Question

The compressibility of water $5\times {10}^{10}{m}^2{N}^{-1}$ The decrease in volume of $100ml$ of water when subjected to a pressure of $15MPa$:

• A. $0.25ml$
• B. $0.50ml$
• C. $0.75ml$
• D. $1ml$

Answer 1

The correct option is C $0.75ml$

Given,

Compressibility, $k=5\times {10}^{-10}{m}^2{N}^{-1}$

Volume is $V=100mL$

Change in pressure $\Delta P=15\times {10}^6-0=15\times {10}^{6}Pa$

Compressibility $k=\frac{-\frac{\Delta V}{V}}{\Delta P}$

Decrease in volume,

$-\Delta V=kV\Delta P=5\times {10}^{-10}\times 100\times 15\times {10}^6$

$-\Delta V=0.75mL$

Hence, change in volume is $0.75mL$