LEWIS. — THERMAL PRESSURE. 153 



dependent upon the chance of any one molecule to escape from the phase 

 in question and upon the number of molecules per second which share 

 this chance. This chance for each molecule will depend (1) upon its 

 momentum and (2) upon the various influences that retard its motion 

 outward. The latter are the various attractive forces that have been 

 included in the quantity u. 2 . Therefore in any isothermal change in 

 which a, is coustant neither the momentum * nor the retarding influences 

 vary, and the vapor pressure then will be proportional to the number of 

 molecules coming to the surface per second, and therefore proportional to 

 the thermal pressure. Hence, 



P 1 = kfo <*,*£ = &. (8) 



•* 1 P 2 



Moreover in the general case, when both /? 2 and a 2 change, if we postu- 

 late, as on page 152, that equal changes in (3 2 and a 2 produce equal and 

 opposite effects on the vapor pressure, then we should expect that the 

 change in vapor pressure would be to the total vapor pressure as the 

 effective change in thermal pressure is to the total thermal pressure ; if 

 "effective change" in /3 2 is used to mean the change in /? 2 over and above 

 that required to compensate for change in a 2 . That is, 



dPi _ d(p- 2 -o 2 ) 

 Pi ~ ' & " W 



Comparing this equation, derived from kinetic considerations, with 

 the one which has been proved thermodynamically, namely, equation (7), 



dP x _rf(&-a 2 ) 



Pi 



G?) 



it is evident that the only assumption necessary to make the two identi- 

 cal is the following: The thermal pressure of any phase is equal to the 

 pressure which the substance would exert if under the same conditions, 

 it should behave as a perfect gas. 



Objection to this assumption cannot be made on the ground that it is 

 not sufficiently simple : but is it too simple ? What has become of the 

 correction " b " of van der Waals, to say nothing of all the complications 

 that may exist in a liquid or solid phase ? It must be confessed that the 

 above assumption seems, at first sight, absurdly simple and quite improb- 

 able. I shall attempt to show, however, that this assumption is not only 



* Whether this momentum is quite constant will be considered later. 



