384 Prof. R. Clausius on the Theoretic Determination of 



has the value 1. By this substitution the foregoing equation 

 is transformed into 



^_J: 27(« + £) ,«x 



UT~v-u S6{v + fif w 



In order to apply this equation to the process of vaporiza- 

 tion, we will, for distinction, denote the pressure of saturated 

 vapour by P, and employ for the volume of the saturated 

 vapour and the liquid standing under the same pressure the 

 symbols s and cr, which I have also previously used. Now, as 

 the equation must hold good for the liquid as well as for the 

 saturated vapour, we can form from it the following two equa- 

 tions: — 



P _ 1 f 27(a + /3) ' 



RT"o— u 86>(V + /3) 2? " * ' " w 



_P_ 1 27(a + /3) 



PT~s-« 86>(s + /3) 2 { J 



Further, to express that the external work performed in the 

 vaporization must be equal to that which would be obtained 

 with the same increase of volume if the pressure changed in 

 accordance with the theoretic isothermal and the formula cor- 

 responding thereto, we have to put 



?(»-•)=£ 



pdv; 



and if in this we put for p the value determined by equation 

 (2), then perform the integration, and divide the resulting 

 equation by RT, we get 



P , ..«-.« 27Q + /3) / 1 1 \ 



For convenience we will also introduce the following sim- 

 plified symbols : — 



n= 7 = 



RT ' ~ ' *-> I (6) 



w = a — u, W = s — cc. J 



Equations (3), (4), and (5) then become : — 



w 80(ic+7) 2 ' K ' 



W 80(W + ?) 2 ' K ' 



n( w- w )=iog5-§(^- w L_). (in.) 



