842 Dr. R. D. Kleeman on the Radius of 



Stefan * has shown that the internal molecular latent heat 

 of evaporation is equal to twice the work done in. moving a 

 molecule from the interior o£ the liquid to the surface. Let 

 us obtain, reasoning on the same lines, an expression for the 

 internal latent heat per unit volume, supposing the internal 

 energy is expended only in overcoming the attraction between 

 the molecules which produces surface tension. The energy 

 expended in moving a layer of liquid of unit area and thick- 

 ness dz from the surface of the liquid out of. the range of the 

 molecular forces is 



C° l 

 dz \ <f> (x) . dx. 



We will suppose the layer taken so thin that the energy 

 necessary to further separate the molecules till they are out 

 of each other's sphere of action is small in comparison with 

 the energy expended in removing the layer. Next let us 

 calculate the work done in moving a layer of liquid of unit 

 area and thickness dz from the depth c x to the surface of the 

 liquid. A moment's consideration will show that the alge- 

 braical sum of the work done against the attraction of the 

 surface layer of thickness c x is zero. The work done in 

 bringing the layer to the surface is obviously therefore 



4>{x) . dx, 



■i 



which is the same expression as the above. The sum of these 

 two expressions is the latent heat of a volume of liquid equal 

 to dz, or 



-f 



<fi (a?) . dx, 



where L is the latent heat of unit volume. Differentiating 

 this equation with respect to c 2 we obtain 



S= 2 ^) w 



Eliminating Mc^ from equations (1) and (2) we obtain 



A d\ 

 Cl = 4 JL' 



if L 2 denote the latent heat of unit mass L 1 p = L, and 

 dh=dh l . p + hi . dp, and the equation may be written 



d\ / T dli-i 



i dx /t , 

 43-/1* + , 



dpi l ' r dp' 



Wied. Ann. xxix. p. 665 (1886V 



