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The Limitations of the Weston Cell As a Standard of Electromotive Force

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The Limitations of the Weston Cell As a Standard of Electromotive Force Home Search Collections Journals About Contact us My IOPscience The Limitations of the Weston Cell as a Standard of Electromotive Force This content has been downloaded from IOPscience. Please scroll down to see the full text. 1909 Proc. Phys. Soc. London 22 369 (http://iopscience.iop.org/1478-7814/22/1/327) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 130.102.42.98 This content was downloaded on 03/10/2015 at 01:04 Please note that terms and conditions apply. WESTON CELL AS STANDARD OF ELECTROMOTIVE FORCE. 369 XXVI. The Linzitntioizs of the Weston Cell as a Standard of Electromotive Force. By S. W. J. SMITH,M.A., D.Sc., Lecturer on Physics, Inzperial College of Science aid Technology. $1. THIS paper contains an attempt to explain Mr. F. E. Smith’s recent experiments on the cadmium amalgams of the Weston cells 1- in terms of the theory of solutions. The manner in which, according to this theory, the amal- gams crystallize is indicated, and it is shown why, with this mode of crystallization, the effect of the slowness of diffusion is so pronounced, and also why sudden cooling to a tempe- rature below the freezing point of mercury must produce a comparatively uniforin alloy. The cause of the most obvious differences between the behaviour of the “chilled” and of the “ slowly cooled” amalgarns is then at once apparent. But there are certain much less obvious differences of which, in view of the importance of the Weston cell as a standard (if for no other reason), it is desirable to know the cause. ’ An all-fluid amalgam, of course, yields the same E.M.F. whether previously chilled or cooled slowly. An all-solid alloy, on the other hand, always gives a higher E.M.F. when solidified by chilling. The E.M.F. of the chilled amalgam thus in general equals or exceeds that of the slowly cooled amalgam. But in the range of the two-phase alloys, over which the E.M.P. varies comparatively little with the total percentage of Cd, the opposite is true. The E.M.F. of the slowly-cooled amalgam now either equals or exceeds that of the chilled amalgam. The excess never amounts to more than a few hundred- thousandths of a volt ; but is important in measurements of the highest precision and requires explanation. It is shown that this phenomenon may be due to elcctro- lytic surface effects arising from the lightness and want of * Rend illay 27,1910. t PYOC.Piiys. Soc. vol. xxii. 1910, pp. 11-40. VOL. XXII. 2c 3 70 DR. S. W. J. SMITII ON THE WESTON CELL uniformity of composition oE the solid grains in the slowly cooled alnnlgnms. Instances of similar effects, liable to escape noticc, are to be found aiiioiigst the data for the all-solid alloys. FinalIy, the question as to whether there is any range over wliicli the E.M.F. is absolutely iiiclc1)endcnt of tile percentage oE cadmium is discussed. Theory mid experiment alike suggest tlra t the E.M.F. must rise as the percentage increases ; but tlie T ariatioil frequently does not amount to more t1i:in a few niilliontl~s of a volt for one per cent. variation of tlie cndiniuni content. Q 2. A ?node of c?ystallization of binnr,y allojs.-!L'he various ways in which fluid inistnres of two mctnls can frccze h:ive been carefully studied within receiit years. One Fig. I. AS A STANDARD OF ELECTROMOTIVE FORCE. 371 ordinates represent temperatures. The melting point of A is 8,. Tlie " freezing point curve ') O,,LI'C( gives the tempera- tures at which different alloys begin to solidify, and shows that the freezing point rises continuously as the percentnge of B in the iiiisture increases. The " melting point curvs " @,& gives the composition of the solid which depcsits from any particular liquid when it begins to fkeeze. Thus a cooling fluid containing $7 per cent. of B begins to freeze at I) and y is the percentage of B which the solid first deposited con- tains. At any given temperature (@), liquid and solid alloys c;in exist in eqnilibriuni only when their percentage composi- tions have definite values (represented by m and y respectively). The thermodynamical method of accounting for this condition of equilibrium is referred to Inter ($5 12 and 14). Roozeboom was the first to suggest that the thermal variation of the constitution of cadtniuni amalgams may be determined Ey curves like those of fig. 1, so long as the percentage of cadmium does not pass a certain limit (not exceeded in the experinieiits discussed below), and this suggestion was found to accord with various experimental data obtained by Bijl. 6 3. Recent expe~imeiztson cadnzium am~1gams.