( G43 ) 



x 

 0.9, thai loo. — mav not become smaller than the required value 

 xi 



11.5, or in other words, for the maximum in temperature to be 



reached, the critical temperature of one component must be about 



ten times as high as that of the other. A system, in which hydrogen 



occurs, will most likely show the temperature maximum when the 



other component has its critical point above 0° C, but already when 



the more volatile component is nitrogen or oxygen, we shall be more 



restricted in the choice of the other component. For then the latter 



must have its critical point at about 1000° C. resp. 1250 ('. If 



ether were the more volatile component, this temperature would 



almost amount to 4500° C. 



This conclusion is hard I v affected when we put the temperature 



of the melting point not at l '„, but at 1 / 3 of the critical temperature, 



as it really is for a number of substances whose critical temperature 



and melting temperature are known. It is true that this consi- 



V 



derably increases the second member of equation (2), and so — , but 



in the same ratio — increases too, so that the quotient remains about 



unchanged. This is most easily seen when the condition on which a 

 temperature maximum occurs, is written : 



an Vo ^ an 



<^ 0.1 or lO(i. j- log. v v — log. vi <^ log. 0.1. 



X v VI ' (Go 



XI 



Now for log. — we may introduce the value from the equation *): 



xi 1 — x _ / ƒ dTk 1 dpt 

 I — xi x \T dx pi dx 



and write for log. v : 



MRT ST,. 



log. v v = log. = log. MRT -f- ƒ — — 1 — log. p k . 



Pe- 

 so that the condition becomes : 



T 



dTk ) 1 dpk 



1 + — — log. p k — log. vi — ƒ -f log. MET < log. 0.1. 



ll-dx) pk dx 



7 



So an increase of T will only affect the first term and the term 

 log. MRT, and the logarithmic change of the latter will certainly 

 amount to less than the change of the former. This now increases 

 when T becomes smaller, hence when at 7 T =: l / a T/- the inequality 



i) These Proc. Vil, p. 559. 



