16 



GRAPHICAL METHODS IN THE 



distinctly visible. The line of liquidity is a curve AB (fig. 5) deter- 

 mined by the relation between t and ^. This curve is also an iso- 

 metric. Every point of it has a definite 

 volume, temperature, entropy and 

 energy. The latter is indicated by the 

 isodynamics E 1 E 1 , E 2 E 2 , etc., which 

 cross the region of partial vaporization 

 and terminate in the line of liquidity. 

 (They do not in this diagram turn and 

 follow the line.) If the body pass 

 from one state to another, remaining 

 liquid, as from M to N in the figure, 

 the heat received is represented as 



_^ usual by the area MNnm. That the 



r> work done is nothing, is indicated 

 by the fact that the line AB is an 

 isometric. Only the isopiestics in this diagram are superposed in 

 the line of fluidity, turning downward where they meet this line and 

 following its course, so that for any point in this line the pressure is 

 undetermined. This is, however, no inconvenience in the diagram, as 

 it simply expresses the fact of the case, that when all the quantities 

 v, t, e and ij are fixed, the pressure is still undetermined. 







m n 

 Fig. 5. 



Diagrams in which the Isometrics, Isopiestics, Isothermals, Iso- 

 dynamics and Isentropics of a Perfect Gas are all Straight 

 Lines. 



There are many cases in which it is of more importance that it 

 should be easy to draw the lines of equal volume, pressure, tempera- 

 ture, energy and entropy, than that work and heat should be repre- 

 sented in the simplest manner. In such cases it may be expedient to 

 give up the condition that the scale (y) of work and heat shall be 

 constant, when by that means it is possible to gain greater simplicity 

 in the form of the lines just mentioned. 



In the case of a perfect gas, the three relations between the quanti- 

 ties v, p, t, e and rj are given on pages 12, 13, equations (A), (B) and (D). 

 These equations may be easily transformed into the three 



v log t = log a, (H) 



log t = log C, (l) 



j] c log e a log v = ; (j) 



so that the three relations between the quantities logv, logp, logt, 

 log e and r\ are expressed by linear equations, and it will be possible 

 to make the five systems of lines all rectilinear in the same diagram, 



