LEWIS. — THERMAL PRESSURE. 167 



where F ' (v) is an unknown function of v, and c v is the molecular heat at 

 constant volume, T some arbitrary temperature. Comparing this with 

 equation (16), we obtain 



m = rVT+%-Tfi*£*T. (19) 



Now, substituting d Z7from (17), and bearing in mind that a = —=—, we 

 obtain 



dv dv J j' 1 dv w 



This is the closest insight that we can obtain at present into the general 



form of — 1- t-j but it is sufficient to show that in general the total 



dv dv s 



change in energy is not identical with the change in potential energy, 



dc v . 

 at least when -7- is not zero. 

 dv 



If we could pass continuously from the liquid to the gaseous state, and 

 equation (16) were assumed to hold good continuously throughout the 

 process, the total work of the process could be found, and would be equal 

 to the actual work done in the evaporation of the liquid. From equation 

 (16), 



jpdv— I dv — jadv, 



or 



/"a v, C u - 



pdv = RT\n~— I adv; 



dX 1 , • 



'or, since a = — — , the total work is 

 d v 



5 _ r 



V 2 J r , 



ETlu-- ~dX. 



v 2 



The work done in evaporation at the same temperature is P'(y l — v 2 ), 

 where P' is the vapor pressure. We may write, therefore, 



P\ Vl -v 2 ) = R Tin ^ - [''dX. 



Now, if d X were always equal to d U, we could write 



E Tin - = (U x - U 2 ) + P'iv, -v 2 ) = L, (21) 



where L is the common heat of evaporation. 



