Abstract
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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
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.
References
Zandt, T., Sabuga, W., Gaiser, C. & Fellmuth, B. Measurement of pressures up to 7 MPa applying pressure balances for dielectric-constant gas thermometry. Metrologia 52, S305–S313 (2015).
Moldover, M. R. Can a pressure standard be based on capacitance measurements? J. Res. Natl Inst. Stand. Technol. 103, 167–175 (1998).
Pavese, F. & Molinar Min Beciet, G. Modern Gas-Based Temperature and Pressure Measurements Ch. 7 (International Cryogenics Monograph Series, Springer, 2013).
Fellmuth, B., Gaiser, C. & Fischer, J. Determination of the Boltzmann constant—status and prospects. Meas. Sci. Technol. 17, R145–R159 (2006).
Gugan, D. & Michel, G. W. Dielectric constant gas thermometry from 4.2 K to 27.1 K. Metrologia 16, 149–167 (1980).
Gaiser, C. et al. Final determination of the Boltzmann constant by dielectric-constant gas thermometry. Metrologia 54, 280–289 (2017).
Schmidt, J. W. et al. Polarizability of helium and gas metrology. Phys. Rev. Lett. 98, 254504 (2007).
Gaiser, C. & Fellmuth, B. Polarizability of helium, neon and argon: new perspectives for gas metrology. Phys. Rev. Lett. 120, 123203 (2018).
Mohr, P. J., Newell, D. B., Taylor, B. N. & Tiesinga, E. Data and analysis for the CODATA 2017 special fundamental constants adjustment. Metrologia 55, 125–146 (2018).
Puchalski, M., Piszczatowski, K., Komasa, J., Jeziorksi, B. & Szalewicz, K. Theoretical determination of the polarizability dispersion and the refractive index of helium. Phys. Rev. A 93, 032515 (2016).
Cencek, W. et al. Effects of adiabatic, relativistic and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium. J. Chem. Phys. 136, 224303 (2012).
Garberoglio, G., Moldover, M. R. & Harvey, A. H. Improved first-principles calculation of the third virial coefficient of helium. J. Res. Natl Inst. Stand. Technol. 116, 729–742 (2011).
Shaul, K. R. S., Schultz, A. J., Koffke, D. A. & Moldover, M. R. Path-integral Mayer-sampling calculations of the quantum Boltzmann contribution to virial coefficients of helium-4. J. Chem. Phys. 137, 184101 (2012).
Rizzo, A., Hättig, C., Fernández, B. & Koch, H. The effect of intermolecular interactions on the electric properties of helium and argon. III. Quantum statistical calculations of the dielectric second virial coefficients. J. Chem. Phys. 117, 2609–2618 (2002).
Cencek, W., Komasa, J. & Szalewicz, K. Collision-induced dipole polarizability of helium dimer from explicitly correlated calculations. J. Chem. Phys. 135, 014301 (2011).
Gaiser, C. & Fellmuth, B. Highly-accurate density-virial-coefficient values for helium, neon and argon at 0 °C determined by dielectric-constant gas thermometry. J. Chem. Phys. 150, 134303 (2019).
Egan, P., Stone, J., Scherschligt, J. & Harvey, A. H. Measured relationship between thermodynamic pressure and refractivity for six candidate gases in laser barometry. J. Vac. Sci. Technol. A 37, 031603 (2019).
Rourke, P. M. C. et al. Refractive-index gas thermometry. Metrologia 56, 032001 (2019).
Jousten, K. et al. Perspectives for a new realization of the pascal by optical methods. Metrologia 54, S146–S161 (2017).
Zandt, T. et al. Capabilities for dielectric-constant gas thermometry in a special large-volume liquid-bath thermostat. Int. J. Thermophys. 32, 1355–1365 (2011).
Migliori, A. & Maynard, J. D. Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens. Rev. Sci. Instrum. 76, 121301 (2005).
Fellmuth, B., Bothe, H., Haft, N. & Melcher, J. High-precision capacitance bridge for dielectric-constant gas thermometry. IEEE Trans. Instrum. Meas. 60, 2522–2526 (2011).
Łach, G., Jeziorski, B. & Szalewicz, K. Radiative corrections to the polarizability of helium. Phys. Rev. Lett. 92, 233001 (2004).
Heller, D. F. & Gelbart, W. M. Short range electronic distortion and the density dependent dielectric function of simple gases. Chem. Phys. Lett. 27, 359–364 (1974).
Acknowledgements
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
Contributions
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.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
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.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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.
Rights and permissions
About this article
Cite this article
Gaiser, C., Fellmuth, B. & Sabuga, W. Primary gas-pressure standard from electrical measurements and thermophysical ab initio calculations. Nat. Phys. 16, 177–180 (2020). https://doi.org/10.1038/s41567-019-0722-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-019-0722-2