We review recent determinations of the Boltzmann constant kB and the differences T − T90 that used cylindrical acoustic gas thermometry (c-AGT). These determinations measured the acoustic resonance frequencies of argon gas enclosed by metal-walled, cylindrical cavities. (Here, T is the thermodynamic temperature and T90 is the temperature measured on the International Temperature Scale of 1990, ITS-90.) In the range 234–303 K, the standard uncertainty of c-AGT ranges from 1.9 × 10−6 T to 2.6 × 10−6 T. This uncertainty is much smaller than the errors in ITS-90; therefore, c-AGT can help improve ITS-90. Moreover, we are extending c-AGT up to 1358 K. With increasing temperatures, c-AGT becomes advantageous relative to AGT based on quasi-spherical cavities because long cylindrical cavities (1) naturally fit into cylindrical heat pipes or multi-shelled thermostats; (2) provide the immersion required by transfer temperature standards, such as long-stemmed platinum resistance thermometers; and (3) have more useful, low-frequency acoustic resonances. In preparation for high-temperature c-AGT, we identified suitable materials for fabricating cylindrical cavities and we developed techniques for measuring acoustic resonance frequencies using sources and detectors outside the high-temperature thermostat. We also considered alternative test gases and optimal dimensions of cavities.
REFERENCES
1.
R. L.
Rusby
, R. P.
Hudson
, M.
Durieux
, J. F.
Schooley
, P. P. M.
Steur
, and C. A.
Swenson
, “Thermodynamic basis of the ITS-90
,” Metrologia
28
, 9
(1991
).2.
T. J.
Quinn
, T. R. D.
Chandler
, and A. R.
Colclough
, “A new determination of the gas constant by an acoustical method
,” Nature
250
, 218
(1974
).3.
M. R.
Moldover
, J. B.
Mehl
, and M.
Greenspan
, “Gas‐filled spherical resonators: Theory and experiment
,” J. Acoust. Soc. Am.
79
, 253
(1986
).4.
K. A.
Gillis
, M. R.
Moldover
, and A. R. H.
Goodwin
, “Accurate acoustic measurements in gases under difficult conditions
,” Rev. Sci. Instrum.
62
, 2213
(1991
).5.
I. M.
Mills
, P. J.
Mohr
, T. J.
Quinn
, B. N.
Taylor
, and E. R.
Williams
, “Redefinition of the kilogram, ampere, kelvin and mole: A proposed approach to implementing CIPM recommendation 1 (CI-2005)
,” Metrologia
43
, 227
(2006
).6.
J.
Fischer
et al, “The Boltzmann project
,” Metrologia
55
, R1
(2018
).7.
M. R.
Moldover
, J. P. M.
Trusler
, T. J.
Edwards
, J. B.
Mehl
, and R. S.
Davis
, “Measurement of the universal gas constant R using a spherical acoustic resonator
,” Phys. Rev. Lett.
60
, 249
(1988
).8.
L.
Pitre
, C.
Guianvarc’h
, F.
Sparasci
, A.
Guillou
, D.
Truong
, Y.
Hermier
, and M. E.
Himbert
, “An improved acoustic method for the determination of the Boltzmann constant at LNE-INM/CNAM
,” C. R. Phys
10
, 835
(2009
).9.
M. R.
Moldover
, S. J.
Boyes
, C. W.
Meyer
, and A. R. H.
Goodwin
, “Thermodynamic temperatures of the triple points of mercury and gallium and in the interval 217 K to 303 K
,” J. Res. Natl. Inst. Stand. Technol.
104
, 11
(1999
).10.
G. F.
Strouse
, D. R.
Defibaugh
, M. R.
Moldover
, and D. C.
Ripple
, “Progress in primary acoustic thermometry at NIST: 273 K to 505 K
,” AIP Conf. Proc.
684
, 31
(2003
).11.
D. C.
Ripple
, G. F.
