# The Kilogram - the Unit of Mass

The 26th General Conference on Weights and Measures (CGPM) has adopted a revision of the International System of Units (SI) on 16th November 2018, effective from 20th May 2019. As a result, all SI units refer to fixed values of seven constants of nature. In the new SI, the kilogram will be derived from a fixed value of the Planck constant h (in conjunction with fixed values of the frequency of the unperturbed ground state hyperfine transition frequency of the 133Cs atom ΔvCs and of the speed of light in vacuum c) [1-4]:

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 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 and ΔvCs.

As a consequence of the new definition, the standard uncertainty (k = 1) of the mass of the international prototype of the kilogram with respect to the Planck constant amounts to 0.010 mg (relative 1 × 10-8). This uncertainty contribution needs to be taken into account in the dissemination of the mass unit after 20th May 2019. After completion of the first key comparison of realisations of the new definition of the kilogram, mass calibrations at PTB will be traceable in the new SI to a consensus value, determined from the comparison in accordance with the CCM Recommendation G1 (2017) [5, 6].

Literature

[1]    Resolutions of the 26th meeting of the General Conference of Weights and Measures (CGPM), Versailles, 13-16 November 2018,
https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf

[2]    PTB: Research on the new SI,
https://www.ptb.de/cms/en/research-development/research-on-the-new-si.html

[3]    Draft mise en pratique for the definition of the kilogram in the new SI:
www.bipm.org/utils/en/pdf/si-mep/MeP-kg-2018.pdf

[4]    Bureau International des Poids et Mesures: The International System of Units (SI), Draft of the 9th SI Brochure, 02/2019,
https://www.bipm.org/utils/en/pdf/si-revised-brochure/Draft-SI-Brochure-2019.pdf

[5]    Consultative Committee for Mass and Related Quantities (CCM): Report of the 16th meeting (18-19 May 2017) to the International Committee for Weights and Measures,
https://www.bipm.org/utils/common/pdf/CC/CCM/CCM16.pdf

[6]    Consultative Committee for Mass and Related Quantities: CCM short note on the dissemination process after the proposed redefinition of the kilogram. Version 1.4, 19/06/2018,
www.bipm.org/utils/en/pdf/si-mep/short-note-kg-dissemination-2018.pdf

### The international prototype of the kilogram

The international prototype of the kilogram is a cylinder 39 mm in height and 39 mm in diameter. It consists of an alloy of 90 % platinum and 10 % iridium (density of appr. 21500 kg/m3) and is maintained at the International Bureau of Weights and Measures (BIPM) in Sèvres near Paris. The national prototypes of the signatories of the Metre Convention are official copies of the international prototype of the kilogram, made of the same material with the same dimensions and surface properties.

### National prototype of the kilogram No. 52 of the Federal Republic of Germany

The national prototype of the kilogram of the Federal Republic of Germany is maintained under two bells jars at standard ambient conditions at the PTB in Braunschweig.

About every 10 years, its traceability to the international prototype at the BIPM is reconfirmed. The secondary standards of stainless steel are linked up with the national prototype once a year.

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## Prototype Balance of the PTB

The most accurate balances of the PTB are high-resolution 1 kgmass comparators. They are accommodated in a pressure-tight enclosures. Mass comparisons can be performed with standard deviations of less than 0,4 µg ( ≤ 4•10-10 kg).

Prototype balances are used for the:

• link up of PTB’s secondary standards with the national prototype
• realisation of the mass scale starting from 1 kg down to 100 g
• calibration of mass standards and weights (nominal values 100 g, 200 g, 500 g, 1 kg) with smallest uncertainties according to the CMC1  tables of the BIPM2
• mass determination of silicon spheres used as primary standards of the solid density and for the determination of the Avogadro constant

Furthermore, with these balances mass determinations are performed under vacuum conditions (≤ 0,1 Pa). Air buoyancy and sorption effects are investigated and corrected by means of comparison measurements in air and in vacuum.

1 Calibration and measurement capabilities
2 kcdb.bipm.org/appendixC/

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Mass comparator Mettler M_one
for measurements in a pressure-tight enclosure in air under constant pressure and in vacuum, automatic weight exchange mechanism with 6 positions, nominal load 1 kg, standard deviation (typ.) ≤ 0,4 µg

Mass comparator Sartorius CCL1007
for measurements in a pressure-tight enclosure in air under constant pressure and in vacuum, automatic weight exchange mechanism with 8 positions, nominal load 1 kg, standard deviation (typ.) ≤ 0,2 µg

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