Thermodynamic St of Fluids. 311 



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

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

 determined by tlie 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 separ- 

 ate state, of wliich the Ijody is capable, in any continuous manner, so 

 that states dilFering infinitely little are associated with points wliicli 

 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 

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

 isometric, isopiestic, isothermal, isodynamic, ise)itro2)ic,\ 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, wliich 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, Avhich we may call the tcork and the heat of the p)ath.\ 



processes are concerned,) viz : the fundamental equation witli equation (4) gives the 

 three relations existing between v, p, t. e and ff, and these relations being known, 

 equations (2) and (3) give the work W and heat R for any change of state of the 

 fluid. 



* The metliod usually employed in treatises on tliermodynamics, in which tlie 

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

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



f These lines are usually known by the name given them by Raukine, adiahatic. 

 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. 



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

 tlie diagram properties whicli belong to the associated states of the bod}'. Tluis it 

 can give rise to no amljiguity, 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 re- 

 ceived by the body in passing tlirough the states associated with the points of tlie 

 line. In like manner also we may speak of the body moving along a line in the dia- 

 gram, instead of passing througli the series of states represented by the line. 



