94 Chapter VI 



provided it be reversible, the work done in accomplishing it must 

 be the same quantity W, while if the process be not reversible the 

 work done will be greater than TF. 



Whatever then be the mechanism by which the secretion takes 

 place, we may assert definitely, and beyond the possibility of error, 

 that free energy to at least the value W must have been provided, 

 presumably at the expense of oxidative processes. 



How then can we calculate W, the least work which must be done 

 in the secretion of a volume F litres of urine ? 



Let the blood be assumed to contain the several constituents 

 AU A-2, ... A n at molecular concentrations* c 1? c 2 , ... c n , and the urine 

 secreted from this blood to contain the same bodies in concentrations 

 GI, Co', . . . c n '. Then the minimum work which it is necessary to do to 

 separate this urine from the blood is 



W=VRT 



c' c' 



' log -- - (C/ - d) + C 2 ' log -- - (C-2 - C,) + . . . , 



G\ ^2 



where R is the gas constant (approximately two calories) and T the 

 absolute temperature. 







Now each of the terms c'log -- (c' c), which may be written 



C 



log - - ( 1 ; ) , can be shown mathematically to be positive 



__ c \ c j J 



for all values of c' and c. Hence whatever type of urine has been 

 secreted W is the sum of a series of positive terms, and is therefore 

 positive. Every constituent A, therefore, whose concentration is 

 greater or less in the urine than in the blood, has added its quota 

 to the total minimum work it is necessary to do to secrete that 

 urine. 



It has been assumed that the minimum work which is necessary 

 to separate a given urine can be calculated merely from the freezing 

 points of urine and blood. This is absolutely fallacious. These lower- 

 ings of freezing points give no clue as to the value of the expression 

 for W given above : they merely tell us the value of the two ex- 

 pressions 



C\ ~r C% T T Cji, 



and Ci+c-2 + ...+ c n ', 



and therefore of the part of the expression for W given by 



* Concentrations reckoned in gr. mols. per litre. 