Strouse
, and M. R.
Moldover
, “Acoustic thermometry results from 271 to 552 K
,” Int. J. Thermophys.
28
, 1789
(2007
).12.
R.
Underwood
, M.
de Podesta
, G.
Sutton
, L.
Stanger
, R.
Rusby
, P.
Harris
, P.
Morantz
, and G.
Machin
, “Further estimates of (T − T90) close to the triple point of water
,” Int. J. Thermophys.
38
, 44
(2017
).13.
M. B.
Ewing
and J. P. M.
Trusler
, “Primary acoustic thermometry between T = 90 K and T = 300 K
,” J. Chem. Thermodyn.
32
, 1229
(2000
).14.
G.
Benedetto
, R. M.
Gavioso
, R.
Spagnolo
, P.
Marcarino
, and A.
Merlone
, “Acoustic measurements of the thermodynamic temperature between the triple point of mercury and 380 K
,” Metrologia
41
, 74
(2004
).15.
L.
Pitre
, M. R.
Moldover
, and W. L.
Tew
, “Acoustic thermometry: New results from 273 K to 77 K and progress towards 4 K
,” Metrologia
43
, 142
(2006
).16.
K.
Zhang
, X. J.
Feng
, J. T.
Zhang
, Y. Y.
Duan
, H.
Lin
, and Y. N.
Duan
, “Determination of T – T90 from 234 K to 303 K by acoustic thermometry with a cylindrical resonator
,” Metrologia
57
, 024004
(2020
).17.
C.
Gaiser
and B.
Fellmuth
, “Highly-accurate second-virial-coefficient values for helium from 3.7 K to 273 K determined by dielectric-constant gas thermometry
,” Metrologia
58
, 015013
(2021
).18.
C.
Gaiser
et al, “2022 update for the differences between thermodynamic temperature and ITS-90 below 335 K
,” J. Phys. Chem. Ref. Data
51
, 043105
(2022
).19.
H. C.
McEvoy
et al, “Methodologies and uncertainty estimates for T − T90 measurements over the temperature range from 430 K to 1358 K under the auspices of the EMPIR InK2 project
,” Meas. Sci. Technol.
32
, 035001
(2020
).20.
J.
Fischer
, M.
de Podesta
, K. D.
Hill
, M.
Moldover
, L.
Pitre
, R.
Rusby
, P.
Steur
, O.
Tamura
, R.
White
, and L.
Wolber
, “Present estimates of the differences between thermodynamic temperatures and the ITS-90
,” Int. J. Thermophys.
32
, 12
(2011
).21.
X. J.
Feng
, K. A.
Gillis
, M. R.
Moldover
, and J. B.
Mehl
, “Microwave-cavity measurements for gas thermometry up to the copper point
,” Metrologia
50
, 219
(2013
).22.
K.
Zhang
, X. J.
Feng
, K.
Gillis
, M.
Moldover
, J. T.
Zhang
, H.
Lin
, J. F.
Qu
, and Y. N.
Duan
, “Acoustic and microwave tests in a cylindrical cavity for acoustic gas thermometry at high temperature
,” Philos. Trans. R. Soc., A
374
, 20150049
(2016
).23.
L.
Pitre
, F.
Sparasci
, D.
Truong
, A.
Guillou
, L.
Risegari
, and M. E.
Himbert
, “Measurement of the Boltzmann constant kB using a quasi-spherical acoustic resonator
,” Int. J. Thermophys.
32
, 1825
(2011
).24.
M.
de Podesta
, R. J.
Underwood
, G.
Sutton
, P.
Morantz
, P.
Harris
, D. F.
Mark
, F. M.
Stuart
, G.
Vargha
, and G.
Machin
, “A low-uncertainty measurement of the Boltzmann constant
,” Metrologia
50
, 354
(2013
).25.
R. M.
Gavioso
, D.
Madonna Ripa
, P. P. M.
