Topic: I measured the density of my silver/gold coins... - page 2. (Read 16261 times)

I measured a densitiy of 10.40 g/cm³. Slightly less heavy than silver, as expected.

much better results using mintymarks method:


(click image above for google doc, these are single measurements of 7 individual coins)



As expected, the Casascius 10 BTC round has lower density than silver because of the sticker and space (filled with paper and maybe some air) behind it.

The scale zeroed in much quicker than with my first setup. I conclude that the higher weight of the water cointainer in my first setup (about 150g, scale max is 200g) as opposed to the weight of the frame used here (< 3g) really did add a lot of inaccuracy in the scale.

Repeated measurements had a variation of +/- 0.01g max (resulting already in a ~0.24% jump in resulting "error").

Thanks mintymarks, now I have a much better method at hand.

https://docs.google.com/spreadsheet/ccc?key=0Au-mVSBh0PA4dFRMMTV5RmM5S0ppZDVJSVR6RUROb2c#gid=0

But please note: each row is a seperate coin, so we're talking about 15 distinct coins. I did take multiple measurements for 2 of the coins, but only recorded one.

If you would put the spreadsheet on Google docs I might look at it more.

I notice that one measurement for each coin is in disagreement with the later measurements on the coin.

I would add some other calculations.  From the average density of the coin, calculate the weight of water that you expect for the measured weight of the coin, also, calculate the expected weight of the coin given the measured weight of water.

thanks for these tips, I'll try to do my best.

The variation between measurements was (if I recall correctly) up to 0.03 g. There have even been some outlieres with something like 0.08 if I recall correctly. I tried this on a couple of measurements with 2 of the coins. The variation was present only on the measurements using the container. The simple weighing of the coin showed max of 0.01 g variation.

I'll do the (modified) process on my 10 BTC silver round when I have some time.

The sticker plus the volume (and paper) below it we could probably estimate pretty well. How thick is the hologram and how deep the "inlet" in the coin for the paper with the key? They weight of sticker+paper we can probably neglegt or guesstimate also.

A fake would not be from the claimed mint, though

Yes.  And the evaporation rate of the water.
Those balances cost $5,000.

holy f..k! That is cool! I will try this and see if I can get better accuracy from my scale this way.

Thanks for taking the time to explain (and make that great drawing) for me

Watch for air bubbles when suspending the object into water. Gently tap the thread to get rid of them.

Clean the object, handle with gloves (non-powdered).

Use distilled water, and read the density from the table for the particular temperature.

Repeat several times. What is the variation between measurements? Is it random, or is there a consistent up or down trend?

Make sure the balance is level.

I'm curious to know how a Casascius silver coin would stack up, but the sticker and private key paper would probably throw things off by quite a bit.

Ok, I'll explain the "frame" a bit more. You can make it out of a coathanger, but ideally something a bit flimsier is lighter and so better. It does not have to  be totally rigid, if it moves out of shape, it doesnt matter. I use copper wire because its easy to bend and holds its shape.

Here is a diagram:                                                  .------------.
                                                                           |              |
                                                                     ________        |
     Scales                                                         :::::::::         |
     Table edge     ===========================       |
                                                                                          |
                                                                                          |
     Bent Wire Frame                                                 .-----------.
                                                                            .
     Cotton Thread                                                    .
                                                                            .
                                                                            .
                                                                   |        .        |
     Object                                                      |      |||||     |
                                                                   |                 |
                                                                   |                 |
     Beaker of water                                        |                 |
                                                                   |                 |
                                                                    .__________.

                                                                       
The frame can be C shaped, it doesnt have to be rectangular, the important point is that the object is directly under the place where it rests on the scales so that it balences.  In fact it will pretty much hang that way anyway.

I have drawn a table in here, and you do want the scales to be horizontal and not moving, so this is quite a good way to do it. You take two mass measurements as |I explained, first with no beaker or water, then you raise the beaker and note the loss of weight due to boyancy with the object fully submerged.

Now one problem here is that any airbubbles that stick to the object represent an inaccuracy. Really you would like to use a bit of soap to prevent this, but that might alter the purity of the water. If you use a very small amount this would probably be a good idea. There is an alternative however. You can use any liquid provided that you take its density into account, so if you decided to use say parafin, because you will not get air bubbles in parafin because of the low density. But you probably do not know the density of parifin given thatit may vary quite a bit from sample to sample. So, use a known good coin or other object as a "calibration", that gives you the density acurately, which you can then use in your calculation of the 2nd object. The known good coin in fact can be anything you know the volume of, a freshly minted coin is convienient since you know the mass and the density of the material its made to high accuracy, so you know the volume!! But A 1cc cube or other known volume  of anything that sinks (in parafin) would be just as good.

Yeah, this is probably overkill, the smidgeon of soap method would be much simpler and probably work just fine.

again: I meant error of my measurement. I'm sure these coins are both legit and 99.9+% pure silver.

This is very interesting and I am impressed by your research. But I am sure that such prestigious mints have a very high standard of quality control; I find it hard to believe those margins of error are accurate.

thanks for the clarifications...


Sounds great, I'd love to be able to do that. I understand your point about the accuracy deteriorating with higher weight and I'd like to avoid that.

Can you maybe find or produce a drawing of that frame and the other stuff? I'm still having problems. The setup I come up with in my mind has other problems... I'm probably thinking too complicatedly.


I'm not sure what you mean by "you're displacing water out of the cointainer". No water leaves the container (except after the measurement is complete and I remove the coin some drops stick to the coin of course). I'm weighing the container with the water first (resetting scale to 0), then I'm submersing the coin hanging it from the string (so it doesn't touch either the floor of the container of the top of the water). The scale then shows the weight of the displaced water. (Actually I did it a little differently: For resetting the scale I put the coin (attached to the string but not hanging from it) into the container (so it's laying on the ground of the container). Scale shows zero at that point. Then I lift it up while keeping it submerged to it doesn't touch the ground or surface. That's why the scale show a negative value in my shot (the weight of the displaced water minus the weight of the coin)).

Well, for a start at no point does the weight of the beaker of water go on the scales. Your photograph seems to show the beaker of water on the scales. The point about these small scales is they are very accurate for small masses, less so for larger masses. Especially so as regards repeat readings which of course is what counts. Partly its a percentage thing. So its much better to not weigh large weights as far as you can. My method does involve weighing a wire frame so that you can weigh under the scales (and submerse the dangling object in water, which of itself is never weighed. You could use a 100 ton bucket of watter when weighing a 10g coin, and it would make no difference.

I think you are displacing the water out of the contain. There is an acuracy problem with this, and that is that surface tension may result in inconsistent results. Its inherrently sticky, and a few drips more or less may splut out as you do it. Any amount of grease or detergent on the object may also change the surface tension and that is worse. You may say its a trivial amount, but the point is, its multiplied by the comparatively large area of the top of the beaker. So it ends up as quite a bit.

My method also used the bouyancy principle and find the volume of the coin by "weighing" the displaced water. I also suspend the coin from a thread. I don't see how his method differs at all from what I did, practically. Am I overlooking something?

We're getting closer!: http://en.wikipedia.org/wiki/Spectrum_analyzer

Here's more fun science - remove silver tarnish: http://scifun.chem.wisc.edu/homeexpts/tarnish.html

Both silver sulfide and silver oxide have a lower density than pure silver.

The programming, I think, would be the hardest. Though one could always just use a frequency analyzer and compare each coin against a known good example.