22 PROCEEDINGS OP THE AMERICAN ACADEMY. 



st.nit volume the Bame in the 1 i < i » 1 1 « 1 and it- vapor, the equation assui 

 the Bimpler form 



R Tin-'- =PY- T - 11 l\ (84) 



where v t and <•_ represent the molecular volumes in the liquid and gase- 

 respectively. From the previous section we know that the 

 term // will enter simply as a volume correction. The exact manner in 

 which it so enters may be best Bhown by finding the free energj <>f the 

 I icess of liquefaction from the work that might be done if the vapor 

 were compressed isothermally and continuously until it reached the liquid 

 condition. This work would be equal to J'/> dv, andjo can be found in 

 terms of v from the equation of condition which holds good throughout 

 tin- process. From equation (27) 



rt dm 



P" V-f{v) dv ' 



Therefore 



A = Jj' h -=£y-Ar ) d >--f 



IX 



R T 

 The integration of — dv is only possible when the form of J 



is known; but sincey(^) does not change greatly, and since it is only an 

 important part of the expression when y is small, it may be regarded as 

 a constant, and equal to the value of f{ v ) in the liquid state, or l>\. This 

 value may be found from equation (33). Then the above equation 

 becomes 



A = U T\u '±^ + u, 



< i — Ol 



and for equilibrium from equation "(11), A = P V. 



R Tin V *~\ l = P V- U. (85) 



P] — o l 



Since h x is but small compared with v a , we may replace v a — 6j by 

 Sine- /' represents the change of internal energy in vaporization, and 

 /' V the externa] work, — /' + P V will be equal to the ordinary beat of 

 vaporization per gram-molecule, including the external work. This whole 

 quantity may be designated by L. Then 



BT\n— ZL-szL. (86) 



< i — h 



