Thermodynamics of Fluids. 329 



area of the circuit in tlie ciitro})y-temperatiire diagram, i. e., to find 

 the work or heat required. We may find the work of any patli by 

 applying tlie same process to the circuit formed by the path, tlie iso- 

 metric of the final state, the line of no pressure (or any isopiestic ; see 

 note on page 3 1 8), and the isometric of the initial state. And we may 

 find the heat of any path by applying the same process to a circuit 

 formed by the path, the ordinates of the extreme points and the line 

 of absolute cold. That this line is at an infinite distance occasions no 

 difficulty. The lengths of the ordinates in the entroi^y-temperature 

 diagram which we desire are given by the temperature of points in 

 the path determined (in either diagram) by equidistant ordinates. 



The properties of the part of the entropy-temperature diagram rep- 

 resenting a mixture of vapor and liquid, which are given on page 323, 

 will evidently not be altered if the ordinates are made proportional to 

 the logarithms of the temperatures instead of the temperatures simply. 



The representation of specific heat in the diagram under discussion 

 is peculiarly simi^le. The specific heat of any substance at constant 

 volume or under constant jaressure may be defined as the value of 

 (dHx ldH\ . ! dn \ / dn \ 



Ut) ^^t/f '^-^"Ui^gi ""'[dio^h 



V ' p ^ ' V '^ p 



for a certain quantity of the substance. Therefoi'e, if we draw a dia- 

 gram, in which x-=.i} and y =: log t, for that quantity of the substance 

 which is used for the determination of the specific heat, the tangents 

 of the angles made by the isometrics and the isopiestics with the 

 ordinates in the diagram Avill be equal to the specific heat of the 

 substance determined for constant volume and for constant pressure 

 respectively. Sometimes, instead of the condition of constant volume 

 or constant pressure, some other condition is used in the determination 

 of specific heat. In all cases, the condition will be represented by a 

 line in the diagram, and the tangent of the angle made by this line 

 with an ordinate will be equal to the specific heat as thus defined. If 

 the diagram be drawn for any other quantity of the substance, the 

 specific heat for constant volume or constant pressure, or for any other 

 condition, will be equal to the tangent of the proper angle in the 

 diagram, multiplied by the ratio of the quantity of the substance for 

 which the specific heat is determined to the quantity for which the 

 diagram is drawn.* 



* From this general property of the diagram, its character in the case of a perfect 

 gas might be immediately deduced. 



