Question

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

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

Answer 1

The correct option is B

24 cc

Compressibility factor $\left(K\right)=\frac{1}{B}$
$B=\frac{1}{K}=\frac{1}{6\times {10}^{-10}{N}^{-1}{m}^2}B=\frac{P}{-\frac{\Delta V}{V}}-\frac{\Delta V}{V}=\frac{P}{B}=\frac{4\times {10}^{7}N/m^2}{\left[\frac{1}{6\times {10}^{-10}}\right]N^{-1}{m}^2}\frac{\Delta V}{V}=24\times {10}^{-3}L=24cc\Rightarrow [{10}^{-3}L=1cc]$