XI. Gkaphical Methods in the Thermodyxamics of Fluids. 



By J. WiLLAKD GiBBS. 



Although geometrical rejaresentations of propositions in the ther- 

 modynamics of fluids are in general use, and have done good service 

 in disseminating clear notions in this science, yet they have by no 

 means received the extension in respect to variety and generality of 

 which they are capal)le. So far as regards a general graphical 

 method, which can exhibit at once all the thermodynamic properties 

 of a fluid concerned in i-eversible processes, and serve alike for the 

 demonstration of general theorems and the numerical solution of par- 

 ticular problems, it is the general if not the universal practice to use 

 diagrams in which the rectilinear co-ordinates represent volume and 

 pressure. The object of this article is to call attention to certain dia- 

 grams of diflerent construction, which aftbrd grapliical metliods co- 

 extensive in their applications with that in ordinary use, and prefer- 

 able to it in many cases in respect of distinctness or of convenience. 



QUANTITIES AND RELATIONS WHICH ARE TO BE REPRESENTED BY THE DIAGRAM. 



We have to consider the following quantities : — 

 y, the volume, ^ 



p, the pressure, j „ . , . . 



, , , , \ 01 a given bodv m aiiv 



t, the (absohite) temperature, r , ? 



6, the energy, I 



?/, the entropy, J 



also IT'^ the work done, \ by the body in passing from one 



and //, the heat received,* ) state to another. 



These are subject to the relations expressed by the following differ- 

 ential ecpiations : — 



* Work spent upon the body is as usual to be considered as a negative quantity of 

 work done by the body, and heat given out by the body as a negative quantity of heat 

 received by it. 



It is taken for granted that the body has a uniform temperature throughout, and that 

 the pressure (or expansive force) has a uniform value both for all points in the body 

 and for all directions. This, it will be observed, will exclude irreversible processes, 

 but will not entireh' exclude solids, although the condition of equal pressure in all 

 directions renders the case very limited, in which they come within the scope of the 

 discussion. 



