’ 
Ve, 
Ves yt 
too we separate into three parts | + { ao f The last integral 
vo Vey Veg 
is now zero according to the law of Avoerapo. The middle one 
we find from the equation already used above: 
2 
Ver 
by differentiating, taking into consideration that the limits of the 
integral are functions of wv. 
We get: 
2 a d a a 
pe p ve |? pe Ver Ve, 
= de 4- | p— (ve —Ve,) + Pe—— Pe St 
| Een | [ = Ora. 5 li dc EE 
Vo, 
Now at the limits of the integral p is pe; we retain therefore on 
the left and the right only the first members. 
Ve, 
De 9 > (dp 
Finally the first part | Er dv. As we were allowed to neglect 
Pad 
Ve, Vo 
free. we might be inelined to think that this term too might be 
Uy 
omitted. 
But as follows form the equation of state: 
Op MRT db daa 
de — (v—b)? dir Wace per 
this integral appears to be of higher order than the other for small 
values of » — 6. We therefore retain it. Carrying out the integration 
we get: 
MRT db dage Wve, 
vb dev _{vo 
Here we may substitute p + a/v*, for MRT/v—h, so that our 
expression for the thermodynamic potential becomes: 
| ae 
My, = MRT1(1-2) + pavo — pevo + MRT + MRT lp./p,-2 ee (ves =ve) + 
i d ( ie db ( a a | dal 1 1 KT 
C2 = Wie Ee TEN er at (ea TEER 
daz be! dz [v‚,' vo’ | See OE pet) 
ie 
This value must now be equated to the thermodynamie 
potential of the same substance in pure condition. As we suppose 
