Energy in Diffusive Convection. 527 



The work done per second equals 



.A [ { 9 U + -^| + k -f + (h~ 6J (1 + % } 



1 -{(^-^ + .L 1+ ^_-^JJ ; 



1 — £ fc 



or noting that L 1 = a 1 + c + & 1 , L 2 = a 2 + c-f 6 2 , it equals 



It may be mentioned that the work done equals zero when 

 v = (in this case there is an impervious obstruction to the 

 flow) ; and when 



2k P T gTL 2 gTLx 



-7- + — 5 r^Lr+/;(^i-^) T=0 



l — e k 1—^ h 

 (if -r- is small), i. e. when 



/j _ 6&(fl 2 — ai + ^i — ^ 2 ) 

 I^ + V 



(In this case there is no obstruction whatever to the flow.) 



The work done by the apparatus is a maximum when v is 

 approximately half the latter value. Work is done on the 

 apparatus when v is negative, or v is greater than 



M(a % - ai + 6 1 -6 2 )/(L 1 2 + L 2 2 ). 



Calculation, by means of Energy Equations, of the Rate 

 at which Work is done. 



Before tackling the problem, it will be well perhaps to make 

 some preliminary remarks with regard to what occurs in the 

 upper and lower compartments. The dissolved substance is 

 being continually carried to the top of L 1? for example, and 

 falling from there to the bottom of the upper compartment. 

 The heat generated by the fall equals the product of the weight 

 transmitted into the fall. 



On the other hand, when the dissolved substance is ab- 

 stracted from the bottom, the weakened solution rises to the 

 top of the lower compartment. Diffusion into the weakened 

 solution, whilst it is rising, will doubtless occur, but the action 



