# Today’s best value for the Boltzmann constant k:

## Boltzmann constant k will have a fixed value in the new SI system

Today’s accepted best value of Boltzmann’s constant is the “2010 Codata value”:

k = 1.380 6488 . 10-23 JK-1, and the standard uncertainty is:

su = 0.000 0013 . 10-23 JK-1

## Fundamental constants and the SI system of units:

Each fundamental constant Q is a product of a number {Q} and a base unit [Q]:

Q = {Q} x [Q],

for example Boltzmann’s constant is:

k = 1.380650 x 10-23 JK-1.

Thus we have two ways to define the SI system of SI base units:

- we can fix the units [Q], and then measure the numerical values {Q} of fundamental constants in terms of these units (method valid today to define the SI system)
- we can fix the numbers {Q} of fundamental constants, and then define the units [Q] thus that the fundamental constants have the numerical values {Q} (future method of defining the SI system)

## Boltzmann constant k and the new framework for the SI system of units:

Over the next few years the SI system of units will be switched from the today’s method (1.) where units are fixed and numerical values of fundamental constants are “variable”, i.e. determined experimentally, to the new method (2.) where the numerical values of the set of fundamental constants is fixed, and the units are defined such, that their definition results in the fixed numerical values of the set of fundamental constants. This switch to a new definition of the SI system requires international agreements, and decisions by international organizations, and this process is expected to be completed by 2018.

## Boltzmann constant k and the SI unit for temperature Kelvin:

Today’s method (1.) above is problematic: The SI unit of temperature, Kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature at the triple point of water. The problem is that the triple point depends on many factors including pressure, and the precise composition of water, in terms of isotopes and impurities. In the current definition the water to be used is determined as “VSNOW” = Vienna Standard Mean Ocean Water. Of course this is highly problematic, and the new method (2.) will not depend on VSNOW any longer.

In the new system (2.) the Kelvin will be defined as:

Kelvin is defined such, that the numerical value of the Boltzmann constant k is equal to exactly 1.380650 x 10-23 JK-1.

## Measurements of Boltzmann constant k:

In order to link the soon to be fixed numerical value of Boltzmann’s constant to currently valid definitions of the Kelvin, and in particular to determine the precision and errors, it is necessary to measure the value of Boltzmann’s current in terms of today’s units as accurately as possible, and also to understand and estimate all errors in the measurement. Several measurements of Boltzmann’s constants are being performed in laboratories around the world, particularly at several European and US laboratories.

### Dr Michael de Podesta, National Physical Laboratory (NPL), UK

Arguably today’s best measurement has been performed by Dr Michael de Podesta MBE CPhys MInstP, Principal Research Scientist at the National Physical Laboratory NPL in Teddington, UK, who has kindly discussed his measurements and today’s status of the work on the system of SI units and its redefinition with me, and has greatly assisted in the preparation of this article. Dr Podesta’s measurements of Boltzmann’s constant have been published in:

Michael de Podesta et al. “A low-uncertainty measurement of the Boltzmann constant”, Metrologia **50** (2013) 354-376.

Dr Podesta’s measurements are extremely sophisticated, needed many years of work, and cooperations with several other laboratories. Dr. Podesta and collaborators constructed a highly precise resonant cavity filled with Argon gas. Dr. Podesta measured both the microwave resonance modes of the cavity to determine the precise radius and geometry, and determined the speed of sound in the Argon gas from acoustic resonance modes. Dr Podesta performed exceptionally accurate measurements of the speed of sound in this cavity, which can be said to be the most accurate thermometer globally today. The speed of sound can be directly related to 3/2 k.T, the mean molecular kinetic energy of the Argon molecules. In these measurements, Dr. Podesta very carefully considered many different types of influences on his measurements, such as surface gas layers, shape of microwave and acoustic sources and sensors etc. He achieved a relative standard uncertainty of 0.71. 10-6, which means that his measurements of Boltzmann’s constant are estimated to be accurate to within better than on millionth. Dr. Podesta’s measurements directly influences the precision with which we measure temperature in the new system of units.

Over the last 10 years there is intense effort in Europe and the USA to build rebuild the SI unit system. In particular NIST (USA), NPL (UK), several French institutions and Italian institutions, as well as the German PTB (Physikalische Technische Bundesanstalt) are undertaking this effort. To my knowledge there is only very small or no contribution from Japan to this effort, which was surprising for me.

## Boltzmann constant k – today’s best value

Today’s accepted best value of Boltzmann’s constant is the “2010 Codata value”:

k = 1.380 6488 . 10-23 JK-1, and the standard uncertainty is:

su = 0.000 0013 . 10-23 JK-1

Copyright·©2014-2015 ·Eurotechnology Japan KK·All Rights Reserved·