Testing Specific Gravity Of Coins: A Brief Demo

I'm pretty sure that the method of calculating the specific gravity is very good, but in terms of calculating the percentage composition for silver copper alloys, I wondered if you have to correct for non linearity in the density. For example, I've worked in the ethanol industry. If you take a liter of ethanol, and a liter of water, and mix them together, the result is only 1.92 liters. So I made the calculation for silver / copper.

Silver and copper form a eutectic alloy of 0.719 Ag + 0.281 Cu. If you have more silver than that, the coin will be partially the eutectic alloy and partially pure silver (google eutectic silver copper to learn more). With less silver, it will be partially pure copper and partially the eutectic mixture. The eutectic mixture calculates to have a density of 1/(0.719/10.49 + 0.281/8.96) = 10.0097. The specific density of the eutectic alloy, (which is sold as brazing supplies, for example, as "Silvaloy") is 10.009. So the calculation works, and this will give you the right answer.

As far as why the coin came out 0.75 silver, I think it's likely because of errors in your measurements. You shouldn't have Sa = Sw, for example. And if you make an error of 0.01 in your measurement of any one of Wa, Sa, Sw, Sa it will give an error of about 3% in your calculated specific gravity, and around 30% in your calculation for the percentage silver. (To see this, change one of your inputs to the calculation by 0.01 and recalculate.) So for the accuracy of your measurements, the coin could have just about any silver percentage.

As far as improving this, it would be better to have a bunch of coins so you're not looking for small differences. Or get a much more accurate scale. And since what you're really interested in is the difference in weight between in air and in water, it would be better to design the experiment so you measure this difference directly instead of subtracting absolute measurements. That could be done by arranging for some counterbalance which is also either in water or air. Hmmmmmm.

Nice thread.

I did weigh some of GB copper pennies and half pennies also Ireland digital scale by weight and troy ounce,even try to weigh the coins of GB those that are silver those that are in boundaries from .7 to .5 percent something like that just incase other composition struck in different composition no luck.

Quite difficult have to weigh the coppers three times by wieght and troy ounce at least I did try,since GB pennies have different composition and an expert mention about pyx the variables are factors increase it fun like a playground,and it compose of 3 metals,others are saying using MD having different sound for different metals.

Nice additional info about the specific gravity,I did even seach on the web about condutivity or electricity,circular rod is more good form of conductor but applied with coins,it might be difficult just like a tester,like a small diode will emit a small amount of electricity will maybe know the conductibility and metal or its composition,Im not an electrician do not know how to made one.

Even thinking electron configuration and conductibility.

Maybe combination of all.

Hope there will be at home alternative for x ray flourecence expert say its not easy to acces and dont know if it is expensive.

Good thou nice math problem for math book.physics and its applied.