Thennodynamics of Fluids. 321 



Case of a perfect gas. 

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

 constant quantity of it tlie j)roduct of the volume and the pressure 

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



pv ■= at, (a)* 



5 = ct. (b) 



The significance of tlie constant a is sufliciently indicated by equation 

 (a). Tlie significance of c may be rendered more evident by differen- 

 tiating equation (b) and comparing the result 



d€ =z c dt 

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



da — dH-d TF, d W= p dv. 

 If dv = 0, d W= 0, and c?//= c dt, i. e., 



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 consid- 

 ered, a and c both vary as the quantity, and c-f-a is constant; also, 

 that the value of c-^a for difterent 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 j) and t 

 from the general equation (4), viz : 



ds = t dr] — p dv, 

 which is then reduced to 



and by integration to 



ds 1 a dv 



e c c V ' 



logs = ^- ^ log v.l (I,) 



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

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

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

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



\ A subscript letter after a differential co-efScient is used in this article to indicate 

 the quantity which is made constant in the differentiation. 



I If we use the letter e to denote the base of the Naperian system of logarithms 

 equation (d) may also be written in the form 



r/ a 



c c 



e = e V 



This may be regarded as the fundamental thermodynamic equation of an ideal gas. See 



