LIQUIDS AND ALUED EXPERIMENTS. 1 7 



but the density, p, of this mixture is not given. If, however, m is observed 

 p may be computed (equation 31). If p = p 



-m = ankj{h"+2h'")-ak a {n-h"pg)/{h"+2h'") (33) 



depending upon two nearly equal counter-currents, since II is relatively 

 large. If eventually p = p a , since R a p a = R h p = R h p h , 



-m = ak a h"p w g (34) 



the diffusion of air alone due to the head h". 



Finally, in a manner similar to the above, one may deduce 



n (h" T +2h"') i p ^ Ra ka + R » kh) ~ Ra ka h " p » g } ^ 



V = 



18. Continued. Potential Energy of the gas mixture. — If the mixed 

 gases are to be separated, the work to be done is given by 



IF = ^ ft log^/n+^ log^ a /n (36) 



since the hydrogen is to be compressed isothermally from v and p h to II 

 and the air similarly from v and p a to II, v being the volume of gas while 

 transpiration is taking place at U. = p h -\-p a . Thus the work per unit of 

 volume is 



*-^**i&Wi*-i,tfSs(e (37) 



If there is eventually to be but a single gas present, the above equation for 

 W must be modified, to include the relative importance of the head h" of 

 water on the imprisoned gas. In other words, 



p h +p a = Il + h"p w g = II + p' (say) 

 and therefore 



™^^^U + P^-±l^ (38) 



Hence, if p h is equal to zero, on expansion (since p'/U is also very small) 



Y=(n+*0 (^ + • • ^)=P' = U'p w %, nearly. 



The potential energy per unit of volume is constant. 



The rate at which potential energy is lost per second on mixture is per 

 unit of volume 



w -, /n+// \; p p h >(n+p'-p h ) n+v '- p » , . 



7 =-M> g (— f- -ij+ 7 iog A ^y (39) 



if v=o, dW/dp h = — "J log 



n+P'-p* 



Pn 

 iip h = o, dW/dv = W/v 



If pfi^H+p' or p a = o, initially, 



W v p h v 



— =-p\ogo+p h -\og— = -p\ogo+p -, nearly. 



