The7'niO(lynamics of Fluids. 



325 



Fig. 



metric. Every point of it lias a definite volume, temperature, entropy 

 and energy. The latter is indicated by the isodynamics EjE^, E.;,E2, 

 etc., which cross the region of par- 

 tial 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 IVI to N in the figure, the 

 heat received is represented as usual 

 by the area MNnm. That the 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 y, t, e and if are fixed, 

 the pressure is still undetermined. 



DIAGRAMS IN WHICH THE ISOMETRICS, ISOPIESTICS, ISOTHERMALS, ISODYNAMICS 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 l)e repre- 

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

 give up the condition that the scale (;/) 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 ;/ are given on page 321, equations (a), (i?) and (d). 

 These equations may be easily l)e transformed into the three 



log 2) -j- log V — log t = log a, (ri) 



log e — log t =. log c, (t) 



7f — c log e — a log V = 0; (.i) 



so that the three relations between the quantities log v, log/>, log t, 

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

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

 the distances of the isometrics being proportional to the diflferenccs 



