Respuesta :
Answer: The length of copper wire that can be produced is 40.2 m
Explanation:
We are given:
Mass of chalcocite = 5.23 lb = 2374.42 g (Conversion factor: 1 lb = 454 g)
79.8 % (m/m) of copper
This means that 79.8 grams of copper is present in 100 grams of chalcocite
Applying unitary method:
In 100 grams of chalcocite, the mass of copper present is 79.8 grams
So, in 2374.42 grams of chalcocite, the mass of copper present will be = [tex]\frac{79.8}{100}\times 2374.42=1873.42g[/tex]
To calculate volume of a substance, we use the equation:
[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]
Density of copper = [tex]8.96g/cm^3[/tex]
Mass of copper = 1873.42 g
Putting values in above equation, we get:
[tex]8.96g/cm^3=\frac{1873.42g}{\text{Volume of copper}}\\\\\text{Volume of copper}=\frac{1873.42g}{8.96g/cm^3}=209.08cm^3[/tex]
To calculate the length of the wire, we use the equation:
[tex]V=\pi r^2h[/tex]
where,
V = volume of copper wire = [tex]209.08cm^3=209.08\times 10^{-6}m^3[/tex] (Conversion factor: [tex]1m^3=10^6cm^3[/tex] )
r = radius of the copper wire = [tex]\frac{d}{2}=\frac{0.1019}{2}=0.051in=1.29\times 10^{-3}m[/tex] (Conversion factor: 1 in = 0.0254 m)
h = length/ height of the copper wire = ?
Putting values in above equation, we get:
[tex]209.08\times 10^{-6}m^3=(3.14)\times (1.29\times 10^{-3})^2\times h\\\\h=\frac{209.08\times 10^{-6}}{3.14\times (1.29\times 10^{-3})^2}=40.2m[/tex]
Hence, the length of copper wire that can be produced is 40.2 m
