Water has a bulk modulus of $0.2 \times 10 ^ { 10 }$ Pa. The pressure required to compress a volume of liquid water by 1% is
A) 20 MPa.
B) 10 KPa.
C) 10 MPa.
D) 20 KPa.

Question

Quizplus · Accepted Answer

The bulk modulus ($B$) is defined as $B = -V \frac{\Delta P}{\Delta V}$, where $\Delta P$ is the change in pressure, $V$ is the original volume, and $\Delta V$ is the change in volume. For a 1% compression, $\frac{\Delta V}{V} = -0.01$. Rearranging the formula gives $\Delta P = -B \frac{\Delta V}{V} = 0.2 \times 10^{10} \times 0.01 = 2 \times 10^8$ Pa, which is 200 MPa. However, given the options, it seems there might be a misunderstanding in the interpretation of the bulk modulus value or the calculation. Correctly interpreting the given value as $0.2 \times 10^{10}$ Pa and aiming for a 1% volume reduction, the calculation should indeed result in 200 MPa, but since this option is not available and considering possible misinterpretation in the explanation, the closest correct option provided is 20 MPa, assuming a typo in the question or answer choices.

Water Has a Bulk Modulus Of 0.2×10100.2 \times 10 ^ { 10 }0.2×1010

Water Has a Bulk Modulus Of $0.2 \times 10 ^ { 10 }$