374 SCIENCE PROGRESS 



a small value or to zero at the absolute zero. This is unlikely 

 for all types of solutions, and would probably not be the case 

 for a mixture of two nearly identical isomerides. In the 

 extreme case of mixtures of two isotopes, we have substances 

 which are nearly identical in chemical properties. It seems 

 improbable that two such isotopes would undergo any appreci- 

 able change in heat capacity on mixing. In this case, therefore, 

 we may conclude that the entropy change on mixing is practic- 

 ally the same at ordinary temperatures as at absolute zero. 



Doubt is raised even with regard to pure liquids composed 

 of a single constituent, for the distinction between a solution 

 and a liquid is to a large extent artificial. Water is regarded as 

 a pure substance, yet it is probably composed of several mole- 

 cular species which are in equilibrium at ordinary temperatures. 

 This might not be the case if water is supercooled to a very low 

 temperature. The same doubt applies to the two forms of 

 sulphur Sa and S^. There seems to be no reason to believe that 

 these liquids fall within the scope of the third law. On the 

 other hand, there are both theoretical and experimental reasons 

 for the validity of the third law in the case of crystalline solids. 



The third law is restated as follows : " If the entropy of each 

 element in some crystalline form be taken as "zero at the abso- 

 lute zero, the entropy of any pure crystal is zero, and the 

 entropy of any other substance is greater than zero." 



Gibson, Latimer, and Parks have determined the entropies 

 of formic acid and urea from measurements of Cp over a range 

 of temperatures down to 71° K. From these data they have 

 calculated the free energies of these two substances, and 

 compared the values with those obtained from equilibrium 

 measurements. 



The values which have been obtained agree with those of 

 Branch {J.A.C.S., 191 5, 37, 2316) for formic acid, and those 

 of Lewis and Burrows {J.A.C.S., igi2, 34, 993, 1575) for urea. 



The specific heats of ethyl and propyl alcohols and their 

 equimolar mixture have been studied in the liquid state down 

 to 78° K., and it is shown that down to this temperature the 

 heat capacity of the mixture is practically the same as the 

 mean of the heat capacities of two pure substances. This fact 

 indicates that the entropy difference between the equimolar 

 mixture and the two pure substances persists without appreci- 

 able diminution down to these temperatures, and probably to 

 the absolute zero. The specific heats of crystalline and liquid 

 ethyl alcohol also seem to indicate that if the entropy of the 

 crystalline form be zero at 0° K., then the entropy of the super- 

 cooled liquid is not zero. 



Lubrication and Chemical Constitution. — ^The relationship 

 between chemical constitution and lubrication has been in- 



