# Kilogram

### The Unit – kilogram, kg (manokaramu)

Mass and its related quantities, such as pressure and density, are amongst the most commonly encountered quantities in our everyday lives. They are used in everything from supermarkets to international trades; and from manufacturing and transport to scientific research.

The SI unit of mass is the kilogram (kg). Before 1889, the kilogram had been defined as the mass of a litre of water at 4 °C. The first General Conference on Weights and Measures (CGPM) in 1889 sanctioned the use of a highly-polished cylinder of platinum-iridium – the International Prototype Kilogram (IPK) – to define the standard of mass. For more than a century, this physical artefact served as the world’s kilogram, and it, along with its six official copies, are stored under controlled conditions inside a vault at the Bureau International des Poids et Mesures (BIPM), Paris.

The need for a new definition of the kilogram – one based on a natural constant that is invariant over time – was established several decades ago. Despite careful handling, on four occasions since its inception, mass comparison studies between the IPK and its copies have shown mass divergences of up to 70 µg. As a consequence, the accuracy of other critical measurement units that depend on the kilogram, such as the newton (force), pascal (pressure), joule (energy) and ampere (current), could be called into question. The accuracy with which these units could be realised was, in fact, limited by the uncertainties in the stability of the IPK.

The role of the IPK changed forever on 20th May 2019. This was part of a wider revision of the SI that involved moving away from material artefacts, and instead defining all base units in terms of a set of constants of nature. For the kilogram, that constant was the Planck constant, h, which links the amount of energy a photon carries to the frequency of its electromagnetic wave. The new definition is as follows:

“The kilogram is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 x 10-34 when expressed in the unit J s, which is equal to kg m2 s-1 , where the metre and the second are defined in terms of c (the speed of light) and ΔVCs (the caesium frequency).”

Since the 1970s, several national laboratories worked on primary methods capable of realizing the new definition of the kilogram. There are currently two techniques that can achieve relative uncertainties of a few parts in 108:

One method involves counting the atoms in a pure silicon-28 sphere. The mass of this sphere can be first expressed in terms of the mass of a single silicon atom, and X-ray imaging is used to determine the actual number of atoms present in the crystal. Through the Avogadro’s constant, which can be linked to the now-fixed value of the Planck constant (h = 6.626 070 15 x 10–34 kg m2 s–1), this method allows mass to be expressed in terms of constants of nature

The second method uses an apparatus known as the Kibble balance to obtain a value for Planck’s constant by comparing the gravitational force on a test mass with the electromagnetic force on a coil carrying current in a magnetic field. When the current and voltages on the coil are measured using the Josephson effect and the quantum Hall effect, a direct link can be established between mass and the Planck constant.

Basing the definition of mass on Planck’s constant not only makes the kilogram more stable, but it allows the kilogram to be realised in any corner of the earth, rather than relying on a physical artefact stored in Paris. Although the definition of the kilogram has changed, all reliable mass measurements in New Zealand can still be referenced to MSL’s primary kilogram for the immediate future.

### Technical Capability

We are leading experts in mass, pressure, density and volume measurements. We have the capabilities to perform high-accuracy calibration of reference weights and pressure measuring instruments, and carry out measurements of the density and volumes of solid objects and liquids. We do this by using state-of-the-art mass comparators and balances, pressure balances, deadweight testers, differential pressure generators, barometers, densitometers and hydrostatic weighing, supported by ongoing research in methods and analysis. We can also provide advice on the measurement of other mass-related quantities, such as flow, force, torque and hardness.

### Our Research

Our main focus is on building a unique Kibble balance based on a twin pressure balance, which offers to be a relatively cost-effective way to disseminate the kilogram following the redefinition. Other mass research includes: improved methods and analysis of mass comparison, stability of mass artefacts following cleaning of surfaces, and automatic weighing systems. We’re interested in pressure balance elastic distortion and generation of small absolute and differential pressures. In density measurements, we focus on the development of electronic densitometers, calibration and reference liquids.

### Relevant Publications

1 C M Sutton, M T Clarkson and Yin Hsien Fung, “The MSL Kibble balance weighing mode^{”}, CPEM 2018 Conf. Digest., Paris, France, July 8-13, 2018.

2 M Stock, S Davidson, H Fang, M Milton, E de Mirandés, P Richard and C Sutton”, Maintaining and disseminating the kilogram following its redefinition”, Metrologia 54 (2017) S99.

3 C M Sutton, M T Clarkson and W M Kissling, “The feasibility of a watt balance based on twin pressure balances”, CPEM 2016 Conf. Digest., Ottawa, Canada, July 10 - 15, 2016.

4 M T Clarkson, C M Sutton and R Mason, “An apparatus for accurate measurement of the temperature dependence of permanent magnetization”, Measurement Science & Technology 25 (2014) 085902, published 8 July 2014.

5 C M Sutton and M T Clarkson, “A magnet system for the MSL watt balance”, Metrologia 51 (2014) S101-S106, published 31 March 2014.

6 C M Sutton, “Progress with MSL’s watt balance - and differences from other watt balances”, presented to the APMP TCM Technical Workshop, Taipei, Chinese Taipei, 25 - 26 November 2013.

7 C M Sutton, M P Fitzgerald and K Carnegie, “Improving the Performance of the Force Comparator in a Watt Balance based on Pressure Balances”, CPEM 2012 Conf. Digest., Washington DC, USA, pp.468-469, July 1-6, 2012.

8 K. Jones, L. A. Christian and C. M. Sutton, “Coil Correction for Oscillatory Calibration of a Watt Balance”, CPEM 2012 Conf. Digest., Washington DC, USA, pp. 330-331, July 1-6, 2012.

9 L A Christian, T J Stewart and C M Sutton, “Investigation of ac voltage measurement requirements for an oscillatory dynamic mode version of the watt balance”, CPEM 2010 Conf. Digest., Daejeon, Korea, pp.151-152, June 13-18, 2010.

10 C M Sutton, M P Fitzgerald and D G Jack, “The concept of a pressure balance based watt balance”, CPEM 2010 Conf. Digest., Daejeon, Korea, pp.131-132, June 13-18, 2010.

11 C M Sutton, “An oscillatory dynamic mode for a watt balance”, Metrologia**46** (2009) 467-472.

12 C M Sutton, “On Watt Balance Design for a Non-Artefact Kilogram”, Proceedings of Asia-Pacific Symposium on Mass, Force and Torque (APMF 2007), Oct 24 – 25, 2007.

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