TEMPERATURE AND THE PROPERTIES OF GASES 33 



state. Suppose, however, that the temperature is raised above the 

 boiling point and the pressure increased enough to preserve some 

 liquid. The vapour pressure will rise with the temperature 

 until a point is reached at which the liquid meniscus vanishes 

 suddenly with a very small increase of temperature and cannot 

 be re-obtained by any increase of pressure. The liquid has 

 passed to the gaseous state through the critical point. 



The investigation of the exact behaviour of substances at 

 this point and the means of determining the exact values of the 

 constants are questions of great interest, but we are concerned 

 for the moment with the values of these quantities only. 

 Suppose we have these for some series of substances and we 

 divide the pressure volume and temperature of these under any 

 conditions by the critical values. The result is known as the 

 " reduced "pressure (-zr), volume (</>), and temperature (0), so that 

 7r = p/pc, etc. Thus far everything is the result of experiment, 

 and we may turn to the guiding principle mentioned above. 

 This was enunciated by J. D. van der Waals as the deduction 

 from the theoretical equation of state deduced by him in 1873. 

 This equation will be duly considered, but the great principle 

 deduced from it and known as the " law of corresponding states " 

 is of wider application. It may be said to generalise matter, to 

 reduce everything to one substance under different conditions, as 

 it states that " All substances have the same properties at the same 

 reduced pressure, volume, and temperature. 11 



When one takes into consideration the great complexity of 

 many molecules and the extraordinary range of properties ex- 

 hibited, from helium with a melting point of less than 3 K. to 

 such a substance as iodobenzene, which is one of those which 

 have a high critical point which has been determined with 

 some accuracy (Tc = 721 K.), it is remarkable that the coinci- 

 dence should be as good as it is. However, even with sub- 

 stances which are chemically elementary and in which there 

 is no association of vapour molecules on approaching the 

 liquid state, there are many differences which appear to be 

 connected with chemical properties, as substances of similar 

 chemical characters fall into classes in which the divergences 

 may be exceedingly small. In most cases the divergences are 

 unexplained : probably there are not at present sufficient 

 accurate data on which any more comprehensive generalisation 

 could be based. The successful solution of this further prob- 



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