The compressibility of water is $6 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{N}$. If one litre of water is…
The compressibility of water is $6 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{N}$. If one litre of water is subjected to a pressure of $4 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$, then the decrease in its volume in millilitre will be
10
20
24
15
Solution
Bulk modulus $B=-\frac{P}{\Delta V / V}$
$-$ ve sign shows that with an increase in pressure, a decrease in volume occurs
Compressibility $\mathrm{K}=\frac{1}{\mathrm{~B}}=-\frac{\Delta \mathrm{V}}{\mathrm{PV}}$
Decrease in volume,
$\Delta \mathrm{V}=\mathrm{PVK}=4 \times 10^{7} \times 1 \times 6 \times 10^{-10}$
$=24 \times 10^{-3}$ litre $=24 \times 10^{-3} \times 10^{3} \mathrm{~cm}^{3}$
$=24 \mathrm{~cc}$
.