160 Physical Properties [OH. vn 



182. We know on experimental grounds ( 74) that d3> is very small. 

 If we take d<& = 0, equation (382) assumes the form 



........................... (384), 



and we have (equation (287)) 



P = Th = B "> T ' ,;,,.,,,, ,:v Ml 

 so that the equation becomes 



d& = ffdS + RvtFcb ........................ (385). 



183. If we do not neglect the term d<3>, the calculation becomes con- 

 siderably more difficult, for the intermolecular pressure -or will do work when 

 the gas expands. 



Let us write r = T c + -cr i , 



where r c is the part of w produced by collisions i.e. encounters in which 

 the molecules are so close that they cannot approach any nearer, and CT; is 

 the part of -57 produced by the outstanding intermolecular forces between 

 pairs of molecules not in contact. 



We have already calculated a value for cr; we must now try to calculate 

 vTi and ia c separately. 



As in the treatment of Van der Waals' cohesion ( 141), we can denote 

 the density inside the gas by p, and that at the boundary by p . The 

 equation giving rs (equation (378)) can then be expressed in the more 

 complete form 



Vb (pa) - V 



~W~' 

 expressing that i/ 6 is calculated for a density p . 



Let us now imagine a rigid plane surface of area unity set up and 

 held rigidly at rest at some point inside the gas. This alteration will not 

 affect the distribution of density inside the gas, for the field of inter- 

 molecular force will exist on both sides of the area. The pressure produced 

 by molecular impacts on either side of the area will of course be the same, 

 say pi. Treating this surface as we have already treated the surface which 

 forms the true boundary of the gas, we obtain equations giving the constant 

 P in the form 



,,,,,-, P = OT;+ ,G, 



by considering an area at a distance just greater than from the fixed 



2 



area ; and 



P = VTi+pi 



by considering an area at a distance just less than - from the fixed area. 



