Question

The approximate depth of an ocean is $2700\, m$. The compressibility of water is $45.4 \times 10^{-11} Pa ^{-1}$ and density of water is $10^{3} kg / m 3 .$ What fractional compression of water will be obtained at the bottom of the ocean?

• A. $1.0 \times 10^{-2}$
• B. $1.2 \times 10^{-2}$
• C. $1.4 \times 10^{-2}$
• D. $1.8 \times 10^{-2}$

Answer 1

Answer: (B)

compressibility is given as $K =\frac{\frac{\Delta V }{ V }}{\Delta P }$
$\Delta V =K\times \Delta P \times V$
Substituting values $\Delta P =\rho \,gh \,Pa $,
$ K=45 \times 10^{-11} Pa ^{-1}$
$\frac{\Delta V }{ V }=45 \times 10^{-11} \times \Delta P$
$\frac{\Delta V }{ V }=45 \times 10^{-11} \times 10^{3} \times 10 \times 2700$
$\frac{\Delta V }{ V }=1.2 \times 10^{-2}$