344 



phases is defined by (6). By (13) is defined wiietlier tlie (emperaluie 

 is rising or falling; by , (15) is defined whether the pressure is in- 

 creasing or decreasing. 



We write the isovoliimetrical reaction: 



/, i\=x^ F, 4 . . .:;t)ctK, + ^7+1 ^?+i + .-..• • (17) 



wherein all reaction-coefficients have been taken positive. Now we 

 have : 



^ {W)v = x^H^ -f ^./+i //</+i + ....- ^i^^i - K^^. - . . ■ . 



2 (A X)v = Xg X^ + XqJ^x XqJ^.x -[-.... A, A-j — A, X^ — • . . . 



Now we assume that we have written reaction (17) in such a 

 way that it proceeds on addition of heat from the left to the right; 

 consequently ^[IH)\ is positive. In order to determine the sign of 

 2{Xx)y -we have to dissolve A, A, . . . from (12) and we must know 

 the partition of the new substance between the different phases; 

 this may be found from (6). 



In some cases the sign of ^fP.^Oris known, however, at once 

 without this calculation. When f.i. the new substance occurs oidy 

 in one or more of the phases, which arise in (17) on addition of 

 heat, consequently in Fq Fy-^i . . . , then is £i\ =: .r, =r . . . x^—i = 

 and, therefore 2 {?.x)v is positive. It follows then from (13) that 

 {dT)x is negative. 



When, however, the new substance occurs only in one or more 

 of the phases, which arise in (17) on withdrawing heat, then 

 XqXq^x... are zero, so that 2i {Xx)v is negative. Then it follows 

 from (13) that {d2^)x is positive. 



When, however, the new substance occurs in both groups of 

 phases, then only a calculation more in detail may decide on the 

 sign of 2[}.x)y and consequently also on the sign of {dT)x. 



Now we represent the isentropical reaction also by 



X,F,-\-KF,^....:^lqFq^Xq+lFq^,-\- (18) 



However we have to take 'in mind, that A^ X^ . . . in this case, 

 must not be dissolved from (12) but from (14). Consequently in (18) 

 A, A, . . . shall have not only other values than in (17), but one or 

 more of them may have also other signs, so that they must be 

 transferred from the one part to the other. Now we have: 



2 {X V)h = XqVq^ ^9+1^9+1 + ....- A, F, - A, F, - ... . 



^ (A X)ü ^IqXq -{- A^_|_i XqJ^x -f- — Aj .fj — A, ;C, — . . . . 



Now we assume that reaction (18) is written in such a way that 

 it is proceeding from left to right with increase of volume. Conse- 

 quently 2{XV)h is positive. When the new substance occurs only 



