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Primary gas-pressure standard from electrical measurements and thermophysical ab initio calculations


Mechanical standards for measuring gas pressure up to 7 MPa based on a piston–cylinder system are known with relative uncertainties on the order of 1 ppm (ref. 1). The challenges in an experimental realization lie in determining the effective area of special pressure balances and in accounting for the pressure distortion. Comparisons of the mechanical pressure standard with independent methods to exclude sources of systematic uncertainty are currently available only around 0.1 MPa at the required uncertainty levels. Here, such an independent cross-check is performed up to 7 MPa based on electrical measurements of helium gas. Enabled by recent progress in ab initio calculations, pressure can be accessed through measurement of the dielectric constant. By using theoretical values for the polarizability and the virial coefficients of helium, the change in capacitance and hence the pressure can be determined up to 7 MPa. The relative uncertainty of this method is below 5 ppm and can serve as a new primary pressure standard complementary to the mechanical pressure standard. This answers the long-standing question whether a pressure standard based on capacitance measurements could be devised2.

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Fig. 1: Schematic illustration of the two completely different ways of measuring pressure p.
Fig. 2: Results of the comparison of mechanical and electrical pressure measurements.

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Data availability

The data represented in Fig. 2 are available in Supplementary Data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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Identification of commercial equipment and materials in this paper does not imply recommendation or endorsement by PTB, nor does it imply that the equipment and materials identified are necessarily the best available for the purpose.

Author information

Authors and Affiliations



C.G. and B.F. developed the DCGT set-up and supervised the whole project. W.S. conceived the idea of the mechanical pressure measurement and supervised the development and calibration work. C.G. performed the experiments. C.G. and B.F. analysed the data and wrote the manuscript. All authors contributed to scientific discussion of the manuscript.

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Correspondence to Christof Gaiser.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Jorge Torres Guzmán and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Data

The complete dataset of Fig. 2 is listed. The first six columns contain the left part of the figure and columns 10–16 contain the right part. Each column has an individual header further specifying the content.

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Gaiser, C., Fellmuth, B. & Sabuga, W. Primary gas-pressure standard from electrical measurements and thermophysical ab initio calculations. Nat. Phys. 16, 177–180 (2020).

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