87 



siderations. A partiele, nanielj, lluil begins a new patli at some 

 place, is subjected to the influence of tlie i)i"essure />, prevailing 

 there, and in the layer, where it terminates this path, it is subjected 

 to the in general entirely diiFerent pressure p^ of this layer. 

 Van der Waals' first equation runs: 



^mA^w„* + jot'i = ^mNu'n'' + pv^ . . . . (1') 



, a / a\ 

 The expression pi\ — ( pi\ 1 is for a monatoinic fluid the 



V. 



heat of evaporation for the molecular weight, ^^ -\- pi\ — -(^i -\- l>i\^- 

 We s'lall now have to apply a modification to this equation, when 

 the layers between which the interchange of pai-ticles takes place, 

 are taken in the capillai'y layer. Here we shall iiave, as it were, 

 an evaporation from a space under the jiressure p^ towards a space 

 under the pressure p\, and a condensation in opposed direction. 

 Hence our first equation becomes : 



ImNu,,^ + p.v-oQ -~~~ = bnA\'^ + p\v'-a<,' - ^ ^ • (1) 



The equation which expresses that for a stationary state a group 

 of particles from one layer will be replaced by a grouj) of particles 

 from the other layer becomes just as van der Waals puts: 



1 «* 1 « , 



Un dUn = — e tl n du n • 



V — b v' — b 



Now from (1) follows : 



Un du,i = It', I dll'n 



and our second relation becomes therefore 



V — b v' — b 



hence : 



(2) 



v' — b hmNu,,^ — \mNu'n 

 loq 



p „V — ao — p„v—aü I 



v — b imiV«' MET 



or 



"''^"2 ^-^^^^^%(^-^) +P«^ ^ "''^''2 ^"'^"^^^^ ^'"'^^''-^^ +^'^"' = '^^^ ^^) 



or 



