RECENT ADVANCES IN SCIENCE 373 



PHYSICAL CHEMISTRY. By W. E. Garner, M.Sc. University 

 College, London. 



The Third Law of Thermodynamics and the Entropy of Solutions 

 and Liquids. — An interesting contribution to the study of the 

 third law of thermodynamics has been pubhshed by Lewis and 

 Gibson {J.A.C.S., 1920, 42, 1529). The third law of thermo- 

 dynamics as stated by Nernst requires that the change in 

 entropy accompanying any process which involves only solid 

 and liquid substances approaches zero as the absolute zero of 

 temperature is approached ; he, however, considered that 

 solutions required closer study. Planck has shown that this 

 statement of the third law must be modified when processes of 

 solution are concerned. Assuming that the entropy of every 

 elementary substance is zero at the absolute zero, he states 

 the third law as follows : the entropy of any pure substance 

 at absolute zero is zero. Lewis and Gibson {J.A.C.S., 191 7, 

 39, 2554) have collected together a good deal of evidence to 

 show that the third law is valid for pure substances. In the 

 examples given, good agreement was obtained between the 

 values of the entropy calculated from the equation AF — 

 AH = TAS, and those determined from the specific heats at 

 constant pressure. 



In the present paper considerations are brought forward 

 which lead to the conclusion that some, and perhaps all, solu- 

 tions are to be excluded in the statement of the third law. The 

 two liquids benzene and toluene, when mixed together, form 

 an almost perfect solution ; that is, one in which there is no 

 evolution of heat on mixing, and in which the vapour pressures 

 and fugacities obey Raoult's law. The increase in the entropy, 

 on producing one mol of the mixture containing equal molar 

 fractions of the two constituents, is given by the equation 



AS = Rln2 = I '4 cal. per degree. 



Since the heat capacity of the mixture is about equal to the 

 sum of the heat capacities of the pure constituents, AS must 

 be nearly independent of the temperature, for we have the 

 thermodynamic relation 



dAS _AC, 

 dT T 



where ACp is the difference between the heat capacity of the 

 solution and the heat capacity of the pure substances from 

 which it is produced. If AC^ remains zero down to the absolute 

 zero, AS will remain constant and equal to Rln2 ; but if, as 

 seems likely, AC^, varies, owing to the solutions ceasing to be 

 perfect at the lower temperatures, then AS may be reduced to 



