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Direct Determination of Air Density in a Balance Through Artifacts

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Direct Determination of Air Density in a Balance Through Artifacts JOURNAL OF RESEARCH of the National Bureau of Standards Vol. 83, No.5, Septem ber- October 197B ::> I Dired Detennination of Air Density in a Balance Through Artifads Charaderized in an Evacuated Weighing Chamber. W. F. Koch Center for AnalytiCXJI Oremistry, National Bureau of Standards, Washington, DC 20234 R. S. Davis and V. E. Bower Centerfor Absolute Physirol Quantities, National Bureau of Standards, Washington, DC 20234 June 29, 1978 This paper describes a s imple device wh ich permit s mass comparisons in air without appea l to the correction for ai r buoyancy. The device consists of a ca nister which is evacuated and weighed on a laboratory balance with a mass inside. A second we ighing of another mass in the evacuated cani ster provides th e des ired ma ss com parison. The method was used to deter'm ine the mass difference between two sta inl ess steel weights of widel y differing densi ties. With knowledge of this mass difference and of the volume difference one may, by a simple air weighing of the two objects, determine directl y the densit y of the ai r in the balance case. Densiti es of air d etermin ed by this method were compared with those calc ul ate d from the barometric pressure, the temperature, and the relati ve humidity of the laboratory a ir. The experime nt a l and calculated va lues agree th roughout to within 1.0 fL g cm- 3 (w here the norm al air densit y is about 1.2 mg cm- 3). The calculated and ex perimental values of day-to-day fluc tuations in air densit y agree to wi thin 0.5 p..g cm- 3 . Key wo rd s: Buoyancy of a ir; dens it y; mass compari sons in vacuo; precise we ighing; vacuum; vacuulll weighing. 1. Introduction (NBS) is beli eved to be no greater than 0.3 ppm with respect to the NBS maintained units. To keep to 1-2 ppm the In recent years, th e authors have parti c ipated in two uncertainty of the measure me nt of the Faraday constant, the separate electroc hemi cal studies of the Faraday constant. mass measurements, with all th eir correcti ons, must have an Koch and Diehl made a determinati on of the Faraday by the uncertainty of no greater than about 0.9 ppm, irrespective of coul ometric titrati on of a base, 4-aminopyridine [I];l Bower the materi als used. Of the various corrections to be applied to mass determi­ and Davis have made a series of determinations by the nation, such as those for the sensitivity of the balance, the anodic dissolution of high-purity silver into perchloric acid calibration of the standa rd weights, etc., the correction for solution [2]. Both of these measurements were designed to the air buoyancy appears as the least amenable to d irect provide values of the Faraday constant wi th uncertainties of ,L, determination. For the buoyancy co rrecti on, one almost about one ppm. A constant of such accuracy might make a always relies on a calcula ti on of air de nsity by so me contribution toward the resolution of the discrepancy between algorithm whose entries are such laboratory observables as the values for the Faraday obtained directly (electroc hemi­ the barometric pressure, the te mperature, the relati ve humid­ cally) and indirectl y (by calculation from accurately known it y and , sometimes, the carbon dioxide conte nt of the air. phys ical constants). For details on this last point th e reader The general question of the limits of validity of the various is referred to Taylor et al. [3], and Cohen and Taylor l4]. closely related air density algorithms advanced in the scien­ The accuracy of an electroc hemical measuremen t can be tific literature and the question of the direct precise deter­ no greater than that of the associated mass measurements. mination of air density in a balance chamber are matters of The uncert ainty in th e definiti on and transfe r of the electrical ) considerable moment at present to the metrological commu­ . units into the Faraday laboratory in the Electri cal Measure­ nity. The urgency of these questions, among others, led the ments and Standard s Division, Na ti onal Bureau of Standards Bureau Intern ational des Poids et Mesures to hold a meeting I :> on precision mass determinations in November 1976 at I Figures in brackets indicate lit era ture references allhe end of this paper. Sevres, France [5]. 