Energy in Diffusive Convection. 523 



interest in the work, the author has taken advantage of the 

 Christmas vacation to study the question in some detail. 



On the Fall of Temperature when Diffusion occurs upwards 

 if the Solution has a Density greater than that of Water, 



Consider a vertical cylinder of length Qi + l 2 ) 

 and sectional area A. Let d 2 equal the density 

 of length Z 2 , and d l the density of length l v 

 Let it be assumed that there is no change of 

 volume when the two liquids mix. 



Taking a plane through the bottom of the 

 cylinder as one where bodies at rest possess 

 zero potential energy, it can readily be seen that 

 before mixing, through diffusion or otherwise, 

 the potential energy 



Fig. ], 



I 2 

 d 2 Ag^- +d 



.V, (?,+ £} 



t 













h 













h 







The liquids also possess energy due to the heat they 

 contain. 



Let Si = thermal capacity of unit mass of liquid of density d±. 

 Ss— „ » j j solution „ d 2 . 



S = „ „ „ mixture. 



t = temperature (absolute scale) before mixing. 

 h = „ » after „ 



The energy, before mixing, in the form of heat equals 



f \ Al Y S ± dt + \ ° d 2 Al 2 $ 2 dt. 



The combined potential and thermal energy equals 



d 2 Ag l ^+d 1 Agl 1 fl 2 + l j-^ r°rf 1 AZ 1 S 1 ^+ C°d 2 Al 2 8 2 dt. 



Let mixing take place without the addition or withdrawal 

 of heat. Neglecting the heat of combination, the expression 

 for the combined energy now equals 



Equating the two expressions, dividing throughout by A, 

 and rearranging, 



2 



h I d.k 



Jo 



M*+ [°dM$ 2 dt= [\d x h 



Jo Jo 



+d 2 l a )Sdt. 



