Question

If the copper is drawn into wire whose diameter is 8.00mm , how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3.
(Assume that the wire is a cylinder whose volume is V=πr2h, where r is its radius and h is its height or length.)

Answer 1

Answer on Question#38855-Chemistry-Inorganic Chemistry

Question

If the copper is drawn into wire whose diameter is $8.00 \, \text{mm}$ , how many feet of copper can be obtained from the ingot? The density of copper is $8.94 \, \text{g/cm}^3$ .

(Assume that the wire is a cylinder whose volume is $V = \pi r2h$ , where $r$ is its radius and $h$ is its height or length)

Answer

The volume of the copper ingot $(V)$ is calculated as a quotient of mass $(m)$ to the density $(\rho)$ of copper:

$$V = \frac {m}{\rho}$$

The wire is a cylinder whose volume is

$$V = \pi r ^ {2} h,$$

where $r$ is its radius and $h$ is its height or length.

When equating the equations we have

$$\pi r ^ {2} h = \frac {m}{\rho},$$

whence

$$h = \frac {m}{\rho \pi r ^ {2}}$$

We know that:

$$\rho = 8. 9 4 \mathrm {g} / \mathrm {c m} ^ {3}$$ $$r = d / 2 = 8. 0 0 / 2 = 4. 0 0 \mathrm {m m} = 0. 4 0 0 \mathrm {c m}$$ $$\pi = 3. 1 4$$

When substituting the values into the equation we will get the answer in $\mathbf{cm}$ , while it is asked "how many feet". 1 cm = 0.03281 feet, so the formula to get the copper length in feet is:

$$h = \frac {0 . 0 3 2 8 1 \cdot m}{\rho \pi r ^ {2}} = \frac {0 . 0 3 2 8 1 \cdot m}{8 . 9 4 \cdot 3 . 1 4 \cdot 0 . 4 ^ {2}} = 0. 0 0 7 3 0 5 \cdot m$$

Since it is not specified, what is the mass of the ingot, let us calculate the wire length for the mass values from $1\mathrm{g}$ to $1000\mathrm{g}$ . Some discrete results are given in table below

Table

The length for any mass from the calculated range may be determined using the graph