Question
Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 × 109N/m2.
✓
Answer
Given:
Bulk modulus of water B = 2.1 × 109Nm-2
In order to decrease the volume (V) of a water sample by 0.01%, let the increase in pressure be P.
$\frac{\text{v}\times0.1}{100}=\triangle\text{V}$
$\Rightarrow\frac{\triangle\text{V}}{\text{V}}=10^{-4}$
From B $=\frac{\text{P}\text{V}}{\triangle\text{V}},$ We have:
$\Rightarrow\text{P}= \text{B}\Big(\frac{\triangle\text{V}}{\text{V}}\Big)$
$=2.1\times10^{9}\times10^{-4}$
$=2.1\times10^{5}\text{N}/\text{m}^2$
Hence, the requred increase in pressure is 2.1 × 105Nm-2.
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