THERMODYNAMICS OF FLUIDS. 3 



On the other hand W and H are not functions of the state of the 

 body (or functions of any of the quantities v, p, t, e and rj), but are 

 determined by the whole series of states through which the body is 

 supposed to pass. 



Fundamental Idea and General Properties of the Diagram. 



Now if we associate a particular point in a plane with every separate 

 state, of which the body is capable, in any continuous manner, so that 

 states differing infinitely little are associated with points which are 

 infinitely near to each other,* the points associated with states of 

 equal volume will form lines, which may be called lines of equal 

 volume, the different lines being distinguished by the numerical value 

 of the volume (as lines of volume 10, 20, 30, etc.). In the same way 

 we may conceive of lines of equal pressure, of equal temperature, of 

 equal energy, and of equal entropy. These lines we may also call 

 isometric, isopiestic, isothermal, isodynamic, isentropicj and if neces- 

 sary use these words as substantives. 



Suppose the body to change its state, the points associated with the 

 states through which the body passes will form a line, which we may 

 call the path of the body. The conception of a path must include 

 the idea of direction, to express the order in which the body passes 

 through the series of states. With every such change of state there 

 is connected in general a certain amount of work done, W, and of heat 

 received, H, which we may call the work and the heat of the path. I 

 The value of these quantities may be calculated from equations (2) 



and (3), 



dW=pdv, 



W=fpdv, (5) 



; (6) 



* The method usually employed in treatises on thermodynamics, in which the rect- 

 angular co-ordinates of the point are made proportional to the volume and pressure of 

 the body, is a single example of such an association. 



t These lines are usually known by the name given them by Rankine, adiabatic. If, 

 however, we follow the suggestion of Clausius and call that quantity entropy, which 

 Rankine called the thermodynamic function, it seems natural to go one step farther, and 

 call the lines in which this quantity has a constant value isentropic. 



+ For the sake of brevity, it will be convenient to use language which attributes to 

 the diagram properties which belong to the associated states of the body. Thus it can 

 give rise to no ambiguity, if we speak of the volume or the temperature of a point in the 

 diagram, or of the work or heat of a line, instead of the volume or temperature of the 

 body in the state associated with the point, or the work done or the heat received by 

 the body in passing through the states associated with the points of the line. In like 

 manner also we may speak of the body moving along a line in the diagram, instead of 

 passing through the series of states represented by the line. 



