118 Physical Properties [CH. vi 



that the actual forces of cohesion are adequately represented by this permanent 

 field of force, it will be easy to calculate the influence of this field of force 

 upon the pressure. 



For the field of force can be regarded as exerting an inward pressure, 

 say p-i per unit area, upon the outermost layers of molecules of the gas. 

 Clearly this pressure must be supposed proportional jointly to the number of 

 molecules per unit area in this layer, and to the intensity of the normal 

 component of force. Each of these two factors is directly proportional to the 

 density of the gas, so that p l will be proportional to the square of the density. 

 Let us suppose, then, that 



Pi = cp 2 , 



where c is a constant depending only on the nature of the gas. The 

 molecules are now deflected upon reaching the boundary, not by impact 

 alone, but as the total result of their impact with the boundary and of the 

 action of the supposed field of force. In other words they may be supposed 

 acted on by a total pressure p + p l or p + cp 1 , instead of by the simple pressure p. 



Hence equation (279) must be further amended by writing it in 

 the form 



(p + cp*)(v-b) = RNT ........................ (280), 



or again, replacing p by Nm/v, 



i ........ (281), 



where a = cN 2 m?. 



This is Van der Waals' equation connecting p, v and T. It will be 

 noticed that a and b are constants for the same mass of gas, but depend on 

 the amount of gas as well as on its nature, a being proportional to the square 

 and b to the first power of the amount of gas. 



135. One factor which is overlooked in the argument by which this 

 equation is obtained, is that when cohesion forces exist, some molecules 

 which would have reached the boundary had there been no cohesion forces, 

 may never reach the boundary at all, being deflected by the cohesion forces 

 before their paths meet the boundary. Actually, then, these molecules 

 exert no pressure on the boundary, whereas Van der Waals' argument 

 supposed them to exert a negative pressure. As a consequence, equation 

 (281) admits of negative values for p, whereas an examination of the physical 

 conditions shews that p is necessarily positive. 



This objection, however, is of no weight so long as it is clearly recognised 

 that equation (281) is true only to the first order, as regards deviations from 

 Boyle's Law. 



