Entropy 



By KARL K. DARROW 



MANY of the important ideas of physics are of such recent birth that 

 if they still seem hard to grasp, it may be contended that the world 

 has not yet had the time to assimilate them. Of entropy this cannot be 

 said; with its centenary almost upon us, entropy is ancient compared with 

 most of the concepts which baffle the student today. Yet an aura of mys- 

 tery seems to envelop it still, and two other things inseparably joined to it: 

 the scale of temperature called absolute, and the Second Law of Thermo- 

 dynamics. One is driven to wonder why the three of them resist the 

 understanding so tenaciously, and certain reasons are not hard to find. 

 Thus, to speak of the three as "joined together" is too weak, for it implies 

 that they can at least be taken in a certain order for didactic purposes, the 

 student ascending from the one to the next and finally to the last. Actually 

 they are much too tightly interlocked for this, a sort of trinity one and in- 

 divisible, which must be apprehended as a whole if ever to be properly 

 grasped at all. Again, the Second Law has been expressed in many different 

 ways, and it is one of the oddest things in science to see how various authori- 

 ties can claim that the law is obeyed absolutely without exception, while 

 they themselves cannot agree how to state it. A further cause of trouble 

 lies in the unlucky boundary between chemistry and physics, which nowhere 

 harms these sciences more than in the study of entropy. Like the worst of 

 the old-fashioned boundaries of Europe, it wanders capriciously across the 

 natural lines of intercourse and trade, cutting off the traditional chemist 

 from the origin and development of some of his most valuable ideas, cutting 

 ofif the traditional physicist from some of the finest verifications of the 

 thought of his fore-runners. It will be the principal object of this paper to 

 dwell on these verifications, abolishing the barrier so far as may be feasible. 

 First to illustrate how the three ideas are tangled up together, I give one 

 of the most useful of the definitions of entropy: when a system passes in a 

 reversible way from one to another state, at a constant absolute temperature T, 

 its change of entropy AS is equal to the heat Q which it absorbs, divided by T. 

 That both the entropy and the absolute temperature have slipped into this 

 definition is all too obvious; as for the Second Law, it lurks underneath the 

 phrase "in a reversible way." Quite evidently we are invited to master all 

 the three in a single mental operation, but quite as evidently this is impos- 

 sible. A breach must somehow be made in this hard and unified surface, 



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