TnteUic/ence and MUcellaneous Articles. 471 



ON THE EXACT MEASURE OF THE HEAT OF SOLUTION OF SUL- 

 PHURIC ACID IN WATER. BY M. CROULLEBOIS. 



The heat produced by the mixture o£ monohydrated sulphuric 

 acid with variable quantities of water has been already measured 

 by divers phy.^ieists ; but their results present rather great diver- 

 gences. M. Pfaundlcr lias recently resumed the investigation of 

 this question, and has represented by a simple formula the quan- 

 tity Q„ of heat evolved by 1 molecule of 80 ^ H^ when n molecules 

 of water are added. The formula is 



But the work accomplished by M. Pfaundler, notwithstanding the 

 progress realized, is still incomplete ; for the preceding formula 

 doss not include the temperature at which the determinations were 

 effected. Now M. Kirchhoff has shown, long since, that the 

 thermic effect is intimately connected with the tension of the 

 vapour of water emitted by the solution, and consequently with 

 the temperature. Doubtless it is here that we must seek the ex- 

 planation of the divergent results. In view of these facts I shall 

 compare the numbers furnished by M. Pfaundler's formula with 

 those which may be deduced from the relation given by M. Kirch- 

 hoff. This relation can be obtained in several ways, and more 

 quickly than it was by the illustrious physicist in his memoir on 

 the internal energy of bodies. Here we shall proceed as follows : — 

 Consider two states, A and B, of the operative substance. In 

 the state A an indefinitely small quantity dx of water is in presence 

 of the acid, at the absolute temperature t ; in the state B the same 

 quantity is in solution in the acid, at the same temperature. It is 

 possible to pass from one state to the other by two different paths : 

 either the solution is effected directly, and the variation of internal 

 energy, approximately equal to the heat evolved, is c?Q ; or else the 

 two extreme states can be joined by moving a characteristic point 

 upon three isothermal lines. 



1. The solution emits the quantity dx of vapour, at tension/; 

 the variation of internal energy is dn={l—Afa)dx. 



2. This vapour, separated from the dissolvant, is compressed at 

 the temperature t so that /becomes equal to F; the variation of 

 energy is nil. 



3. After the limit of saturation is attained, the compression is 

 continued till the weight dx of vapour is brought back to the liquid 

 state; the variation of energy is du' = {h — A^i:,)dx. 



I, L, /, r, A have the usual significations ; o- and 2 designate 

 respectively the difference between the volume of the vapour and 

 that of the liquid under the corresponding tensions /and E. 



It is known that the variation of internal energy depends only 

 on the initial and the final state ; we have therefore 



cZQ = cZ?f ' — c?M = L I 1 — — J dx^ 



