PRESSURE AND TEMPERATURE 45 



we get at once the necessary conclusion that the pressure is 

 a linear function of the absolute temperature, when the 

 volume is constant. 



p =v^- b T -T* = cT - lc - 



In this expression k vanishes for sufficient dilution, leav- 

 ing the pressure proportional to the absolute temperature, 

 according to the limit-law of Gay-Lussac. The more 

 general relation mentioned above is very approximately 

 true, as is indicated, e.g. by the following numbers for 

 pentane l : 



Temperature 40 60 80 100 120 160 200 240 280 

 Pressure 857 920 981 1040 noo 1219 1334 1451 1571 mm. 

 Difference 63 61 59 60 2x60 2x63 2x59 2x60 mm. 



A second numerical relation between two bodies depends 

 on the law of correspondence, and gives that at equal 

 fractions of the critical temperatures, the saturation pres- 

 sures are equal fractions of the critical pressures. In the 



T 



following table are given the reduced temperatures ^ for 



J- k 



hexane, pentane, and benzene, at equal reduced pres-? 



P 



sures -=- : 



CTT /I TT r\ TT 



6 -"-14 ^5 -"-12 ^6 -"-6 



I I I I 



0-7372 0-959 0-957 o< 957 



0-4423 o 896 0-890 0-891 



0-2064 0815 0-806 0-805 



0-0442 0-691 0-678 0-677 



T 

 From the agreement of the values for -=- which though 



J- k' 



not perfect is very close, it follows that with the aid of any 

 comparison substance the vapour pressure at given tempera- 

 ture of any other substance is calculable, if one knows the 

 critical temperature and pressure of the latter. 



1 Kose-Innes and Young, Phil. Mag. 1899, p. 353. 



