I don’t know about you, but when I studied engineering I always assumed that all the units we used had been agreed on by groups of scientists and were infallible. To my surprise, four units are now being redefined in terms of natural constants rather than properties of specific pieces of matter. The kilo, ampere, and mole are three of the units under revision. Researchers working on redefining the kelvin have announced they have rederived the Boltzmann constant with unprecedented accuracy.
The Boltzmann constant relates how much energy something has to its temperature and is in units of Joules/K. Currently, kelvin scale is based off the triple point of water, which happens when water can exist as a solid, liquid, and gas at 0.01C or 273.16K. Since the end of the last decade, groups of researchers have worked to obtain the Boltzmann constant at unprecedented levels of certainty using new tech. Once this constant was obtained, it could then be used to derive the kelvin temperature scale as a function thereof.
The first team to achieve this announced its findings last week. The team from the National Physical Laboratory (NPL) in Teddington, UK, was led by researcher Michael de Podesta. Six years was spent achieving the remarkable engineering and precision required by the nature of their experiment.
To find the Boltzmann constant, the team used acoustic thermometry -- determining the speed of sound in a known volume of air at a specific temperature. First, they had to fill a very specific volume with argon gas. Then, the team sent sound waves in the form of musical notes at different frequencies across this volume. In order to find the Boltzmann constant, one must find how much energy is in a given body of matter. In the case of the argon gas, the energy of the gas is directly related to the speed at which sound travels through it.
The NPL collaborated with the Scottish Universities Environmental Research Center (SUERC) and with Cranfield University. The team at Cranfield was responsible for creating this highly precise volume to use in the experiment. To do this, they used a single-crystal cutting tool to produce four copper hemispheres. They put the two best hemispheres together to create a triaxially ellpsoidal resonator. The reason the volume was not a perfect sphere is because a sphere is prone to complicated resonance within it, which would complicate the experiment.
The team fitted microwaves, of a specific frequency, inside this volume to accurately measure the volume of the space -- down to one thousandth of a millimeter (about 600 atoms). Knowing the nearly exact volume, they could then conduct the acoustic test. These tests used Gras Type 40DP acoustic transducers and were performed at the same temperature -- experimentally chosen at 0.01C or the triple point of water -- to finally derive the speed of sound across the argon gas:
1/2mv2 = 3/2kbT (looking for the kb)
Once the speed of sound is derived, this energy measurement is used to derive the Boltzmann constant. A Matlab script took data points on an Excel spreadsheet to perform data fitting. According to this first test, the new and improved constant is 1.380 651 56 (98). The part in parenthesis is the uncertainty UR = 0.71x10^-6, .71 ppm, or about half of what it used to be. This result is enough to officially redefine kelvin.
Before you go throw away your kelvin thermometer, it’s important to state a couple of things. First off, another research team from the Laboratoire National de Métrologie et d'Essais (LNE) in Paris repeated the experiment and got a different value with a slightly bigger uncertainty of 1.24 ppm. This discrepancy will have to be understood, and many more repetitions of these experiments must be done before the new constant is adopted by all. Another reason to keep your current thermometer is that the new constant will have negligible effects on temperatures near the triple point of water. However, the new definition of kelvin will influence those studying at temperature extremes.
Mike Moldover developed the first musical argon experiment he used to determine the Boltzmann constant at a record accuracy back in 1988. It’s only a matter of time before we see others reproduce the experiment and find the right constant and redefine other units of measurement. The consequences could be unforeseen when it comes to describing the coldest of space or the hottest matter around stars and black holes. The NPL results were published in the journal, Metrologia on behalf of the Comité international des poids et mesures (CIPM).