Restriction to the Application o/Carnot's Principle. 187 



passes through the dialyser will be able to dissolve some more 

 sodium-sulphate crystals. The apparatus (fig. 1) was accord- 

 ingly arranged with excess of crystals in the beaker C, as well 

 as in the dialyser A. The following are the details of the 

 experiment : — 



1SS8. Nov. 20 ; 5 p.m. Dialyser set up with 3 layers of 

 parchment-paper and excess of crystals (Na 2 S0 4 , 10H 2 O) in 

 both A and C. Saturated sodium-sulphate solution in A. 

 Apparatus completely protected from evaporation. 



Dec. 5 ; 4 p.m. Temp, of solutions (before mixing) = 14°*4. 



On pouring both solutions into a stoppered bottle which had 

 lain some days beside the apparatus, the temp, rose to 15°*2. 



Rise of temperature =0 o, 8. 



Bottle now stoppered (one mgrm. sodium-sulphate crystals 

 added to promote further crystallization). 



Dec. 10. Crystals have formed in the bottle. 



Temp, of solution . . . =14°'2 



Mass of solution . . . =26*156 grams 



Mass of crystals . . . = 2'446 „ 



Now I find the latent heat of solution of crystallized sodium 

 sulphate to be 64*6, and the specific heat of a saturated solu- 

 tion at 15° about *97 ; so that if the mixed solutions had 

 been kept under adiabatic conditions while the crystals were 

 forming, there would have been a total rise of temperature of 

 more than 3 degrees (due allowance being made for the 

 increased solubility at higher temperatures). 



The mechanical availability would then be 



/* 273+ 1;-4 



J273 + 14-4 



&.M.(fl--273 + 14-4)tffl 



where M is the mass of the substance, and Jc its specific heat 

 at the temperature 6. Putting 



k = constant = *97, 



the above expression becomes 



•97xJM|(290'4-287-4)-287-41og e ||^|^ 



= about 500,000 M ergs. 



That is, after descending under gravity through an average 

 height of about 2 cm., the solution has increased the motivity 

 of the system by an amount sufficient to raise itself vertically 

 through more than 5 metres. 



