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Improving acoustic determinations of the Boltzmann constant with mass spectrometer measurements of the molar mass of argon



Inseok Yang, Laurent Pitre, Michael R. Moldover, Jintao Zhang, XiaoJuan Feng, Jin Seog Kim


We determined accurate values of ratios among the average molar masses MAr of 9 argon samples using two completely-independent techniques: (1) mass spectroscopy and (2) measured ratios of acoustic resonance frequencies. The two techniques yielded mutually consistent ratios (RMS deviation of 0.16x10-6 MAr from the expected correlation) for the 9 samples of highly-purified, commercially-purchased argon with values of MAr spanning a range of 2x10-6 MAr. Among the 9 argon samples, two were traceable to recent, accurate, argon-based measurements of the Boltzmann constant kB using primary acoustic gas thermometers (AGT). If our values of MAr ratios are accepted, the difference between two, recent, argon-based, AGT measurements of kB decreases from (2.77+/-1.43)x10-6 kB to (0.16+/-1.28)x10-6 kB. (Unless otherwise stated, uncertainties are one standard uncertainty.) This decrease enables the calculation of a meaningful, weighted average value of kB with a relative standard uncertainty ur(kB)0.8x10-6. Our absolute values of MAr are traceable to two, completely-independent, isotopic-reference standards; one was prepared gravimetrically at KRISS in 2006; the other was prepared from isotopically-enriched 40Ar for NIST's 1988 measurement of kB. The absolute values of MAr determined using the KRISS standard have the uncertainty ur(MAr) = 0.60x10-6; they agree with values of MAr determined at NIM using an AGT within the uncertainty of the comparison ur(MAr) = 0.93x10-6.


Boltzmann constant, molar mass, argon isotope, mass spectroscopy, acoustic gas thermometer, acoustic thermometer


Yang, I. , Pitre, L. , Moldover, M. , Zhang, J. , Feng, X. and Kim, J. (2015), Improving acoustic determinations of the Boltzmann constant with mass spectrometer measurements of the molar mass of argon, Metrologia, [online],, (Accessed July 20, 2024)


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Created September 29, 2015, Updated October 12, 2021