and Pyroelectric Properties of Matter. 11 



take one of the six variables x, y, z, £, rj, f as the volume v, 

 which it is made to occupy in any particular condition, and the 

 remaining five will not affect its physical properties, and will 

 therefore disappear from all the preceding equations ; and the 

 state of the fluid will be completely defined by the values of 

 the two independent variables v, t. Then, if p denote the pres- 



sure, we must have 



dw 



since — pdv is the work done upon a fluid in compressing it 

 under pressure p from a volume v to a volume v + dv. But 

 from (9) we have 



de _dw d dw 



dv dv dt dv 



and, therefore, 

 and 



Hence (13) becomes 



*2M c*> 



(dv\ 

 — J expresses the assumed relation between the natu- 

 rally independent variables v, t. If this be such that the pres- 

 sure is constant, we have 



dp 



' dv - d* 

 dt ~ _dp ; 



dv 



and, K being now the specific heat under constant pressure, we 

 have finally 



dv 



10. These equations (14) and (15), together with the unmo- 

 dified equation (12), which retains the same form in all cases, 

 express the general thermodynamic relations between the 

 intrinsic energy, the pressure, and the specific heats of a fluid. 

 If we eliminate e, we have 



