Question

The compressibility of water is 4 x 10${}^{-5}$ per unit atmosphere pressure. The decrease in volume of 100cm${}^3$ water under a pressure of 100atm will be

• A. 0.4 cm${}^3$
• B. 4 x 10${}^{-5}$cm${}^3$
• C. 0.025 cm${}^3$
• D. 0.04cm${}^3$

Answer 1

The correct option is A 0.4 cm${}^3$

1 atm pressure $={10}^{5}N/m^2$
$C=\frac{1}{B}=4\times \frac{{10}^{-5}}{{10}^5}{m}^2/N$
$=4\times {10}^{-10}{m}^2/N$
$P=100atm,V=100c{m}^3$
$\frac{{10}^{10}}{4}=\frac{-100\times {10}^5}{\frac{\Delta V}{100\times {10}^{-6}}}$
$\frac{{10}^{10}}{4}=\frac{-{10}^3}{\Delta V}$
$\Delta V=-4\times {10}^{-7}{m}^3$
$=-0.4c{m}^3$
-ve sign indicates that volume is decreased.