Question

The compressibility of water is $6\times {10}^{-10}{N}^{-1}{m}^2$. If one litre is subjected to a pressure of $4\times {10}^{7}N{m}^{-2}$, the decrease in its volume is then

• A. $10cc$
• B. $24cc$
• C. $15cc$
• D. $12cc$

Answer 1

Answer: (B)

$24cc$

Bulk modulus $B=-\frac{P}{\Delta V/V}$
$-ve$ sign shows that with an increase in pressure, a decrease in volume occurs
Compressibility $K=\frac{1}{B}=-\frac{\Delta V}{PV}$

Decrease in volume,

$\Delta V=PVK=4\times {10}^7\times 1\times 6\times {10}^{-10}$

$=24\times {10}^{-3}litre=24\times {10}^{-3}\times {10}^3{cm}^3$

$=24cc$