388 REPORT — 1886. 



but was calculated from that for a half normal solution on grounds wliich I cannot 

 here set forth ; it may be affected by a somewhat greater error than the other 

 numbers, though not so great as to make the succession irregular or to account for 

 the irregularity of the succession. 



As may be seen from these numbers, there appears to exist a certain relation 

 between the internal friction and the conductivity of normal solutions, so that 

 to a great extent the higher the conductivity the smaller is the internal friction. 

 A detailed carrying out of this law is, however, impossible, since marked excep- 

 tions occur. Of the seventeen salts examined five are exceptions, viz., KNO3, 

 NaNOg, K/;03, KO.H3OJ, and ]\IgSO^. The exceptional behaviour of NH^Cl as 

 compared with KCl may be only apparent. (It is not unlikely that when salts of 

 lower conductivity are examined the exceptions may become more numerous and 

 more strongly marked.) 



In the hope that my note, though inconclusive, may add a little to the material 

 for discussion of a difficult subject, I subscribe myself 



Yours, &c., 



Stante Akrhenius. 



Electrochemical Thermociynamics. 



\_Since submitting proof sheets I have been f avowed with the folloiving most 

 interesting letter from Professor J. Willakd Gibbs. — 0. L.] 



New Haven : January 8, 1887. 



Dear Sir, — Please accept my thanks for the proof copy of your Report om 

 Electrolysis in its Physical and Chemical Bearings,which I received a few days ago 

 with the invitation, as I understand it, to comment thereon. 



I do not know that I have anything to say on the subjects more specifically 

 discussed in this report, but I hope I shall not do violence to the spirit of your 

 kind invitation or too much presume on your patience if I shall say a few words 

 on that part of the general subject which you discussed with great clearness in 

 your last report on pages 745, fi". (Aberdeen). To be more readily understood, I 

 shall use your notation and terminology, and consider the most simple casa 

 possible. 



Suppose that two radicles unite in a galvanic cell during the passage of a unit 

 of electricity, and suppose that the same quantities of the radicles would give 6e 

 units of heat in uniting directly, that is, without production of current ; wiU the 

 union of the radicles in the galvanic cell give 36e units of electrical work ? 

 Certainly not, unless the radicles can produce the heat at an infinitely high 

 temperature, which is not, so far as we know, the usual case. Suppose the 

 highest temperature at which the heat can be produced is t", so that at this tem- 

 perature the union of the radicles with evolution of heat is a reversible process ;. 

 and let t' be the temperature of the cell, both temperatures being measured on the 

 absolute scale. Now 6e units of heat at the temperature t" are equivalent to 



/' tf' — t' 



6e— units of heat at the temperature t', together with J0e-l_-_ units of mecha- 



t ^ 



nical or electrical work. (I use the term equivalent strictly to denote reciprocal con- 

 ■vertibility, and not in the loose and often misleading sense in which we speak of 

 heat and work as equivalent when there is only a one-sided convertibility.) 

 Therefore the rendement of a perfect or reversible galvanic cell would be 



Z6e ^^~ units of electical work, with 6e — units of (reversible) heat, for each 



t" t 



unit of electricity which passes. 



You will observe that we have thus solved a very different problem from that 

 which finds its answer in the Joule-Helmholtz-Thomson equation with term for 

 reversible heat. That equation gives a relation between the E. M. F. and the 

 reversible heat and certain other quantities, so that if we set up the cell and 

 measure the reversible heat, we may determine the E. M. F. without direct 

 measurement, or vice versa. But the considerations just adduced enable us to 

 predict both the electro-motive force and the reversible heat without setting up 



