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riddles >> easy >> How much silver?
(Message started by: icon on Dec 15th, 2020, 6:22pm)

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Title: How much silver?
Post by icon on Dec 15th, 2020, 6:22pm
This is not really a riddle but more from a practical POV. I also thought that this could be an interesting exam question...

I bought a fry pan. 12" diameter and 3.25" Height. It was tin plated but deteriorated. I went and got it silver plated, which involved removing tin, cleaning the surface and then electroplating it.

Once I got that done, I was informed of the cost and that the surface has approx 56 micron thickness of silver. Assuming that surface is flat and other elements are not important for my problem (such as rivets that hold the handle), I wanted to calculate how much actual silver in grams was deposited in my pan. Obviously, I do not have before and after weight, so I can't do it that way. What made me wonder is when I inquired if it can be electroplated to 100 microns, they told me yes, but cost will be 3-4x. As of this moment silver cost is \$24.59 per troy oz, it made me even more curious...

Here is what I know..

diameter is 12" (perfect circle for our discussion)
height is 3.25" (height is uniform)
thickness of silver is 56 microns (thickness is uniformed)

Is it possible to calculate how much silver was deposited in this electroplating surface? If not possible to do so accurately, could it be estimated?

TYVM :)

Title: Re: How much silver?
Post by rmsgrey on Dec 16th, 2020, 10:55am
You can calculate the exact volume of silver for various shapes of frying pan that fit those dimensions, to get a range of figures from, say, cone to cylinder. You can also calculate for one-sided or two sided, and also take account of the thickness of the underlying pan.

There is a caveat that we'd be assuming the density of the plating to be the same as the bulk density of pure silver - if the plating process imparts any fine structure, that could mess with the density.

Also, I would expect a significant portion of the cost to come from the power requirements, and the time it takes to perform the plating, not just from the cost of the metal, so I'd be surprised if the price you paid is close to the value of the silver involved.

Title: Re: How much silver?
Post by icon on Dec 16th, 2020, 11:24am
I did the calculations and I arrived at 89grams approx. For 100 microns approx 160grams, but cost is 3-4x, which means, as you said, it must use a  MUCH larger amount of current over a much longer period of time.

I wonder how much and how much longer...

Title: Re: How much silver?
Post by rmsgrey on Dec 17th, 2020, 11:20am

on 12/16/20 at 11:24:26, icon wrote:
 I did the calculations and I arrived at 89grams approx. For 100 microns approx 160grams, but cost is 3-4x, which means, as you said, it must use a  MUCH larger amount of current over a much longer period of time.I wonder how much and how much longer...

It might not be more than a proportional increase in current/time for the plating - it might be that the 56 micron plating is the standard process, so they can do it in batches of a hundred items, while the 100 micron coating is much rarer, so they need to do a separate run for each item, meaning all the overhead has to be covered by that item's charge.

Or it could be a combination of the two possibilities.

Or it could simply be luxury pricing - that there's minimal practical difference between 56 micron and 100 micron, but, because 100 micron has more prestige, they can increase its perceived value by adding an additional surcharge to it.