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) =  \[2 . 1 \times {10}^9 {\text{ Nm }}^{- 2}\]

In order to decrease the volume (V) of a water sample by 0.01%, let the increase in pressure be P.

\[\frac{V \times 0 . 01}{100} = ∆ V\]
\[ \Rightarrow \frac{∆ V}{V} = {10}^{- 4} \]
\[\text{ From B }= \frac{PV}{∆ V}, \text{ we have }: \]
\[ \Rightarrow P = B\left( \frac{∆ V}{V} \right)\]
\[ = 2 . 1 \times {10}^9 \times {10}^{- 4} \]
\[ = 2 . 1 \times {10}^5 \text{ N/ m}^2\] 

Hence, the required increase in pressure is \[2 . 1 \times {10}^5 {\text{ Nm}}^{- 2}\] .