IvIQUIDS AND ALUED EXPERIMENTS. 17 



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

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



-m=aUkJ{h"+2in-aK{n-h"pg)/{h'^-\-2hn (33) 



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

 large. If eventually p = Pa, since R^ p^ = RhPo = Rh Ph> 



-m = akji"p^g (34) 



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



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



ra 



V = 



U{}l"-\-2h"') 



[pniRa K+Rn h) - Ra K h"p^g] (35) 



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

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



w=vpj,\ogpjn+vp^ogpjn (36) 



since the hydrogen is to be compressed isothermally from v and p^ to 11 

 and the air similarly from v and p^to H, v being the volume of gas while 

 transpiration is taking place at Il = pf^-\-pa- Thus the work per unit of 

 volume is 



'^«=7 = ^>^n^.+"'o^'¥"=>°^^^^^^' (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^+p, = n-^h"p^g = Ii + p' (say) 

 and therefore 



T=^>°^5T7^.+("+^')'°^^^^' (38) 



Hence, if pj^ is equal to zero, on expansion (since p' /H is also very small) 



-=(n + />') (^ + • • -J =/'' = A"p.g, 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 



7=-/'>g(^-^-i;+-iog^^^' — w^ ^^9) 



if i=o, dWIdp^^-'Aog ^'^^ ~^^ 



Ph 



a Pn = o, dW/dv = W/v 



li p^ = U.-\-p' or pa = o, initially, 



iv • "^ Ph ' / ^ 



— =-/>logo+/>ft-log— =-p\ogo+p -, nearly. 



