76 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



We might rest satisfied with this conclusion, but additional 

 light will be shed on entropy significance if we consider more 

 in detail the intermediate stages of this evidently irreversible 

 process. The rush of air from the full to the empty tank produces 

 whirls and eddies of a finite character and it is only when these 

 have subsided, by the conversion of the visible or sensible kinetic 

 energy of their particles into heat, that thermal equilibrium 

 obtains. But at each intermediate stage (while still visibly whirl- 

 ing and eddying) the gas possesses entropy, even while in the 

 turbulent condition. This is clear from our present physical 

 definition of entropy, namely, the logarithm of the number of 

 complexions of the state, for it is evident that even in this turbulent 

 state it possesses a certain number of complexions, however 

 difficult mathematically it may actually be to find this number. 

 BOLTZMANN found an expression for a ny condition ; PLANCK gave 

 it the form of Eq. (18), p. 63, 



Entropy = S= constant k / log/- <r, . . . (33) 



where k= 1.346 (io~ 16 ) (in the C.G.S. system) is a universal constant, 

 function / is the law of distribution of the particles and their 

 velocity elements and a = dx'dy'dz'd-dr)-dl > is a sort of fictitious 

 elementary region in a six-dimensional space. From its deriva- 

 tion and definition the value given for entropy S in Eq. (33) 

 depends only on the state of the body at the instant in question 

 and does not at all depend on its history preceding this instant. 



The difference between the value of S for the final state (say, 

 as given for a gas by Eq. 20) and the value of S as given by Eq. (33) 

 for the instant, constitutes the driving motive which urges the 

 gas toward thermal equilibrium. A similar difference or driving 

 motive is the underlying impelling cause of all natural phenomena. 



