Chapter 9, Problem 47P

To determine

Change in volume in percentage.

Answer to Problem 47P

Solution: $0.022\%$ .

Explanation of Solution

Given:The pressure is 200 times of atmospheric pressure.

The Bulk Modulus value for iron is $90\times {10}^9{\text{N/m}}^{\text{2}}$ .

Formula Used:

The Bulk modulus of elasticity is defined as ratio of bulk stress to bulk strain, which is given by

  $K=\frac{\delta P}{\delta V}V$

Where K is bulk modulus, V is the volume, $\text{δV}$ is the change in volume, $\text{δP}$ is change in pressure.

Calculation:

Substitute all the values in above equation and solve for change in pressure

  $\begin{array}{l}K=\frac{\delta P}{\delta V}V\\ \frac{\delta V}{V}=\frac{\delta P}{K}\\ \frac{\delta V}{V}=\frac{200\times 10^5}{90\times 10^9}\\ \frac{\delta V}{V}=2.22\times 10^{-4}\end{array}$

Percentage change is $2.2\times {10}^{-4}\times 100=2.2\times {10}^{-2}=0.022\%$

Conclusion:The volume of iron bathysphere's change at this depth by $0.022\%$ .