Question

Copper can be drawn into thin wires. how many meters of 34-gauge wire (diameter ???? 6.304????10????3 in) can be produced from the copper in 5.01 lb of covellite, an ore of copper that is 66% copper by mass? (hint: treat the wire as a cylinder: v of cylinder ???? ????r2h; d of copper ???? 8.95 g/cm3.)

Answer 1

Covellite ore contains 66% copper by mass thus, in 5.01 lb of covellit, mass of copper will be :

$m_{Cu}=\frac{66}{100}\times 5.01 lb=3.3066 lb$

Converting mass into grams,

1 lb=453.592 g

Thus, 5.01 lb=2272.498 g

The density of copper is $8.95 g/cm^{3}$, calculate volume as follows:

$V=\frac{m}{d}=\frac{2272.498 g}{8.95 g/cm^{3}}=253.91 cm^{3}$

Comparing this volume of cylinder because shape of wire is cylindrical.

$V=\pi r^{2}h=253.91 cm^{3}$

Since, 34 gauge=0.00630 inch

Convert inch into cm,

1 inch=2.54 cm

Thus,

0.00630 inch=0.016002 cm

The diameter of wire is 0.016002 cm, calculate radius as follows:

$Radius =\frac{diameter}{2}=\frac{0.016002}{2}=0.008 cm$

Rearranging equation for volume and putting the values,

$h=\frac{253.91 cm^{3}}{(3.14)(0.008cm)^{2}}=1.26\times 10^{6}cm$

1 cm=0.01 m thus,

$1.26\times 10^{6}cm=1.26\times 10^{6}\times 0.01 m=1.26\times 10^{4}m$

Thus, the length of wire is $1.26\times 10^{4}m$.