( 5ft3 ) 



1 1 



so that we get at loir teniperatiii-es (when — and — may l>e neglecteu 



and i\ ^ b^ may be put): 



loil 



1 

 R2' 



\{b,—l>,) 2l/n,(l/a,— 1/«,)' 



From lliis we see ah'eady, that when A., := A^ (.t =: 6), 



(4) 



l/a, 



l/fli (because 6 must be krgei- than 1), tlien Ion — is alwavs 



negative, i.e. .r., <:^ .i:, . Hence just as little a three phase pressure ]> 



than the two vapour branches, as a minimum critical temperature. 



Let us now proceed te derive tiie condition^for ''"s^.''! from (4). 



Then ( dividing bv —^ 1 we must get 



K 



or as — = — and 



from which tVilhm'; 



6 



+ 1>2 



ö< 



l/.-r 



— (5) 



21/.T-1 ^ ^ 



Hence tliis condition is another than the condition (3) for the 

 minimum critical temperature, and we shall at once examine in 

 how far the two conditions include or exclude each other. 



No more than for .t = (9 does a value of 6 satisfy the above 

 inequality for .-r=r 1. If /9 = 1, then, provided l/^^Vai ^ — '^ l/^ + 1 

 must be ^0; and as this will always be satisfied, .v, will be ^.v, 

 for 6z=i\ on the side of the first component, when .t^\/^. (We 

 found onlv then a minimum critical temperature for (^=1, when 



We can now easily prove, that always : 



4.T j/.T 71 



(3 l/.T— l)^"^2i/.-T^' 

 when -t ^ ' \ For the abo\e leads to : 



(3l/'.T-ir>4l/.-t(2l/.Tr-l), 

 i. e. to fl; — 2 i/jr -|- 1 > 0, which is again alwa^'S satisfied. 



