High-accuracy calibration in the vacuum range 0.3 Pa to 4000 Pa using the primary standard of static gas expansion

Abstract

Static gas expansion provides a convenient primary standard for calibrating pressure gauges in the medium vacuum range. This paper reports on a thorough investigation of the fundamental principle, possible disturbances and achievable uncertainty of such an apparatus. The method is described and model equations for the general case of a non-isothermal expansion of a real gas are derived. As temperature effects play an essential role in the uncertainty budget, the vessels of the apparatus were immersed in a temperature-controlled circulating water bath. In addition, the inherent transient temperature effects originating from the gas expansion process itself were studied experimentally, which leads to a better understanding of these effects. As a result, uncertainties caused by temperature effects could be substantially reduced. Furthermore, deviations between different real gases were studied. The investigations led to greater accuracy of the primary standard apparatus, i.e. an expanded relative uncertainty of 1 10 -3 at a pressure of 10 Pa and of 5 10 -4 at 1000 Pa.

Static expansion primary vacuum standard — Part 1: Determination of the volume ratio of the expansion stage

“…The value of B" for nitrogen is -2 x 10 -9 Pa -1 ± 1 x 10 -9 Pa -1 [6]. For an initial pressure of 127 kPa, the product (p s .u(B")) amounts to 1.27 x 10 -4 .…”

“…The two volumes are initially evacuated. In the method of successive expansion [1,[5][6][7][8], gas is first enclosed in v s at a known pressure p s which can be measured by a resonant silicon gauge (Yokogawa, MT220) of full scale range 130 kPa. The valve 5 is then opened to let the gas expand into the larger volume to an equilibrium pressure (p L ) 1 .…”

“…The volume v s is once again filled with the gas at the same pressure p s and the process of letting it expand into V L is repeated. This process of entrapment of gas in v s at pressure p s and subsequent expansion into V L is repeated N number of times and an estimate of the volume ratio R =(V L +v s )/v s is obtained from the expression [5][6][7][8]:…”

“…It is related to the virial coefficient B with a dimension volume/ amount of substance as B"=B/R m T. R m is the molar gas constant. B" has values of -2.0x10 -9 Pa -1 and -6.2x10 -9 Pa -1 , respectively for the two gases nitrogen and argon [6].…”

Static expansion primary vacuum standard — Part 2: Characterization of two spinning rotor gauges

“…where B" is the virial coefficient [12] as defined in the Part 1 of this paper. Thus a range of pressures can be generated by varying the initial pressure.…”