12 



method is applied. On this, however, depend the forms of the 

 isometrics, isopiestics and isodynamics in the entropy-temperature 

 diagram, and of the isentropics, isothermals and isodynamics in the 

 volume-pressure diagram. As the convenience of a method depends 

 largely upon the ease with which these lines can be drawn, and upon 

 the peculiarities of the fluid which has its properties represented in 

 the diagram, it is desirable to compare the methods under considera- 

 tion in some of their most important applications. We will commence 

 with the case of a perfect gas. 



Case of a perfect gas. 



A perfect or ideal gas may be defined as such a gas, that for any 

 constant quantity of it the product of the volume and the pressure 

 varies as the temperature, and the energy varies as the temperature, i.e.,, 



* 



pv = at t (A) 



e = ct. (B) 



C "*" 



The significance of the constant a is sufficiently indicated by equation 

 (A). The significance of c may be rendered more evident by differen- 

 tiating equation (B) and comparing the result 



de cdt 

 with the general equations (1) and (2), viz : 



If dv = 0, dW=0, and dH=cdt, i.e., 



(dH\ 

 \dt)-'~* 



i.e., c is the quantity of heat necessary to raise the temperature of 

 the body one degree under the condition of constant volume. It will 

 be observed, that when different quantities of the same gas are con- 

 sidered, a and c both vary as the quantity, and c-i-a is constant; also, 

 that the value of c+a for different gases varies as their specific heat 

 determined for equal volumes and for constant volume. 



With the aid of equations (A) and (B) we may eliminate p and t 

 from the general equation (4), viz : 



*In this article, all equations which are designated by arabic numerals subsist for 

 any body whatever (subject to the condition of uniform pressure and temperature), and 

 those which are designated by small capitals subsist for any quantity of a perfect gas 

 as defined above (subject of course to the same conditions). 



t A subscript letter after a differential co-efficient is used in this article to indicate- 

 the quantity which is made constant in the differentiation. 



