282 Free Path Phenomena [OH. xv 



Adiabatic Motion. 



337. The equation of continuity (equation (649)) can be expressed in the 

 form 



Dv 



rw + Mir + ir + ir =. 



Dt \dx dy dz J 



and with the help of this, equation (660) becomes 



/ 



q ~Dt = 3 v Dt ' 



or (ov~$} = 



Dt^ ' 



Thus as we follow an element of the gas in its motion qy~% remains 

 constant. Since 



g=U-2 = .i(7 2 =^ (662), 



this equation simply expresses that pp-% remains constant, as an element 

 is followed in its motion. This is the particular case of the adiabatic law 

 obtained in 201, in which 7 = f . This result we can understand. We have 

 neglected the conduction of heat in making the suppositions of equation 

 (662), and we have supposed the whole energy to be translational on putting 

 A (u* + v 2 + w 2 )=0 in equation (659). We therefore get 7 = f, as in 203. 



III. Q = uv. 



338. We next put Q = uv in equation (656). We have 



Q = (MO + u) (t> + V) = U v , 

 uQ = Vo<?, vQ = w ?, wQ = 0, 

 dg_ dQ_ dQ 



J - "fl ) ~7 - **0 ) ~7 - ^> 



du dv dw 



so that equation (656) becomes 



~i ^ ^ 



+ v ("& + u 



dy 

 giving, upon simplification, 



A(W) = ..................... < 663) - 



