mass and volume measurements on a si sphere performed at ...€¦ · volume measurements •the...
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Mass and volume measurements on a Si sphere performed at the NMISA Mass laboratory
Ronél Steyn
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Content
1. Redefinition of the kg2. Introduction3. Mass measurements4. Volume measurements5. Mass results6. Volume results7. Conclusion
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Redefinition of the kilogram
IPKKibble balance (Watt balance)
Si Sphere
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Introduction
• In 2017 NMISA received a Si sphere from PTB –Braunschweig, to monitor the stability of mass measurements over a period of time.
• The NMISA Mass laboratory has a Si sphere which is not well characterised and was intercompared with the PTB sphere.
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Mass measurements• A Mettler Toledo AT10 005
comparator was used for measurements.
• Weighing range:
1 000 g to 10 000 g
• Readability: 0,01 mg
• Ring weights were used to support the Si spheres and Stainless Steel check weight
• The spheres were compared against stainless steel reference standards and Bouyancycorrection were added
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Weighing equation
The weighing equation used for calculating the mass between the reference and test mass pieces is given by
𝑚𝑡 = 𝑚𝑟 + ∆𝑚 −𝑚𝑟𝑖𝑛𝑔 + 𝐶𝑏
where:
mt = mass of test weight
mr = mass of reference weights
∆𝑚 = average difference in mass
𝑚𝑟𝑖𝑛𝑔 = mass of ring weight
Cb = Buoyancy correction
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Volume comparator
• A Mettler VC1005 automated volume comparator was used for volume measurements
• Weighing range:
1 g to 1 000 g
• Double wall glass container with distilled water in the outer bath and FC-40 in the inner bath• FC-40 is a fluorinert colourless
liquid with density of 1,87 g/ml
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Volume measurement procedure
• FC-40 fluid is thermally stable within a temperature range of -57 ᵒC to 165 ᵒC which makes it suitable for constant temperature measurements
• ClimaLog to measure:• air temperature• relative humidity• air pressurefor applying buoyancy corrections
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Volume measurement procedure
• Temperature sensor close to where weighing occurs
• Fluid density was calibrated with external weights
• Data processing on a computer
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Volume measurements
• Compares the test mass to the reference mass (known volume) and detects the volume difference between the mass pieces
• Results include volume and density
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Volume measurements
• Use conventional mass to determine the volume
• The conventional mass of a body is equal to the mass mc of a standard weight that balances this body under “conventional” conditions:• ambient temperature tref = 20 ᵒC
• air density 𝜌air = 1,2 kg.m-3
• and standard weight density 𝜌std = 8000 kg.m-3
• For a weight of mass 𝑚 and volume 𝑉 this definition may be expressed as
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Volume measurements
• The weighing equation that was used to calculate the volume difference Δ𝑉between the reference and test weight is given by
∆𝑽 =(𝒎𝒄𝒕−𝒎𝒄𝒓) 𝟏 −
𝟏. 𝟐𝟖𝟎𝟎𝟎
𝝆𝒇 − 𝟏. 𝟐−
𝑩∆𝒎𝒘
𝝆𝒇 − 𝟏. 𝟐
where:
• 𝑚𝑐𝑡, 𝑚𝑐𝑟 = conventional masses for the test and reference respectively
• Δ𝑚𝑤 =
• B = is the balance correction factor
• 𝜌air = the air density
• 𝜌bw = is the density of the balance’s internal weights
The volume 𝑉𝑡 of the test weight is found by adding Δ𝑉 to the volume 𝑉𝑟 of the reference
𝐕𝐭 = 𝐕𝐫 + 𝚫𝐕
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Volume measurements
• 200 g stainless steel reference standard was used to determine the density of the spheres
• When a 1 kg silicon sphere is weighed in the liquid, its apparent mass becomes much less because of the buoyancy force acting on the sphere
• A coefficient of thermal expansion of 10,0 ppm/ᵒC was assumed for the Si sphere
•
• SIT FOTO IN!!!!!!!!
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Mass measurement results
Nominal Value
g
Measured Value
NMISAg
Uncertainty
g
MassReference
valueg
Uncertainty
g
Si sphere, SiQPkg_03_b
1 000 1 000,046 36 0,000 15 - -
Checkweight, #5
1 000 1 000,001 53 0,000 13 1 000,001 47 0,000 25
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Mass measurements
• The results of the check weight measurement were 60 µg (0,000 06 g heavier than expected
• Two values are well in agreement to within their associated uncertainties
• The higher uncertainty could be attributed to the comparator used
• Although ring weights had to be used to accommodate the spheres on the weighing pan which was not ideal but the measurements obtained reasonable results
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Volume measurement results
Nominal Value
g
Measured Value
NMISAcm3
Uncertainty
cm3
Reference value
cm3
Uncertainty
cm3
Si sphere, SiQPkg_03_b
1 000 429,805 0,032 429,350 0,019
Check weightMV-E-170 (200. g)
200 24,954 11 0,000 50 24,954 10 0,000 50
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Volume measurements
• The volume results agree to the expected values as confirmed with the check weight used, and within the uncertainty of measurements.
• The PTB Si-sphere measured had a known density value (provided with the sphere) which was used to validate the determined volume values.
• Improvement on the mass measurements and a more accurate value for the coefficient of thermal expansion will improve the volume measurements.
• The volume measurements could be further improved by using another sphere as a standard instead of the stainless steel OIML shaped weight were the differences in volumes are big.
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Conclusion
• The calibration procedures used for mass and density measurements proved to be fit for purpose using the equipment available
• The laboratory will continue to improve the large measurements uncertainties on mass and volume measurements on Si spheres.
• Several possible improvements had been identified to enable the laboratory to adequately monitor the stability of Si-spheres. They include:• reducing the size and weight of the ring weights
• improvement of buoyancy corrections
• more accurate values for coefficient of thermal expansion for Si sphere during the volume measurements
• direct comparison between two spheres will be much more accurate and will improve the measurement uncertainties drastically as proved by measurements done at the PTB
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Thank you
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