- 

 tion, there is a definite isopiestic passing through that point, on one 

 side of which the pressures are greater, and on the other less, than on 



the line itself As |y-| — — ly-1 , the case is the same with the 



isothermal. It will be (convenient to distinguish the sides of the iso- 

 metric, isopiestic, etc., on which the volume, pressure, etc., increase, 

 as the positive sides of these lines. The condition of stability requires 

 that, when the pressui-e is constant, the temperature shall increase 

 with the heat received, — therefore with the entropy. This may 

 be written [f7i( : cZ^] ^ O.f It also requires that, when there is no 



* It is here assumed that, in the vicinity of the point in question, each point in the 

 diagram represents only one state of the body. The propositions developed in the fol- 

 lowing pages cannot l)e applied to points of the line where two superposed diagrams 

 are united (see pages 335-338) without certain modifications. 



dt 

 \ As the notation -j- is used to denote the limit of the ratio of dt to drj^ it would not 



ldt\ 

 be quite accurate to say that the condition of stability requires that \T"/ > 0. This 



Trans. Connecticut Acad., Vol. II. 27 May, 18V3. 



