Question

The compressibility of water is $5\times {10}^{-10}{m}^2/N$ and subjected to a pressure of 15 MPa. The fractional decrease in volume will be

• A. $7.5\times {10}^{-3}$
• B. $5\times {10}^{-3}$
• C. $2.5\times {10}^{-3}$
• D. $1.25\times {10}^{-3}$

Answer 1

Answer: (A)

$7.5\times {10}^{-3}$

Given,

$\beta =\frac{1}{K}=5\times {10}^{-10}{m}^2/N$

$\Delta P=15MPa=15\times {10}^{6}Pa$

Bulk modulus,

$K=-\frac{\Delta P}{{\epsilon }_V}$

where, ${\epsilon }_V=$ volumetric strain

$\beta =-\frac{{\epsilon }_V}{\Delta P}$

${\epsilon }_V=-\beta \Delta P=-5\times {10}^{-10}\times 15\times {10}^6$

${\epsilon }_V=7.5\times {10}^{-3}$

The correct option is A.