Question

The compressibility of water is $5\times {10}^{-10}{\text{m}}^2\text{/N}$. If it is subjected to a pressure of $15\text{MPa}$, the fractional decrease in volume will be:

• A. $3.3\times {10}^{-5}$
• B. $5.6\times {10}^{-4}$
• C. $7.5\times {10}^{-3}$
• D. $1.5\times {10}^{-2}$

Answer 1

The correct option is C $7.5\times {10}^{-3}$

As we know,
$\text{Compressibility}=\frac{1}{\text{Bulk modulus}}$
$=\frac{1}{K}=-\frac{\Delta V}{V\Delta P}$
Given $\text{Compressibility}=5\times {10}^{-10}{\text{m}}^2\text{/N}$
$\Rightarrow -\frac{\Delta V}{V\Delta P}=5\times {10}^{-10}{\text{m}}^2\text{/N}$
$\therefore$ fractional decrease in volume
$(-\frac{\Delta V}{V})=\text{Compressibility}\times \Delta P=5\times {10}^{-10}\left({\text{m}}^2\text{/N}\right)\times 15\times {10}^6\left({\text{N/m}}^2\right)$

Hence, $(-\frac{\Delta V}{V})=7.5\times {10}^{-3}$