407 Our study was undertaken with the aim of making direct, to d",=;", the d,n,;ty of the a;' ;n a b,l,." "". If m ~ accurate measurement of the air density in order to confirm the difference in air weight (divided by g) between M Hand the air density algorithm which we used in computing the M s, and if LlV = V H - Vs, buoyancy corrections to the mass determinations required for " the Faraday experiments. m = (Ms - pVs) - (MH - pVH), or (1) ,( p = (LlM + m)/LlV. 2. The Problem and the Method The evaluation of the buoyancy correction to weighings of The values of p so obtained may be compared to those ;:; 4-aminopyridine, aqueous solutions and other low-density calculated from the atmospheric observables. materials offers some difficulties if one uses high-density The vacuum chamber is a stainless steel tube (fig. 1) with (platinum or stainless steel) standards. The density of 4- one end capped. To the other end is attached a stainless aminopyridine is about 1.27 g cm-3 . The weight standards steel flange with a groove in which is set an O-ring whose are made of stainless steel, density about 8 g cm- 3 . For an profile extends slightly above the groove. A separate flat uncertainty of only 1 ppm in the mass of 4-aminopyridine or stainless-steel cover with a stainless-steel vacuum valve aqueous solutions, the density of air, about 0.0012 g cm - 3 at welded to it reposes on the O-ring. A circular land on the room temperature, must be known with an uncertainty no underside keeps the cover centered on the cylindrical cham­ greater than 0.08 percent. ber. To the vacuum valve is welded a smooth stainless steel We have made a direct physical determination of the air tube which serves to attach the whole chamber to a port on a density in a balance chamber and have compared the results pumping station. Removal of excess material from the valve with the version of the algorithm which is given below. The enabled us to keep the mass of the whole assembly, with a ~ experimental method, based on Archimedes' principle, has 17-g weight inside, within the 100-g capacity of our balance. been used successfully before, notably by Baxter [6] who The principal dimensions of the apparatus are approxi­ used a globe to determine his buoyancy corrections, and by mately as follows: length, bottom to flange, 85 mm; inside Jaquerod and Borel l7], who weighed a float in various diameter of chamber, 27 mm; outside diameter of chamber, samples of air under standard conditions in order to obtain 29 mm; outside diameter of fl ange and lid, 33 mm; overall the variation in density. To this end we have employed height 127 mm. stainless steel artifacts to permit direct measurement of Two weights (fig. 1) were constructed of stainless steel, density of air in a balance . We have been anticipated in the one hollow, the other solid. The hollow weight was con­ use of this principle in recent years by Bowman et al. [8] and structed by capping stainless steel tubing, 0.25 mm thick by Bruhlmans and Eschbach [9]. and 25 mm in diameter with stainless steel sheet 1 mm thick. We have fU11hermore employed a method of determining the mass of these objects by comparisons in vacuo. Rather than using the expensive, but perhaps more accurate, method of placing a balance in an evacuable enclosure, we have constructed an evacuable enclosure which may be weighed on a chemist's analytical balance. Let M Hand M s be the nearly equal masses of a hollow, low density weight and a solid, high density weight, respec­ tively. Let the respective exterior volumes be V H and Vs . Let I M Hand M s be weighed, successively, within an evacuate d enclosure of mass ME and exterior volume V E' Calling the air 1 density p, we have the force equation: where 11M represents the small difference indicated on the optical scale of the balance, calibrated with platinum weights, and g represents the local acceleration of gravity. Providing V E and p are constant throughout the procedure, the mass difference, 11M = M H - M s has been obtained without appeal to an air buoyancy calculation. FIGURE 1. Vacuum weighing device consisting of a stainless steel canister Once thus characterized, the two masses M H and M s, if and cover with vacuum valve . The low-density and high-densit y weights for detennining density of air in a balance their mean densities are sufficiently different, may be used chamber appear at right. 408 The joinings were electron-beam weld ed and machined standard we ights of stai nl ess steel in the balance. All smoo th, and the object was polished to a specul ar finish. The weighings are by double substitution with platinum sensiti v­ result was a weight in the form of a right circular cylinder 50 ity weights.
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