56 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



SECTION C 



DETERMINATION OF A PRECISE, NUMERICAL, EXPRESSION FOR THE 

 ENTROPY OF ANY PHYSICAL CONFIGURATION 



PLANCK modestly says that everything essential in the deter- 

 mination of this expression has been done by L. BOLTZMANN, in 

 his wide range of physical investigation. PLANCK'S discussion, 

 however, is so compact and lucid that it is best suited for our 

 purpose. Keeping this purpose in mind we will here also abbre- 

 viate by dispensing with parts of PLANCK'S fuller proof and content 

 ourselves with the main steps which lead to the desired expression. 

 These main steps are as follows: 



(a) Determination of the general expression for the 



f Probability or 



^ T e . . ... \ of a given physical configuration of 



[ No. of complexions W J 



a known macroscopic state; 



(b) Determination of the general expression for the Entropy S 

 of a given physical configuration of a known macroscopic 

 state; 



(c) Special case of (b) namely, expression for the Entropy S of 

 the state of thermal equilibrium of a monatomic gas; 



(d) Confirmation, by equating this value of S with that found 

 thermodynamically and then deriving well-known results. 



(e) PLANCK'S conversion of the expressions of (b) and (c) into 

 more precise ones by finding numerical values of k 

 in C. G. S. units; in F. P. S. units; 



(/) Determination of the dimensions of the universal constant k 

 and therefore also of entropy in general. 



