AND OF THE SECOND LAW 67 



2.8o 



cules in one pound of air would be ' 00 (ic? 6 ) =o.97(io 25 ). 



2o.oo 



Substituting the numerical value of universal constant k in 

 Eq. (10) we get Eq. (28). 

 For C. G. S. system, Entropy of any natural state, Eq. (28) is 



5 = i.346(io~ 16 ) log e (W) = i.346(io~ 16 ) log e (No. of complexions). 

 For F. P. S. system, Entropy of any natural state, Eq. (28) is 

 S=5.5o(io~ 24 ) ^& e (^) == 5-5( IO ~ 24 ) l& e (No. f complexions.) 



To each of these may be added an arbitrary constant. In 

 Eq. (20) we may substitute directly the equivalent of the product 

 kN found from Eq. (22), and then get for the entropy S of a 

 monatomic gas in the state of thermal equilibrium, 



(f log/+logF). . . . (29) 



When the volume V is known we can now readily find N 

 and then kN numerically, and place this number as a coefficient 

 in Eq. (20). 



Step/ 



Determination of the Dimensions of k or of the Entropy S 



It is at once evident from an inspection of the perfectly general 

 Eq. (10) that the dimensions of Entropy S depend solely on those 

 of the universal constant k. The relation given in Eq. (21) shows 

 at once that dimensions of dS depend upon the quotient found 

 by dividing energy by temperature and the relations given in 

 Eqs. (22) and (25) that the dimensions of constant k also depend 

 on this same quotient. The dimensions of Entropy 6 1 and of con- 

 stant k are therefore identical and this might suffice to show that 

 here neither S nor k is to be regarded as a mere ratio or abstract 



