Precise Dimensions: A history of units from 1791–2018 by Malcolm Cooper Jim Grozier

Author:Malcolm Cooper, Jim Grozier
Language: eng
Format: epub
Publisher: IOP Publishing
Published: 2017-11-16T00:00:00+00:00

Let us now consider whether Thomson at this stage really succeeded in his self-imposed task of measuring absolute temperature. There were three major difficulties. The first one was clearly noted by Thomson himself: the formulae given above require the values of k, the latent heat of steam by volume, but Regnault had only measured the latent heat of steam by weight. Lacking the facility to make the required measurements himself, Thomson converted Regnault’s data into what he needed by assuming that steam obeyed the laws of Boyle and Gay-Lussac. He knew that this was at best an approximation, but thought there was reason to believe that it was a sufficiently good approximation for his purposes (Thomson [1848] 1882, pp 104–5).

Secondly, in calculating the amount of mechanical work, the entire analysis was premised on the assumption that the pressure of saturated steam depended only on temperature. That pressure-temperature relation was not something deducible a priori, but an empirically obtained generalization, whose rigorous reliability was not beyond doubt. Besides, the use of the pressure–temperature relation of steam amounted to a reliance on an empirical property of a particular substance, just what Thomson wanted to avoid in his theoretical definition of temperature. In his defence, however, we could argue that the strict correlation between pressure and temperature was probably presumed to hold for all liquid-vapor systems, not just for the water-steam system. We should also keep in mind that his use of the pressure-temperature relation was not in the theoretical definition of absolute temperature, but only in its operationalization. Since Carnot’s theory gave the assurance that all ideal engines operating at the same temperatures had the same efficiency, calculating the efficiency in any particular system was sufficient to provide a general answer.

Finally, in the theoretical definition itself, absolute temperature was expressed in terms of heat and mechanical effect. We have quoted Thomson above as taking comfort in that ‘we have, independently, a definite system for the measurement of quantities of heat’, but it is not clear what he had in mind there. The standard laboratory method for measuring quantities of heat was through calorimetry based on the measurement of temperature changes induced in a standard substance (e.g. water), but of course that had to rely on a thermometer. Recall that Thomson’s scheme for operationalizing absolute temperature was to express W/H as a function of air-thermometer temperature. A great deal of complexity would have arisen if the measure of H itself depended on the use of the air thermometer (if it had to be kept inside the integral in equation (5.4)). In one place Thomson mentioned using the melting of ice for the purpose of calorimetry, but there were significant difficulties in any actual use of the ice calorimeter (Thomson [1848] 1882, p 106). Still, we could say that in principle heat could be measured by ice calorimetry (or any other method using latent heat), in which case the measure of heat would be reduced to the measure of weight and the latent heat of the particular change-of-state involved.

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