Steur
, C.
Gaiser
, D.
Truong
, C.
Guianvarc’h
, P.
Tarizzo
, F. M.
Stuart
, and R.
Dematteis
, “A determination of the molar gas constant R by acoustic thermometry in helium
,” Metrologia
52
, S274
(2015
).26.
P. J.
Mohr
, D. B.
Newell
, B. N.
Taylor
, and E.
Tiesinga
, “Data and analysis for the CODATA 2017 special fundamental constants adjustment
,” Metrologia
55
, 125
(2018
).27.
L.
Pitre
et al, “New measurement of the Boltzmann constant k by acoustic thermometry of helium-4 gas
,” Metrologia
54
, 856
(2017
).28.
M.
de Podesta
, D. F.
Mark
, R. C.
Dymock
, R.
Underwood
, T.
Bacquart
, G.
Sutton
, S.
Davidson
, and G.
Machin
, “Re-estimation of argon isotope ratios leading to a revised estimate of the Boltzmann constant
,” Metrologia
54
, 683
(2017
).29.
F. J.
Pérez-Sanz
, J. J.
Segovia
, M. C.
Martín
, M. A.
Villamañán
, D.
del Campo
, and C.
García
, “Progress towards an acoustic determination of the Boltzmann constant at CEM-UVa
,” Metrologia
52
, S257
(2015
).30.
X. J.
Feng
, J. T.
Zhang
, H.
Lin
, K. A.
Gillis
, J. B.
Mehl
, M. R.
Moldover
, K.
Zhang
, and Y. N.
Duan
, “Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: New and previous results combined
,” Metrologia
54
, 748
(2017
).31.
J. T.
Zhang
, H.
Lin
, J. P.
Sun
, X. J.
Feng
, K. A.
Gillis
, and M. R.
Moldover
, “Cylindrical acoustic resonator for the re-determination of the Boltzmann constant
,” Int. J. Thermophys.
31
, 1273
(2010
).32.
J. T.
Zhang
, H.
Lin
, X. J.
Feng
, J. P.
Sun
, K. A.
Gillis
, M. R.
Moldover
, and Y. Y.
Duan
, “Progress toward redetermining the Boltzmann constant with a fixed-path-length cylindrical resonator
,” Int. J. Thermophys.
32
, 1297
(2011
).33.
H.
Lin
, X. J.
Feng
, K. A.
Gillis
, M. R.
Moldover
, J. T.
Zhang
, J. P.
Sun
, and Y. Y.
Duan
, “Improved determination of the Boltzmann constant using a single, fixed-length cylindrical cavity
,” Metrologia
50
, 417
(2013
).34.
B. F.
Billing
and T. J.
Quinn
, “Temperature measurement 1975: Invited and Contributed papers from the European Conference on Temperature Measurement held at the National Physical Laboratory, Teddington, 9–11 April 1975
,” Phys. Bull.
27
, 406
(1976
).35.
36.
E.
Tiesinga
, P. J.
Mohr
, D. B.
Newell
, and B. N.
Taylor
, “CODATA recommended values of the fundamental physical constants: 2018
,” J. Phys. Chem. Ref. Data
50
, 033105
(2021
).37.
F.
Sharipov
and M. R.
Moldover
, “Energy accommodation coefficient extracted from acoustic resonator experiments
,” J. Vac. Sci. Technol. A.
34
, 061604
(2016
).38.
M. R.
Moldover
, R. M.
Gavioso
, J. B.
Mehl
, L.
Pitre
, M.
de Podesta
, and J. T.
Zhang
, “Acoustic gas thermometry
,” Metrologia
51
, R1
(2014
).39.
H.
Lin
, K. A.
Gillis
, and J. T.
Zhang
, “Characterization of piezoelectric ceramic transducer for accurate speed-of-sound measurement
,” Int. J. Thermophys.
31
, 1234
(2010
).40.
K. A.
Gillis
, H.
