X, \P, f, AND THE CRITERIA OF EQUILIBRIUM 225 

 or 



A(x + k') = AQ - AW i- A{pv). 



In the case of the steady rectilinear (irreversible) flow of a 

 fluid under its own pressure gradient, we can show that 



AW = Aipv). 



Hence for adiabatic flow of this character, where AQ = 0, we 

 must have 



A(x + k') = 

 or 



X + iQ^ = constant. 



(The relation AW = Aijpv) is easily proved by considering the 

 work done on the moving element of fluid by the adjacent 

 elements at the two opposite ends.) 



If the fluid happens to be a perfect gas, we can obtain a simple 

 expression for %• For, for any fluid whatever, 



L^p dp\t 



V - t 



smce 



d^ = d(e -\- pv — it]) = vdp — rjdt. 



Now, for a perfect gas, ^ = H "^ ) since pv cc t. Hence f — j =0 

 and 



dx - 

 = Cpdi, 



0/"+©/' 



