B 1lb cube of 99% pure copper?

[Coulin]

I've been wrestling with something for a bit. I have one pound of copper (99%) in cube-form. Roughly 1.5 inches on a side. It's essentially a paperweight.

Are those dimensions in the ballpark for relatively pure copper?

 

[Hornbein]

I've been wrestling with something for a bit. I have one pound of copper (99%) in cube-form. Roughly 1.5 inches on a side. It's essentially a paperweight.

Are those dimensions in the ballpark for relatively pure copper?

The volume of the cube is easy to calculate, the density of the cube is easy to find, easy to put them together to get an answer. Can you give it a shot.

 

[Coulin]

I can, I was struggling with the cubic centimeter. Thank you for the push. It's close enough that it's likely the imprecision of measurement that can make up the difference. A pure cube of copper would be 50.625 cmsqd. The results on my item were 55.3.

I was looking at it the other day and saw that it was the same size as three other paperweight cubes on my desk. One is a fidget toy, one is a Lucite display and one is a wooden block. Their manufacture dates span over a decade.

I enjoy copper, aesthetically. I'm trying to figure out why one pound of copper has the same (within a tolerance of a few millimeters) dimensions as things specifically manufactured to be aesthetically pleasing.

 

[Mark44]

A pure cube of copper would be 50.625 cmsqd.

I'll assume the figure is correct, but the units aren't. They should be cm cubed, not squared. The volume should be written as $50.625 \text{ cm}^3$ or as 50. 625 cc, where cc is the common abbreviation for cubic centimeters.

 

[hutchphd]

You have a typo: 60.625 cc

 

[Mark44]

You have a typo: 60.625 cc

Fixed the typo.

 

[gmax137]

I've been wrestling with something for a bit. I have one pound of copper (99%) in cube-form. Roughly 1.5 inches on a side. It's essentially a paperweight.

Are those dimensions in the ballpark for relatively pure copper?

Depends on the size of your ballpark.

"Roughly 1.5 inches on a side" -- if it is 1.495 inches on a side, that reduces its volume by a factor of 0.99. If it isn't really a cube (flat sides, parallel and square) who knows? And how pure is "relatively pure"?

EDIT: Here is a good starting point for the different copper alloys
https://www.onlinemetals.com/en/product-guide#copper

 

[Steve Zissou]

Data:
1 lb of Cu
There are 453.592 grams in a pound
the density of Cu is 8.94 g per cubic cm
1 cubic centimeter is 0.03102 cubic inches

Calculation:
$$
\left( 1\,lb\, Cu \right)\left(\frac{453.592\,g\,Cu}{1\,lb\,Cu}\right)\left( \frac{1\,cm^3}{8.94\,g\,Cu} \right)\left( \frac{0.0610237\,in^3}{1\,cm^3} \right)=3.096181\,in^3
$$
Now, to find the distance of each side of the cube just take the cube root, i.e. raise to the power of 1/3:
$$
=1.457501\,in
$$
Now to account for the weight percent purity of the copper, start with 0.99 of a pound, you'll get something like 1.452626 in on a side. Of course that 1% impurity has its own density, etc.
Anyways, the key here is to realize that units of measure cancel, just like numbers do.

 

[WWGD]

Maybe you can check for the propagation of uncertainty/error in your measurements to see of the difference falls within a reasonable range too?

 

[DaveC426913]

Of course that 1% impurity has its own density, etc.

That impurity is almost certainly going to be a similar metal.
iron: 7.9, nickel: 8.9, zinc: 7.1, tin: 7.3, arsenic: 5.7, lead: 11.3 (which, together, average 8.0)

So, a 1% impurity of a metal (or combination of metals) might - at worst - change the volume/density by an amount on the order of 1/10th of 1%, or - at best - by virtually nothing.

So somewhere between 3.1 and 3.095 volume.

Which, at worst, changes the length of the sides by < 2mil - or about the width of a human hair.

 

[Steve Zissou]

That impurity is almost certainly going to be a similar metal.
iron: 7.9, nickel: 8.9, zinc: 7.1, tin: 7.3, 5.7, 11.3 (which, together, average 8.0)

So, a 1% impurity of a metal (or combination of metals) might change the volume/density by an amount on the order of 1/10th of 1% - or by virtually nothing.

Yep