246 



NA TURE 



[July 12, 1906 



number must be extended, if possible to looo, before the 

 worli of reduction is begun. May I ask for furtfier aid 

 in the matter? I shall be glad to send two or more 

 schedules to anyone who will help to get a faithful record. 



Karl Pearson. 

 University College, London, W.C. 



Thermodynamics of Diffusion. 

 In applying the principles of thermodynamics to diffusion 

 of gases, several pitfalls have to be guarded against. 



In the first place, if we adopt the old definition of 



■entropy in terms of integrals of the form IdQ/T, we are 

 almost certain to go wrong when we come to deal with 

 diffusion. If w-e imagine diffusion to take place between 

 two of the ideal " perfect gases " of our text-books at 

 constant pressure, volume and temperature, and without 

 gain or loss of heat, no quantity of the nature of dQ 

 appears to be associated with the phenomenon, and it is 

 easy to rush to the conclusion that no change of entropy 

 takes place. This danger is avoided if we adopt Mr. Swin- 

 burne's plan of defining entropy in terms of " waste " or 

 unavailable energy relative to an assumed auxiliary 

 medium. By " auxiliary medium " is here meant a 

 medium at uniform temperature T„ which can be used 

 indefinitely as a refrigerator in thermodynamic operations, 

 and any change in the amount of unavailable: energy under 

 such conditions, when divided by the temperature T„ gives 

 the corresponding change of entropy. 



If this definition is adopted we see that the phenomenon 

 of mixing the gases does not in itself suffice to determine 

 the changes of entropy associated with it. The matter 

 can only be decided by an appeal to experience as to the 

 means whereby the gases can be separated or mixed 

 reversibly. The case of an ideal " perfect gas " forms no 

 exception to this statement. 



The proper inference is, not that the diffusion involves 

 no change of entropy, but that the change of entropy, if it 

 exist, cannot be expressed as a sum of differentials of the 

 form <JQ/T. 



The second pitfall occurs when we take the well-known 

 expression for the entropy of a perfect gas in terms of 

 pressure (or volume) and temperature, and try by this 

 means to connect the entropy of the mixture with the 

 entropies of the components. Where we are likely to get 

 into trouble is by ignoring the integration constants in the 

 expressions for the entropy. There is no evidence from 

 mere thermodynamic reasoning that the constant does not 

 change in the process of diffusion. All we can infer is 

 that the change of entropy associated w'ilh the mixing 

 of gases at uniform pressure and temperature is constant, 

 i.e. independent of pressure and temperature. 



To sum up, then, even when we have defined an ideal 

 perfect gas in the ordinary way, and assumed the property 

 that two such gases can mix in a closed vessel without 

 change of pressure and temperature, thermodynamical con- 

 siderations still give us no information whatever as to the 

 change of entropy accompanying diffusion, and on this 

 point a further appeal to experience is necessary. 



This amounts to saying that our definition of perfect 

 gases is still incomplete. What further property shall we 

 assume in order to complete it? If we regard a " perfect 

 gas " as a mere invention on paper, the most tiseftil plan 

 is to. take some simple property which is approximately 

 satisfied in the case of actual gases and assume that this 

 property is accurately satisfied by our perfect gases. Now, 

 actual gases may be separated and re-mixed either by 

 diflTusion through a membrane or by liquefying, or, if pre- 

 ferred, freezing one of the constituents. 



Taking either of these processes, and making suitable 

 assumptions which would render that process perfectly 

 reversible, we are led to the inference that the whole 

 entropy of a mixture of perfect gases should be taken to 

 be equal to the sum of the whole entropies of its com- 

 ponents at the same temperature and partial pressure, 

 i.e. if each component occupied the same volume as the 

 ■final mixture. 



.According to this view, when diffusion takes place at 



NO. 191 5, VOL. 74] 



constant temperature and pressure, there is a gain of 

 entropy and a loss of available energy equal in amount to 

 that which would be incurred if each of the constituents 

 were to expand by rushing into a vacuum until it occupied 

 the same volume as the final mixture. 



There is another way of partially separating the con- 

 stituents of a gas mixture. If the mi.xture be introduced 

 into a field of force such as that due to the earth's attrac- 

 tion, or if we imagine it to be whirled in a centrifuge, the 

 denser gases will predominate in the lower parts of the 

 atmosphere or where the potential is greatest, and the 

 lighter gases will predominate in the upper regions oi' 

 where the potential is least. In this case the partial 

 separation is effected at the expense of work done by the 

 field of force. 



This note does not purport to deal in full detail with 

 the thermodynamics of diffusion, but merely to direct 

 attention to certain points which are easily overlooked. 

 One of the most important of these points is that the 

 possibility of producing mechanical work by the diffusion 

 of gases through a membrane at constant temperature is 

 not necessarily inconsistent with the principles of thermo- 

 dynamics or the ordinary definitions of a perfect gas. 



If anv physicist should claim to have discovered Max- 

 well's demons in connection with the diffusion of gases, the 

 first questions we should ask him are : — 



(1) Can he, without the performance of external work, 

 separate the gases in a mixture in such a way that the 

 temperature is the same at the end as at the beginning, 

 and the separated constituents each occupy volumes smaller 

 than that of the original mixture? 



(2) Can he obtain external work by the mixing of two 

 gases without change of temperature if the initial volume 

 of each gas is not less than the final volume of the 

 mixture? 



(3) .Are his claims based on new experimental evidence? 



G. H. Bryan. 



Early Meteors of the Perseid Shower. 



The moon being new on July 21 this year renders the 

 conditions favourable for observing the earlier members of 

 the great Perseid display. A few of these are usually 

 visible on July 15, and probably just before that night, and 

 it would be interesting if multiple observations of supposed 

 Perseids could be obtained so that their radiants might be 

 definitely assigned without the risk of error. 



A single record of a meteor-flight only permits an 

 assumption to be made as to the apparent radiant, and 

 mistakes frequently result. For example, if a streak- 

 leaving meteor, seen at the July-August epoch, happens to 

 be directed from the northern part of Perseus it will 

 certainly be attributed to the Perseid swarm, though it may 

 quite possibly have had its origin in a different shower 

 from Cassiopeia, Andromeda, Aries, Camelopardus or 

 Auriga. To avoid such errors of allocation it is proposed 

 to maintain simultaneous watches this year between Jul> 

 i^ and 28 from 10 to 12 p.m., and the writer would be 

 glad to hear particulars of any observations for comparison 

 with similar results obtained at Bristol. 



The mean height of the Perseid meteors has already been 

 satisfactorily deduced, but it seems desirable further to 

 investigate the position and motion of the radiant, especially 

 during the last half of July. Such meteors as appear 

 amongst the stars of Perseus or bordering constellations are 

 the best for indicating the exact place of the radiant, and 

 bright metf.'ors should alwavs be carefully registered. ;is 

 they are very likely to have been noticed elsewhere. The 

 centre of radiation travels from near 4> -Andromeda; at 

 the middle of July to a few degrees south of the star- 

 cluster at X Persei at the end, the ephemeris places 

 (Monthly Polices, Ixii., 169) being as under : — 



Date R.A. Dec. I Date R A. Dec. 



July 15 



lS'3 + 4S-9 ' July 25 



,, 17 I7-I+497 , .. 27 



., 19 i8-q+50-5 „ 29 



,, 21 20-8 + 5I-I j ,, 31 



,, 23 22-8 + 5I-8 ' Aug. 2 



Bishopston, Bristol. 



24-9 + 52-5 



27-i-f53-2 



29-3-t-53-8 



3i-6 + 54'4 



33'9 + SS'o 



W. F. Denning. 