- Mr. I?. E. Smith has thrown fresh light upon the problem and provided new material for in veqtigation by examining the effect of " chilling," i. e. of cooliiig the arnalgains suddenly from temperatures at which they are wliolly fluid to a temperature below tlro freezing point of mercury. The most striking result of his experinients is shown in fig. 2, which exhibits (din~raminntic:illy)how, at a constant tcinpcrature, the E.M.F. of a Weston cell alters with the percentnge of Cd in the nin:ilg:im. In one set of esperi- inents, represented by the curve ABCD, the ainalpni was cooled suddenly (as above) to -50' U. and then allowed to rise in temperature to 0' C. before the cell of which it formed part was constructed. In the other set, represented by ABJW, the nuidgain 11 as cooled '' Jowly )' (i. e. froin tlle liquid state to 0" C. in several hours) before being used. On the scale of representation, the curves are identical froin A to C, and BCE is a 1iorizont:il straight line. Tlic BC:! 372 DR. S. W. J. SMITH ON THE WESTON CELL observed time effects and variations in the horizontal parts of the curves are discussed 1,‘I t er. It is easy to anticipate from fig. 1 that the curve for measurements like those of fig. 2 will consist of two bra11clIe~ Fig. 2. joined by an intermediate horizontal portion. For at a given temperature 8, any amalgam containing less than Lt!per cent. Cld would be all-liquid, and any amalg.,am containing inore than y per cent. Cd might be all-solid ; while intermediate amalgams could consist of mixtures in different proportions of z per cent. liquid and ,y per cent. solid respectively. In all-liquid and all-solid umalgams the clectroino tive force would, it is natural to suppose, vary continuously with the percentage of Cd. In mixtures consisting of the same two constituents (in different proportions) it might similarly be expected that the electromotive effect would remain const:int. In this way the general form, either of ABCD or of ACEF, could be accounted for ; but the cause of the dif- ference between the two curves is not iinmediately obvious. 8 4. The $*eezing of slowly-cooled amalganas.--To under- staid the exact significance of fig. 2, it is necessary to consider how a mixture, to whicli fig. 1 applies, freezcs. According to this figure, an alloy containing a per cent, AS A STANDARD OF.ELECTROMOT1VE FORCE. 3i3 Cd should begin to freeze at 8, and should apparently become solid at 62. But, because of the extreme slowness of diffusion in solids, this will happen only when the rate of cooling is so slow that it cannot be dealt with in practice. At the temperature a fluid amalgam containing U per cent. Cd and n solid amalgnm containing b per cent. Cd are in equilibrium. When the temperature is lowered slightly n fluid amalgam containing slightly less than a per cent. Cd will be in equilibrium with a solid amalgam containing slightly less than Z, per cent. A small quantity of the a per cent. amalgam may therefore solidify. As the temperature falls the percentages of Cd contained by fluid and solid amalgains in equilibrium become continu- otisly lower. The amount of solid material will therefore iiicrease; but the percentage of Cd in the newest crystals will always be less than ia those previously .formed. The fluid esisting at any given stage of the cooling will be in equilibrium with the solid with which it is in direct contact, but, since most of the successive growths will take place around earlier crystals, this solid will in general enclose older solid, richer in Cd. There mnst thus be LL continuous diffusion of Cd in the crystallized part of the material from within towards the surface. In any practical case, where the rate of cooling is not infinitely slow, the diffusion outwards will be very graduaI and mill not keep pace with the lowering of temperature. Thus, although (for true equi!ibrium) an amalgam con- taining a per cent. Cd should be all-solid just below e,, a considerable quantity of liquid, containing c per cent. Cd, will remain. The solid in contact with this liquid will contain cc per cent. Cd, but will envelop a considerable quantity of solid richer in Cd than itself, and there will be, in conse- quence, neither so little c per cent. liquid nor SO much a per cent. solid as true equilibrium would imply. A superior estimate of the amount of liquid remaining at 0, can, however, be found. Thus we may imagine that the cooling from ~9~to e,, of an amalganl containiiig a per cent.
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