4 
( 702 ) 
case leads us into the very heart of the question, and thus will 
enable us to get rid of the restricting suppositions from which we 
started. For the ease in question we choose a reaction between a 
number of substances, which takes place without modification of the 
total number of molecules, and for which van per Waats’ equation 
in its simplest form with constant @ and 4 may be taken as equation 
of state both of the mixture of the reacting substances, and of the 
reaction products, 
In this case the entropy of the mixture of the reacting substances 
is given by 
T 
1 
[> Me vo 
4, = (vr MB) log (v, -- 5,) + f — ri dT + Xr HH 2ERrlog rv 
and that of the reaction products: 
P 
we, Pos 2 
n, = (=v MR) log (v, —b,) +f “A dT + SrH+ JRvlogy 
I 
So we get for the difference of entropy: 
Y.— 4, = Zr MR log (v,— b,) — Er MR log (v,—b,) + 
i! If, 
oe Lae eo Peis 
+ a nat a — df + Sr + ~'v logy 
3. What value now does this expression assume at the absolute 
zero? It is clear that no general answer is to be given to this, 
because this value will depend on the way in which we approach 
the absolute zero. For as for 7'=0 necessarily always v must 
1) It is true that strictly speaking we should have to reason as follows. The 
value ¢2—e, for the considered reaction is put equal by Nernst to the difference 
of energy in the formula of van ‘r Horr, and the latter applies to reactions for 
constant volume; so the volume before and after the reaction is kept constant. 
But except in the highly improbable case that exactly bj — bj, one of the two 
volumes, (that of the mixture with the smallest 5), does not become equal to the 
limiting volume. And this leads to obvious absurdity, both because then one of 
the two systems is necessarily unstable, and because of the conciusions which we 
should then further have to draw from the equality of the differential quotients. 
If we are to attach any meaning to NeRNst’s suppositions, we shall have to assume, 
as has been tacitly done in the text, that according to NERNst’s meaning the 
substances are under the pressure of their saturate vapour before and after the 
reaction, and that for the substitution in the equation of vAN ’t Horr we may 
neglect the difference of volume, which in consequence of this necessarily accom- 
panies the reaction. This conception alone can account for the way mentioned in 
the text in which Nernst determines the maximum work (by evaporation and 
condensation without further operations with the condensed system). 
