Question

How much pressure (in atm) is needed to compress a sample of water by $0.4\%$ ? (Assume, Bulk modulus of water $\approx 2.0\times 10^{9}Pa)$

• A. 60 atm
• B. 70 atm
• C. 80 atm
• D. 90 atm

Answer 1

Answer: (C)

Given, percentage change in volume $=0.4\%$
Bulk modulus of water, $B=2\times 10^{9}Pa$
The change in volume of water is given by
$\Delta V=-\frac{p\cdot V}{B}$
where, $p=$ pressure applied on the sample of the matter.
Given,
$\frac{\Delta V}{V}=-0.4\%=\frac{0.4}{100}$
Pressure required, $p=B\left(-\frac{\Delta V}{V}\right)$
$=\frac{0.4}{100}\times 2\times 10^{9}Pa=\frac{0.4}{100}\times \frac{2\times 10^9}{101325}atm$
$=79atm\approx 80atm$
Hence, $80atm$ pressure is needed to compress a sample of water by $0.4\%$.