158 Physical Properties [OH. vn 



179. When no external forces act, the equations of equilibrium (equa- 

 tions (371)) reduce to 



8P = 8P = 8P = 



dx "dy dz 



so that P is constant throughout the gas. 



Obviously, in fact, since the gas is in equilibrium under the action of no 

 forces the total pressure must be the same throughout. At the boundary 

 this total pressure becomes identical with the pressure p calculated in the 

 last chapter. This, then, is the constant value of P. 



Let us, however, examine carefully the form assumed at the boundary by 

 the general equation (equation (370)) 



If we calculate P at a layer at distance just greater than -- from the 



Z 



boundary, we put vr = 0, for the number of molecules whose centres lie 

 between this layer and the boundary is infinitesimal. Also, as explained in 

 176, we take Vb as the value of v, and so obtain 



If, on the other hand, we calculate P at a layer just less than ^ from the 



25 



boundary, we must not put cr = 0, for we have now to take account of the 

 stresses between the boundary and the molecules which are in collision 

 with it. We accordingly put TS=P, and of course v = 0, since no molecules 



can have their centres at a distance less than - from the boundary. Hence 



2* 



we obtain, as has already been foreseen, 



P = p .................................... (377). 



Comparing the values of P given by equations (376) and (377), we obtain 



which is in agreement, as it ought to be, with the value of the pressure 

 calculated in the last chapter (equation (287)). 



If we substitute the value ^ for P in equation (375), we obtain 



Vb~ V 



.(378), 



giving a general expression for the intermolecular pressure, which will be 

 found useful later. 



