6o4 



NA TURE 



[April 30, 1903 



gineering student soon emancipates himself from such 

 pedantry. The student who does not believe in the 

 worth of any kind of calculation or consideration of 

 what is going on in the cylinder is in a permanently 

 worse state, however, than even the unemancipated 

 pedant. Whether he reaches this position through 

 disgust or because he has never made any attempt to 

 compute, it may be premised that he is, or is destined to 

 be, a child of Gibeon. When he says he is designing 

 a new engine-, he means that he is copying an old 

 engine, introducing changes in detail which may or may 

 not be for the worse. Consciousness of his degraded 

 condition causes him to inveigh continually against all 

 knowledge (or, as he calls it, theory) ; all power to 

 compute beyond that which is possessed by the house- 

 keeper. To the man who practises the use of the A<£ 

 diagram, exercising' his common sense, bringing all 

 his other experience to bear, the thermodynamics of 

 heat engines is revealed as it can be revealed in no 

 other way. What is the p,v adiabatic for any kind 

 of wet or dry or superheated steam with any initial 

 pressure? How small is the thermodynamic value of 

 superheating, and how great is its value in giving a 

 dry cylinder? What is the exact benefit of using high 

 pressure steam? In what directions are we to work 

 in gas and oil engines, distinguishing between etfici- 

 ency as to energy and efficiency as to total money 

 values? Compare the commercial values of ammonium 

 anhydride and air as the stuff to be used in refriger- 

 ating machinery. It is really wonderful to see how a 

 man almost Illiterate, innocent of algebra, can use 

 his /,(p diagram of water-steam or air or ammonium 

 anhydride, obtaining in a few minutes answers to 

 problems which the mathematical engineers of twenty 

 years ago spent days in solving. We know men who 

 pet and fondle their slide rules, but the delight of these 

 men is nothing to that of the men who make a dailv 

 companion of their t,<p diagram. 



It is sometimes asked, During a change in which the 

 p or t is not the same for the whole of the stuff; we 

 can calculate the d> at the beginning and end, can we 

 speak of its value in the intermediate states? 



Now we know of no practical problem in which 

 there is need to speak of <f> in the intermediate states; 

 rj>. as carefully defined for the whole stuff, has no mean- 

 ing during the change any more than p or v or /. In 

 the case of a perfect gas allowed to expand freely 

 without doing work, say, to twice its volume, the 

 vessels being non-conducting^, a true p,v diagram of 

 the change cannot be imagined, and a true /,0 diagram 

 cannot be imagined. If, however, we are allow..] to 

 assume, as is usual, that kinetic energy in a gas is' 

 heat, it is probable that if for every infinitely small 

 portion of stuff we find the heat received by it dH at 

 the temperature t, then dHJt for this small portion is 

 a complete differential, and is its entropy, and the sum 

 of all the entropies of all the small portions may be 

 called the entropy of the whole stuff at each instant, 

 although this is outside the definition. From this 

 point of view we may speak of the entropy of the 

 whole as changing continuously from the initial to 

 the final condition. It was no doubt from this point 

 of view that Clausius, in the only place in which he 

 NO. 1748, VOL 67] 



speaks of entropy of a system in which the temperature 

 is not the same throughout, said " the entropy of the 

 universe tends to a maximum." However, it would 

 seem that it is dangerous to go outside the actual 

 definition in our use of the word entropy for the whole 

 of the stuff, and if so we had better say that, as we 

 cannot speak of the p or r of the stuff during such a 

 change as having any meaning, so we ought not to 

 speak of its (f> as having any meaning. Stuff carried 

 cyclically through the same series of changes over and 

 over again, like water in a steam engine or ammonium 

 anhydride in a refrigerator, returns again and again 

 to its original ; passes every cycle through the same 

 changes of cp. 



Unpractical people, that is, people who dislike exact 

 computation, occasionally exhibit annoyance when they 

 are told that they cannot understand how to use the 

 idea of entropy without a little study. This study may 

 b mathematical or experimental, or better, both. If 

 a non-mathematical person will accept in faith a few 

 statements such as will enable him to perform evict 

 computations with a t,<p diagram, it is astonishing how- 

 soon he can understand everything. This is how the 

 late Mr. Willans was enabled to effect his great im- 

 provements in the steam engine. But the unpractical 

 person who is not mathematical and refuses to experi- 

 ni. -n i with diagrams makes the assumption that 

 entropy is something he already knows about under 

 some different name — it is some form of energy or a 

 force or a pudding — and he writes great nonsense 

 about teachers and writers on thermodynamics. If he 

 is not quite ignorant he is more dangerous, for he 

 speaks of the entropy of a quantity of heat in a lurnace 

 of a boiler, and traces the entropv of this heat as it 

 passes to the condenser of a steam engine. Just as 

 we say that two and three are not six, or that the 

 world is not flat, so we say that to speak of the entropy 

 of a quantity of heat is to talk nonsense exactly analo- 

 gous with the volume of a quantity of work. We have 

 exactly the same right to speak of the pressure or 

 volume of a quantity of heat as of its entropy. We can 

 easily speak of the total work obtainable in a perfect 

 engine from a quantity of gas at high temperature in 

 a furnace. We can also see how the energy received 

 by it from fuel might have been received in a 

 very much better way if it is to be made avail- 

 able for the doing of work in a perfect engine. 

 All such "roblems are quite familiar to anyone who 

 uses the /,</) diagram. It is Dr. Diesel's way of look- 

 ing at this latter problem which is now so interesting. 

 The healing and cooling of stuff must be performed 

 In adiabatic compression and expansion. All heat must 

 be given to the stuff at the highest temperature; all 

 heal taken away at the lowest temperature. Not only 

 is this quite clear to users of the t,<]> diagram, but a 

 thing of more importance — the practical need for de- 

 parture from these perfect thermodynamic conditions 

 in actual engines. 



Thermodynamic efficiency is one thing, the efficiency 

 of which we speak when we think of the commercial 

 cost of large cylinders doing on the whole only a small 

 amount Oi useful Work, that is another thing. It is 

 an excellent exercise for a physics student to assume 



