Q135 / 160 · TS EAMCET 2019 (03 May Shift 1) · Physics
How much pressure (in atm) is needed to compress a sample of water by $0.4 \%$ ? (Assume, Bulk modulus of water $\approx 2.0 \times 10^9 \mathrm{~Pa}$ )
- A$60 \mathrm{~atm}$
- B$70 \mathrm{~atm}$
- Correct answerC$80 \mathrm{~atm}$
- D$90 \mathrm{~atm}$
Solution
Given, percentage change in volume $=0.4 \%$ Bulk modulus of water, $B=2 \times 10^9 \mathrm{~Pa}$ 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, $p=B\left(-\frac{\Delta V}{V}\right)$
$$
\begin{aligned}
& =\frac{0.4}{100} \times 2 \times 10^9 \mathrm{~Pa}=\frac{0.4}{100} \times \frac{2 \times 10^9}{101325} \mathrm{~atm} \\
& =79 \mathrm{~atm} \approx 80 \mathrm{~atm}
\end{aligned}
$$
Hence, 80 atm pressure is needed to compress a sample of water by $0.4 \%$.
Hence, the correct answer is option: 'C'.