On the theory of transient hot-wire measurement of the thermal conductivity of electrolytic solutions

In two previous works [2] and [3] the author has presented some investigations concerning measurement of the thermal conductivity of liquids by the transient hot-wire method. The "classical" field of application of this method is pure, dielectric liquids. In [3 ] was described a modification - worked out by the author - of the method to apply also to electrolytic solutions. In that modification the electrically insulating layer round the hot wire used - or proposed - by other authors for electrolytic measurements is avoided. The layer gives rise to practical and theoretical difficulties. For practical reasons it was necessary to limit in [3 ]the discussion of the underlying theory and mainly present the experiments. The purpose of the present work is to go more thoroughly into the theoretical foundation of the modification so that Us underlying idea and sources of error can be understood and estimated better. If one applies a voltage below the decomposition voltage of an electrolytic solution to the electrodes of a simple electrolysis system containing the solution, a pulse of current will pass through the liquid. The (non-linear) differential equation for the development in time of pulses of the simplest type is derived. Current pulses also occur in the modified apparatus and if the effect cf them does not fade out sufficiently fast they disturb the registrations during the measurement. The said equation is generalized to comprise the actual, more complicated apparatus, and on this basis a theoretical justification and explanation of the author's modification - i.e. of the contents of [3 ] - is set forth. In the last section the importance with regard to measurements of the ambiguity of the concept of thermal conductivity of mixtures owing to the so-called "cross-effects" is briefly discussed. The reason why the report is a little lengthy is, among other things, that an attempt has been made to make it a self-contained work, readable also to a researcher who is e.g. an expert in heat transmission, but less familiar with electrode kinetics. (The author himself is not an expert in the last-mentioned field, but has had to study it to some extent). Subsections II a and II b may be skipped by a reader familiar with electrode kinetics. The apparatus described in [3] was only developed te a semiautomatic stage. Now full automation has been introduced and a more comprehensive set of measurements has been carried out with very favourable results. The main purpose of the present report is to serve as a foundation to which can be referred in a final report containing a compact survey of the author's theoretical investigations on the method and giving the new measurements.