Chapter SH, Problem 17.4APP

To determine

To calculate:The difference in mass between a piece of silver and a piece of copper, each of volume $5{\text{ cm}}^3$ .

Answer to Problem 17.4APP

The difference in mass between the silver piece and the copper piece, each of volume $5{\text{ cm}}^3$ , is $\text{8}\text{.0 g}$ .

Explanation of Solution

Given data:

Density of silver $=10.5{\text{ g/cm}}^3$

Volume of silver piece $=5{\text{ cm}}^3$

Density of copper $=8.9{\text{ g/cm}}^3$

Volume of copper piece $=5{\text{ cm}}^3$

Formula used:

Density of any substance,

  $\text{density}=\frac{\text{mass}}{\text{volume}}$

Calculation:

As per the problem,

Density of silver $=10.5{\text{ g/cm}}^3$

Volume of silver piece $=5{\text{ cm}}^3$

Substitute the values of density and volume of silver in the density formula to find the mass of silver piece.

  $\begin{array}{l}\text{density}=\frac{\text{mass }}{\text{volume}}\\ \text{mass}=\text{density}\times \text{volume}\\ m_{silver}=10.5{\text{ g/cm}}^3\times 5{\text{ cm}}^3\\ m_{silver}=52.5\text{ g}\end{array}$

Hence, mass of silver piece is $52.5\text{ g}$

Now,

Density of copper $=8.9{\text{ g/cm}}^3$

Volume of copper piece $=5{\text{ cm}}^3$

Substitute the values of density and volume of copper in the density formula to find the mass of copper piece.

  $\begin{array}{l}\text{density}=\frac{\text{mass }}{\text{volume}}\\ \text{mass}=\text{density}\times \text{volume}\\ m_{copper}=8.9{\text{ g/cm}}^3\times 5{\text{ cm}}^3\\ m_{copper}=44.5\text{ g}\end{array}$

Hence, mass of coper piece is $44.5\text{ g}$

Now, subtract the mass of coper piece from the mass of silver piece to find the difference between them.

So, the difference in mass between a piece of silver and a piece of copper is

  $\begin{array}{l}=m_{silver}-m_{copper}\\ =52.5\text{ g}-44.5\text{ g}\\ \text{=8}\text{.0 g}\end{array}$

Conclusion:

The difference in mass between the silver piece and the copper piece, each of volume $5{\text{ cm}}^3$ , is $\text{8}\text{.0 g}$ .