Question

Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 × 10⁹ N m⁻².

Answer 1

Given:
Bulk modulus of water (B) = $2.1\times {10}^9{\mathrm{Nm}}^{-2}$
In order to decrease the volume (V) of a water sample by 0.01%, let the increase in pressure be P.

$$\begin{gathered} \frac{V\times 0.01}{100}=∆V \\ \Rightarrow \frac{∆V}{V}={10}^{-4} \\ \mathrm{From}B=\frac{PV}{∆V},\mathrm{we}\mathrm{have}: \\ \Rightarrow P=B\left(\frac{∆V}{V}\right) \\ =2.1\times {10}^9\times {10}^{-4} \\ =2.1\times {10}^5\mathrm{N}/{\mathrm{m}}^2 \end{gathered}$$

Hence, the required increase in pressure is $2.1\times {10}^5{\mathrm{Nm}}^{-2}$.