Energy in Diffusive Convection. 529 



second equals 



, vAT rAT \ 



\l — e k 1-e k I 



Let W = rate at which work is done by the apparatus 



D=rate at which heat is absorbed due to diffusion 



along the tubes. 

 F = rate at which heat is produced by the fall of the 



dissolved substance in the upper compartment, and 



the rise of weakened solution in the lower. 

 Y = rate at which potential energy is gained by the 



carriage of dissolved substance from the bottom to 



the top of the diaphragm. 



Then 



W=D-F-V 



I 1 — e "fc 1 1— eT J 



_/ vAT _ eAT \ 



I _ vLi wL 2 1 



\l-e k l—ek/ 



Noting that a 1 + c = L 1 — b x , a 2 + c = L 2 — b 2 , it can be shown 

 algebraically that 



L V \-e~k- 1-e T J 



This is exactly the same result as that obtained in an earlier 

 section. 



General Explanation of the Loss of Heat ivhen Work is 

 done by the Apparatus. 



For simplicity let the thickness of the diaphragm be zero. 



Transmission of dissolved substance along the tubes is 

 accompanied by a fall of substance in the upper compartment, 

 and a rise of weakened solution in the lower compartment, 

 both of which actions produce heat. The rate of production 

 of heat depends on the rate of flow of the liquid. 



The greater the rate at which work is done by the appa- 

 ratus, the less the rate of production of heat. 



The rate of absorption of heat due to transmission of dis- 

 solved substance through the tubes is independent of the 

 flow, and need not be considered in this general explanation. 



