Liquid Spheres — Molecular Diameters. 879 



In the same way, if a large number of liquid spheres 

 coalesce into a given mass, the heat produced would be 

 considerable. 



Let n = the number of these liquid spheres in a gram 

 molecule, 

 d = the diameter of each sphere, 



D — the diameter of the liquid gram molecule sphere, 

 wi = the molecular weight. 

 p e — ih.Q density of the liquid at 6° A, 

 IV = the tension of the envelope about the liquid spheres 

 at 0°A, 

 and L = the latent heat in calories of a gram mass of the 

 gas at the boiling-point. 

 Equating the masses before and after coalescence we have 



r d"=~.D\ 



6 6 



from which d = D .n~*. 



Also, the potential surface energy has been reduced by 

 coalescence from T . nird 2 to T . 7rl) 2 . Therefore the amount 

 which has been transformed into heat is T. 7r(nd 2 — D 2 ), which 

 'by the relation above may be written T . ttD 2 (ii* — 1). Now, 

 since n is very large in comparison with unity, ni — 1 differs 

 but little from m, and thus this amount is T . it D 2 m. Further, 



T .D 3 =— , and we finally see that the potential surface 



energy of the n liquid spheres which is converted into heat 



by their coalescence is I ^ — J . T . ?i% a quantity which 



varies' as the cube root of the number of spheres obeying the 

 .law of coalescence, provided that T remains constant. This 

 will be the case if the temperature remains constant, that is, 

 if the heat is transferred to other masses such as the 

 surrounding air and adjacent bodies. 



Now, when a gram mass of a substance condenses from a 

 gas into a liquid at the same temperature, there is produced 

 L calories of heat energy which is known as the latent heat 

 • of condensation. Equating, therefore, these two amounts of 

 ^energy, we have 



t, /367rm 2 \3 i T T 



/Ljy 



, LJ\ 3 mp 

 irom which n= ^rr- 1 x 



;h*)tt 



3 M 2 



