Uncertainty of Measurement

[SillyOldDufferModerator @sillyoldduffer]

Posted by Andy_G on 22/07/2023 22:10:00:

There is 8% uncertainty in cross sectional area from the diameter measurements…

Can you check density using the Archimedes principle? (Weight in air vs weight in water) …

I think this method makes it possible for Michael to achieve higher accuracy with what he has. (DC31k suggests Archimedes too.)

Density is Mass/Volume. By definition the density of water is 1 because 1g of water occupies a volume of u cunic centimetre (at Standard Temperature and Pressure, 0°C and 1Bar.

Knowing the density of pure Platinum (21.45 g/cc), Michael checked his wire by weighing it and measuring its length and diameter to calculate volume. Two fundamental problems: the accuracy of his scales, and the accuracy of the length and diameter measurement. The latter being suspect because Michael's diameter measurements suggest the wire is not the same diameter throughout, and may not perfectly round.

Archimedes removes the need to measure length and diameter, and the shape of the object doesn't matter. It eliminates two of the three main error sources, leaving only the accuracy of the scale to worry about. (This is a simplification! Although Archimedes is as improvement, there are other, smaller, sources of error which might need attention.)

In the Archimedes method, the scale is set up to measure the sample's buoyancy, in this case Michael's Platinum wire.

• On the scale is placed an open topped container of water
• A gantry is placed across the container
• From the gantry a wire ending in a platform is dropped into the middle of the water
• The scale is zeroed
• The sample (Michael's wire) is placed on the immersed platform, so it is completely underwater
• The scale is read. It registers the samples buoyancy, which is the weight of water displaced.

Michael's scale has a resolution of 20mg but we don't know if it's that accurate (see Robert Atkinson's comments). . That means the accuracy of the scale needs to be established, for which see Kiwi Bloke.

Another issue: pure Platinum is 21.45 times heavier than water, so Michael's perfect scale should read 0.018648019g. Oh dear, that's pretty much on the scale's 20mg limit. The density ratio between water and platinum is too high. No problem as I'm spending Michael's money – either he buys 5x more Platinum, or replaces the water with Mercury!

Or does anyone know of a liquid that's denser that water and cheaper than Mercury?

Dave

[Merddyn’s DadParticipant @merddynsdad]

Posted by SillyOldDuffer on 23/07/2023 12:09:31:

Or does anyone know of a liquid that's denser that water and cheaper than Mercury?

Dave

Beer?

I wish these subjects weren't discussed on this forum , all my plans for today are sidetracked whilst I consider the questions raised – and their solutions and try to remember when I was paid to do just this kind of stuff, how I did it.

In case there is any doubt I read this forum for just this kind of topic – many thanks.

Steve

[Howard LewisParticipant @howardlewis46836]

With all measuring instruments, the subject of calibration is paramount.

Idealy, linerear measurements should be taken under the specified conditions of temperature and humidity for both the instrumens and the item being measured, after a minmum soak time of 24 hours. (As maintained in Standards and Calibration rooms )

Given that the specimen, and measuring equipment are not under standard calibration conditions, and is not straight, making length VERY difficult to measure, will give rise to imprecision in the end result.

Also, having been cut with nippers, the length , and hence volume, again is not precise, so obtaining a result with a small error is almost inevitable.

So, take heart Michael, you did the best that you could under the conditions applicable in this case, and the result was within 5% of the ideal.

Howard.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 23/07/2023 12:09:31:

.

[…]

No problem as I'm spending Michael's money – either he buys 5x more Platinum, or replaces the water with Mercury!

.

I have plenty of Mercury available, Dave … but won’t be doing that any-time soon

Too much risk of contaminating other things.

MichaelG.

[Bruce VoelkerdingParticipant @brucevoelkerding91659]

in the mid 70's while attending University I worked at an R&D Lab of a Company making automotive Lead-Acid Batteries. The Lab also performed on-going Quality Assurance for the Manufacturing Sites in the US. One check was the alloy Composition of the "Lead", it being in Reality an Alloy of ~93% Lead and ~7% Antimony. The Technician would get a small Sample of Lead (maybe 5 grams ?). He would weigh it dry first. Then he would put it in a small Glass Vessel which had a ground Stopper. Distilled Water would then be added, vibrated to remove any Air Bubbles, then the Stopper installed. The Trick to the System was the Stopper had an extremely tiny Hole thru it and the final bit of Water would escape thru it as the Stopper was pushed Home. Then another Weighing was done. I do not remember the Accuracy of the Scale, just that it was a Balance Scale contained within a Glass Enclosure. Nothing was touched by Human Hands – weights were placed with Tweezers. All this was done in a Temperature controlled Lab. A quick Calculation gave the percentage of Antimony.

The Alloy mixture was at the "eutectic" Point, i.e. the point where the conversion from Molten Liquid to solid occurred with minimal change in Temperature. This allowed quick cooling in the Plate Molding Machines, leading to higher Production Rates. Unfortunately, Antimony generates excessive Electrolysis of the Battery Acid causing Water Loss. At the time I was employed there was a big Push to develop a "Maintenance Free" Battery.

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