Lin
, and M. R.
Moldover
, “Perturbations from ducts on the modes of acoustic thermometers
,” J. Res. Natl. Inst. Stand. Technol.
114
, 263
(2009
).41.
M. B.
Ewing
, A. A.
Owusu
, and J. P. M.
Trusler
, “Second acoustic virial coefficients of argon between 100 and 304 K
,” Physica A
156
, 899
(1989
).42.
M. B.
Ewing
and A. R. H.
Goodwin
, “An apparatus based on a spherical resonator for measuring the speed of sound in gases at high pressures. Results for argon at temperatures between 255 K and 300 K and at pressures up to 7 MPa
,” J. Chem. Thermodyn.
24
, 531
(1992
).43.
X. J.
Feng
, H.
Lin
, K. A.
Gillis
, M. R.
Moldover
, and J. T.
Zhang
, “Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant
,” Metrologia
52
, S343
(2015
).44.
K.
Zhang
, X. J.
Feng
, J. T.
Zhang
, H.
Lin
, Y. N.
Duan
, and Y. Y.
Duan
, “Microwave measurements of the length and thermal expansion of a cylindrical resonator for primary acoustic gas thermometry
,” Meas. Sci. Technol.
28
, 015006
(2016
).45.
G.
Sutton
, R.
Underwood
, L.
Pitre
, M.
de Podesta
, and S.
Valkiers
, “Acoustic resonator experiments at the triple point of water: First results for the Boltzmann constant and remaining challenges
,” Int. J. Thermophys.
31
, 1310
(2010
).46.
J. J.
Segovia
, D.
Lozano-Martín
, M. C.
Martín
, C. R.
Chamorro
, M. A.
Villamañán
, E.
Pérez
, C. G.
Izquierdo
, and D.
del Campo
, “Updated determination of the molar gas constant R by acoustic measurements in argon at UVa-CEM
,” Metrologia
54
, 663
(2017
).47.
A. F.
Estrada-Alexanders
, O.
Guzmán
, and B.
Pérez-Vidal
, “High-precision virial coefficients of argon and carbon dioxide from integration of speed of sound data in the pressure–temperature domain
,” Mol. Phys.
110
, 1349
(2012
).48.
B.
Jäger
, R.
Hellmann
, E.
Bich
, and E.
Vogel
, “Ab initio virial equation of state for argon using a new nonadditive three-body potential
,” J. Chem. Phys.
135
, 084308
(2011
).50.
H.
Lin
, X. J.
Feng
, and J. T.
Zhang
, “Perturbation measurement of waveguides for acoustic thermometry
,” AIP Conf. Proc.
1552
, 39
(2013
).51.
H. H.
Chen
, X. J.
Feng
, H.
Lin
, J. T.
Zhang
, C.
Ren
, and K. J.
Wang
, “Study on optimal design of acoustic conduit in gas acoustic thermometer
,” Acta Metrol. Sin.
40
, 7
(2019
).52.
E. W.
Lemmon
, I. H.
Bell
, M. L.
Huber
, and M. O.
McLinden
, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0
, National Institute of Standards and Technology, Standard Reference Data Program
, Gaithersburg
, 2018
.53.
D. C.
Ripple
, D. R.
Defibaugh
, M. R.
Moldover
, and G. F.
Strouse
, “Techniques for primary acoustic thermometry to 800 K
,” AIP Conf. Proc.
684
, 25
(2003
).54.
E.
Vogel
, “The viscosities of dilute Kr, Xe, and CO2 revisited: New experimental reference data at temperatures from 295 K to 690 K
,” Int. J. Thermophys.
37
, 63
(2016
).55.
R.
Hellmann
, B.
Jäger
, and E.
Bich
, “State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties
,” J. Chem. Phys.
147
, 034304
(2017
).© 2023 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved.
2023
U.S. Secretary of Commerce
You do not currently have access to this content.
