398-401] Pressure, Density and Temperature 331 



maximum value, say z/ crit , consistently with the suppositions we have made 

 as to the smallness of the clusters of molecules. Hence there is a certain 

 critical value of T, say jT crit , such that for values of T greater than T crit , 

 equation (773) cannot be satisfied by any physically possible value of v. In 

 other words, at temperatures greater than T crlt<) liquefaction cannot set in, no 

 matter how great v is ; at temperature T crit , liquefaction sets in when the 

 molecular density is v crit .; and at temperatures below T crit , liquefaction sets 

 in as soon as the molecular density reaches some value which is below z> crit- . 



It is therefore obvious that T^ is simply the "critical temperature" 

 in the ordinary sense, and that v crit is the " critical molecular-density." At 

 temperatures above T crit , the molecules can be brought closer together by 

 pressure, and the density can be increased to values greater than v clit , but 

 the suppositions on which we have been working are now violated there are 

 no longer small and separate molecular clusters, but the clusters are crowded 

 into one another by the pressure. Thus at densities above the critical density, 

 the liquid and gaseous states are continuous. For values of T, v below the 

 critical values, it is clear that equation (773) represents that branch of the 

 chain line in fig. 10 (p. 133), which is to the right of the critical point P. 



Pressure, Density and Temperature. 



401. From what has been said, it is clear that when a gas or vapour 

 is at a temperature which is only slightly greater than its boiling point at 

 the pressure in question, it cannot be regarded as consisting of single molecules, 

 but must be supposed to consist partly of single molecules and partly of 

 clusters of two, three or- more molecules. If m is the mass of a single 

 molecule, and if v lt v 2 , v 3 ... have the same meaning as before, the density is 

 given by 



p = m(v 1 + 2vi + 3p,+ ...) (774). 



In calculating the pressure, we must treat each type of cluster as a 

 separate kind of gas, exerting its own partial pressure. We accordingly 

 obtain for the pressure, as in 123, 



1 

 P = ^ (V1 + V1 + v, + ...) 



= RT( Vl +v 2 + i> 3 + ...) (775). 



From a comparison of equations (774) and (775), remembering that 

 PI, z> 2 ... are functions of T and p,it is clear that neither Boyle's Law, Charles' 

 Law nor Avogadro's Law will be satisfied with any accuracy. 



