696 



clear that the above mentioned calculations of the entropy of the 

 gases separately have only sense for another definition of entropy. 

 If the entropy is defined as a function of the probabiHty of the con- 

 dition, it is possible to tind a definite value for this entropy ; but 

 this value will vary with different meaning of the "probability". 

 Thus the expressions derived by Keesom '), Tetrode '), and Sackur ") 

 for the entropy of gases present differences which are the consequence 

 of different definitions of probability. These differences only occur in 

 the constant part ; if these differences cancelled each other in the 

 algebraic sum, a test by the equilibrium determinations could not 

 give a decision about the correctness of the entropy values. When, 

 however, the algebraic sum of the entropies according to Sackur 

 and Tetrode are drawn uj), it appears that these differences continue 

 to exist also in the algebraic sums, and it must therefore be possible 

 from experimental determinations at least if the accuracy is great 

 enough to get a decision which expression is correct. 



While these calculations yield a value for the entropy of the 

 gases separately, Prof, van der Waals Jr. has derived an expression 

 for the "equilibrium constant" of gas reactions, from which the 

 algebraic sum of the entropies can be easily derived; the entropy 

 of the gases separately is again determined here with the exception 

 of a constant. Besides this expression tries to take the variability of 

 the specific heat with the temperature into account^). 1 intend to 

 test this formula and the above mentioned expressions of Sackur 

 and Tetrode b} a number of data from the chemical literature. 



2. The expresdons for the entropy of gases. 



For monatomic gases Keesom, Sackur, and Tetrode give the value 

 for the entropy free from concentration (eventually after recalcula- 

 tion) successively by the following expressions: 



3 3 5 3 



R,_i =-RbiT A- -Rln R - - R In N + ~ RInm — d Rlnh -\- C, . (1) 



/ , 4/3Y/A 

 in which Ci represents according to Keesom RIn ji^R{4:^hi~-\ — \ 1 , 



3 3 



according to Sackur — R In 2jr-\-- R, and according to Tetrode 



1) Keesom. These Proc. XVI, p. 2ï!7, 669, XVII, p. 20. 



2) Tetrode. Ann. cle Phys. (4) 38. 434. 39. 255, (1912). 



8) Sackur. Ann. d. Phys. (4) 36. 958, (1911); 40. 67, 87, (1913). 

 *) These Proc. XVI p. 1082. 



