Uncertainty of Measurement

Michael, a review I wrote on Amazon for kitchen foil may be of some interest. I said:

"In the 'questions and answers' about this product there have been enquiries about the actual thickness of the foil in microns - no number is given in the product description or on the box. Being somewhat obsessive-compulsive about this sort of thing I have measured with a micrometer which I know to be good to +/- 1.5 microns, and get 24 +/-1.2 microns on average. Cutting off a strip, measuring, then weighing on a precision balance gave me 23.7 +/- 1.0 microns. So I think it's fairly safe to say it's 24 micron foil."

I can't remember the details exactly but I made many measurements and used standard mathematical methods to calculate the errors. The point is that the best I could do was about one part in 25 or 4% on dimension - if I had been working the other way (ie to determine the density of the foil) the error would be of the same order.

I once worked as an analyst in the laboratory of a non-ferrous metal foundry. XRF was used as a quick and easy method to ensure the alloys were within spec but could be trusted to only ~ +/- 0.1 %. I'm sure things have moved on but I'd be be surprised if a scrap merchant's gun would be able to achieve even that! And on a tiny piece of wire? I reckon you have to trust the seller and see how it works out for your project.

Robin.

Michael, you say your weighing device isn't calibrated. It may be worth making a standard or two, to calibrate it, perhaps from copper wire. It's generally of pretty high purity, so its density is known, and it's hard enough to allow its diameter to be measured accurately, whilst soft enough to straighten for length measurement.

You haven't mentioned the sensitivity of your weighing device. I've been impressed by the performance of the ultra-simple (see-saw) balances made for ammunition reloading. A friend and I reload with piddling target loads of 1.5 grains (about 0.097 g) of powder. Our scales' calibration agrees within about 0.006 g, and, whilst neither has been calibrated against a standard, they are remarkably consistent, with repeatable measurement. (Yeah, OK, in this case, they're acting more as comparators, but the point is that simple devices can perform quite well).

O.K.

1. The Salter-AND EW60A ‘Electronic Personal Balance’ has a Max Capacity of 60g and a Min. Division of 20mg according to its Specifications.
2. I do have more sensitive weighing equipment, but it’s not accessible at the moment.
3. Robin’s concluding line endorses the decision that I have already made.
4. The main reason for me starting this thread was encourage people to think. … Hence my explicitly rhetorical question.

Mission accomplished.

MichaelG.

A quick and dirty method of checking the balance is to use printer paper. First weigh a few sheets of paper to confirm the gsm (an A4 sheet is 0.06237 m2, so 10 sheets of 80gsm should weigh 49.9g, easily compared with 50cc of distilled water, and if the weight is different you can calculate the gsm for your paper).

Taking 80gsm as an example, a 50mm square should weigh 0.2g a 25mm square 0.05g, and a 10mm square 0.008g so using these you can confirm both the accuracy and resolution of the balance.

(I have had this nagging on my mind since yesterday, finally I remembered using this during A-Levels half a century ago but cannot remember the purpose. Could it have been measuring electrostatic attraction?).

Brian G

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

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

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.

.

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

Too much risk of contaminating other things.

MichaelG.

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.