86 Prof. H. L. Callendar on the Tliermodynamical 



19. Variation of the Covolume b. 



Tan der Waals, in hi? essay on the Continuity of State 

 (Phys. Soc. Translation. 1890. p. 372), gives a theoretical 

 discussion of the effect of the size of the molecules on the 

 length of the free path, from which on certain simple assump- 

 tions he deduces that for moderate pressures the effect may 

 be represented by attributing to the covolume b a value equal 

 to four times the actual volume of the molecules regarded 

 as spheres. The theory indicates, however, that the value of 

 b should diminish with increase of pressure somewhat rapidly 

 when the volume approaches the value 2 b. He verifies this 

 by applying his equation to represent the behaviour of 0O 2 

 as observed experimentally by Andrews. Adopting for the 

 constant a in his equation the value "00874 (the unit of 

 pressure being 760 mm. and the unit of volume the volume 

 of the gas at 0° C. and 760 mm.) he finds values of b ranging 

 from '0023 to *0025 for the vapour, but falling to "0016 and 

 '0018 for the liquid. It appears both on theoretical and ex- 

 perimental grounds that I cannot be regarded as constant 

 for a large range of pressure, and that no weight can be 

 attached to calculations of the critical temperature based on 

 the assumption that b is the same, as in van der TVaals' 

 equation, for both vapour and liquid. It nevertheless appears 

 probable that the range of variation of b is not large, and 

 that its value for moderate pressures is nearly constant with 

 respect to both temperature and pressure. The value of b 

 cannot be determined theoretically, because the actual volume 

 of the molecules is unknown, and because the theoretical 

 assumptions on which the estimate of the ratio 4 is based are 

 extremely uncertain. Meyer, adopting a slightly different 

 assumption, finds that b should be 4 V2 times the volume of 

 the molecules. If we assumed, as many writers have 

 supposed, that the molecules of the liquid at low tempera- 

 ture- are practically in contact, and that the volume of the 

 liquid in this case may be taken as the volume of the mole- 

 cules, we should find, if we multiply by the factor 4 or 4v/2. 

 values of b which are much too large to be reconciled with 

 the observed behaviour of gases at moderate pressures. TTe 

 may. however, assume with some degree of confidence that 

 the volume of the liquid, or the limiting volume of the gas 

 at very high pressures, is a limit below which the value of 

 b at moderate pressures cannot greatly fall : and we mav 

 with propriety reject formulae or experiments which lead to 

 much lower values. The limiting volumes of hvdrogen and 

 COo at high pressures are given by Amagat as 8;7 c. c. and 



