The Boltzmann constant and the new kelvin

If the plans of the International Committee on Weights and Measures (CIPM) are fulfilled [1, 2], in 2018 the 26th General Conference on Weights and Measures (CGPM) will redefine the kelvin by fixing the value of the Boltzmann constant. This will replace the current definition of the kelvin based on the triple point of water (TPW), which has stood since 1954 [3]. The change in definition is not expected to make an immediate or significant difference to measurement practice, except perhaps at very low and very high temperatures [4]. However, in the long term, the change will enable much greater improvements in practical thermometry than have been seen historically. From a technological and metrological perspective, the change is significant. The first temperature scale recognised under the Metre Convention was the constant-volume hydrogen gas thermometer described by Chapuis in 1888, which was used within the BIPM to calibrate mercury-in-glass thermometers [5, 6]. When used to interpolate between the two defining points on the Centigrade Scale at 0 °C and 100 °C, the gas thermometer was repeatable to a few millikelvin, but the measurements were difficult and time consuming. As Callendar reported [5], ‘It is impossible for those who have never worked with a gas thermometer to realise the extent of its shortcomings’. So he and others proposed the use of platinum resistance thermometers (PRT) as a practical alternative. Although Callendar’s platinum-resistance scale was in use from the early 1900s, due to the intervention of the First World War, a platinum resistance scale was not formally adopted as the International Temperature Scale (ITS) until 1927. The ITS-27 used PRTs to interpolate between the oxygen (−182.97 °C), ice (0 °C), steam (100 °C), and sulphur (444.6 °C) points. The scale also used platinum/platinum-rhodium thermocouples to define temperatures between 660 °C and 1063 °C, and Wien’s law for radiation thermometry above 1063 °C (the gold point). The reproducibility of ITS-27 at 100 °C was of the order of a few millikelvin [6], almost as good as the hydrogen gas thermometer. The main benefit of the new scale was that it allowed measurements to be made in hours rather than days, and required less expertise and patience. Subsequently, the 1927 scale has been replaced in 1948, 1968, and 1990, respectively, by the International Practical Temperature Scale (IPTS) of 1948, IPTS-68, and most recently, ITS-90 [5]. All of these scales have a similar structure to ITS-27, with defined fixed points and interpolating instruments, but have been responsible for only modest improvements in the reproducibility of temperature measurements. For example, a recent evaluation of the ITS-90 [7] shows the standard uncertainty at 100 °C is about 0.6 mK, which represents less than a factor of ten improvement over a century. Instead, the main benefits of the new scales have been coverage of wider temperature ranges and closer approximations to the thermodynamic temperature. In many respects, technological advances, especially in electronic instrumentation, have had a much greater impact on thermometry practice by making measurements very much faster and practical realisations of the scales easier. The work of Chapuis and Callendar occurred during a period when science was undergoing two major paradigm shifts. The first shift was the acceptance of the atomic hypothesis: that matter is made of discrete units. The main support for the hypothesis came from statistical mechanics, which had enabled Boltzmann, Gibbs, Clausius, and others to explain key properties of matter and a wide range of thermodynamic observations. Some of the most important results are the equations of state, which inter-relate different thermodynamic quantities, often including temperature. Although Boltzmann published his famous definition of entropy in 1877, the constant of proportionality in Boltzmann’s definition, was not identified as Boltzmann’s constant until 1900 when Planck published his analysis Printed in the UK S213 met © 2015 BIPm & IOP Publishing Ltd 2015 52 metrologia