40 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



and Probability will be a very close one. We therefore place 

 at the head (forefront) of our further presentation the following 

 proposition: " The Entropy of a physical system in a definite 

 condition depends solely on the probability of this state" The 

 permissibility and fruitfulness of this proposition will become 

 manifest later in different cases. A general and rigorous proof of 

 this proposition will not be attempted at this place. Indeed, 

 such an attempt would have no sense here because without a 

 numerical statement of the probability of a state it could not be 

 tested numerically. 



(6) Planck's Formula for the Relation between Entropy and the 

 Number of Complexions 



Now we have already seen, from the permutation consider- 

 ations presented on p. 27, that the Theory of Probabilities leads 

 very directly to the theorem, " The number of complexions included 

 in a given state constitutes the probability W of that state" The 

 next step (omitted here) is to identify the thermodynamically 

 found expression for entropy of any state with the logarithm 

 of its number of complexions. 



PLANCK'S formula for entropy S is: 



5 = 1.35 loge (number of complexions) io~ 16 + constant K; 



here K is an arbitrary constant without physical significance 

 and can be omitted at pleasure; the numerical value in the first 

 term of the second member is the quotient of energy (expressed 

 in ergs) divided by temperature (C) . This certainly gives a phys- 

 ical definiteness and precision to entropy which leaves nothing 

 to be desired. 



PLANCK, in reproducing from probability consideration the 

 dependence of entropy 5 on probability W, finds the relation 



S = k log W+ constant, 

 when the dimensions of 5 evidently depend on those of constant k. 



