54 



with r=2,l and b'k small, e.g. =0,04 — since tiie value of 



will amount to about = 1 + V, X 2,7 =r 1,45 — - will follow : 

 |3"ifc=r 0,69, i. e. vkb"k = 0,QQ. 



So instead of finding a negative value, which varies according to 

 the difTerent assumptions from -0,40 to —0,20 (—0,40 when 

 association is not assumed), we now find an impossibly large positive 

 value for vicb"k- 



And as nobody will think possible the fantastical course of the 

 quantity b following from this, a7iy attempt to account for the course 

 of the characteristic quantity (f in the neighbourhood of Tk, where 



— =z — 7, — while at the same time the ordinary quantities must 

 dm 



retain their known experimental values — by the addition of a factor 



$z=f{v) by the side of a/y' — hence also of van der Waals's 



factor (1 — 7, .c)'» iïi which x is a function oïv — should be rejected. 



In this state of affairs there is nothing left but to assume direct 



dependence of the quantities a or b on the temperature. 



4. The quantities a or b are functions of the temperature. When 

 a or b are temperature-functions, all the relations derived in § 1 

 remain unchanged at the critical point, because in their derivation 

 we only differentiated with respect to v with 2' constant. 



But the value of ƒ, derived in § 2, will in general undergo a change. 



a. When a is a temperature-function, we may put a=:akr, in 



which t = f(--\ From 



=/© 



RT akx 



P = 7 V (1^) 



V ~ V 



dx 



follows, when — (??i = T : Tk) is represented by t' 

 dm 



akx' 1 / , ak x\ ak x' 



or r= — p + 



fdp\ _ R 



\df)~ '^b " Tkv^' ^' ~ ry^ ' v^ J Tkv^ 



Hence also :* 



T fdp\ RT Takx' ^ , ak{x — mr') 



_ -^ 1 = , or = 1 -1 ; , 



p\dT), p{v-b) pTkv' pv' 



or because evidently xk=^l ■ 



Tkfdp\ RTk akx'k , , ak{l—t'k) 



fz= I — 1 = — » or = 1 H 



pk\dTjk pk{vk-hk) pkv'k pkv*k 



