THERMODYNAMICS OF FLUIDS. 



11 



B 



The included area ABCD represents the work done, and the areas 



ABba and CDdc represent respectively the heat received from the 



heater and that transmitted to the 



cooler. The heat imparted by the fluid 



to the regenerator in passing from B 



to C, and afterward restored to the 



fluid in its passage from D to A, is 



represented by the areas BCcb and 



DAad. 



It is often a matter of the first 

 importance in the study of any thermo- 

 dynamic engine, to compare it with a 



o 



Fig. 4. 



perfect engine. Such a comparison will obviously be much facilitated 

 by the use of a method in which the perfect engine is represented 

 by such simple forms. 



The method in which the co-ordinates represent volume and pressure 

 has a certain advantage in the simple and elementary character of the 

 notions upon which it is based, and its analogy with Watt's indicator 

 has doubtless contributed to render it popular. On the other hand, 

 a method involving the notion of entropy, the very existence of which 

 depends upon the second law of thermodynamics, will doubtless seem 

 to many far-fetched, and may repel beginners as obscure and difficult 

 of comprehension. This inconvenience is perhaps more than counter- 

 balanced by the advantages of a method which makes the second law 

 of thermodynamics so prominent, and gives it so clear and elementary 

 an expression. The fact, that the different states of a fluid can be 

 represented by the positions of a point in a plane, so that the ordi- 

 iiates shall represent the temperatures, and the heat received or given 

 out by the fluid shall be represented by the area bounded by the line 

 representing the states through which the body passes, the ordinates 

 drawn through the extreme points of this line, and the axis of 

 abscissas, this fact, clumsy as its expression in words may be, is one 

 which presents a clear image to the eye, and which the mind can 

 readily grasp and retain. It is, however, nothing more nor less than 

 a geometrical expression of the second law of thermodynamics in its 

 application to fluids, in a form exceedingly convenient for use, and 

 from which the analytical expression of the same law can, if desired, 

 be at once obtained. If, then, it is more important for purposes of 

 instruction and the like to familiarize the learner with the second 

 law, than to defer its statement as long as possible, the use of the 

 entropy-temperature diagram may serve a useful purpose in the 

 popularizing of this science. 



The foregoing considerations are in the main of a general character, 

 and independent of the nature of the substance to which the graphical 



