576 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



and the compression of the other takes place adiabatically then the 

 new volumes k\ and k' 2 will be 



From the condition that k\ + k' 2 = k we find 



(k. l /r k 2 Vr\r 



The center of gravity of the whole mass remains at the same altitude 

 wherefore dP = o. 



The available kinetic energy is therefore 



- *T = (T a ) - (f e ) - C,j (T - T>) fidk - ^ J (p - p') dk 



1 



= r ~ : [( fe iA +k 2 p 2 -kp') 



If the difference p l — p 2 is small as compared with the pressure in 

 one of the chambers so that p l — p 2 = ep t then 



p 2 = p x (1 - e) 



P >= Pl (i-h s - k jti.r^l.t 



. \ k k 2 r 2 



- 1 &, k, e 2 



-31--. ^-'.-^i.-g ■ =i'«W 2 



Therefore if T* is the average temperature of the whole mass, then the 



p k 

 average available kinetic energy for the unit mass — l — is given by 



R T 



[V*\ = iyy = k^k, rt* e* 

 ~Y ~2~ '~W r 2 



and when the other circumstances are the same this has its max- 

 imum when 



FC\ — FC*) — /v. 



2 



