248 Mr. Gr. J. Parks on Heat Evolved or 



III. 

 Application of the Laws of Thermodynamics. 



Assuming that the phenomenon of Pouillet is reversible, 

 we may apply the laws of thermodynamics. Let h be the 

 amount of heat developed per square centimetre at the 

 surface of the solid and liquid at constant temperature, let 

 c be the specific heat of the liquid when the surface remains 

 constant, let s be the area of surface of the powder exposed 

 to one gramme of the liquid, the volume of which is supposed 

 to remain constant, let P be the surface-pressure for the 

 given solid and liquid. Then> with the usual notation of 

 thermodynamics, 



dQ, = c .dt — h .ds, (i.) 



and dQ = 7 . dcj>, hence 



r .dcj) = c . dt—h.ds (ii.) 



The variation of the internal energy is 



dU = J.dQ-P.ds = J.c.^-(J.A + P)<&, (iii.) 



where J represents the mechanical equivalent of heat. 

 Imposing the condition that the variation of the internal 

 energy is a perfect differential, we obtain 



T (dc,dh\ dP .. N 



J U + ^r~^ (lv ° 



Imposing the condition that the variation of entropy, d<f>, is 

 a perfect differential, we obtain 



dc dh h , v 



ds + dt=r (V - } 



From equations (iv.) and (v.) we have 



, r dP , M 



h =-J'M (V1 ° 



dc r d 2 F , .. , 



and d s = J'W (vll<) 



Applying these equations to the results obtained for water 

 and silica, we find that the surface-pressure diminishes with 

 rise of temperature, for since heat is evolved when the surface of 

 water and silica is extended, h is positive, and hence from equa- 



tion (vi.)^ 1 is negative. Taking h as '00105 when r is 280° 



