Question

A fractional change in volume of oil is 1 percent when a pressure of $2\times {10}^{7}N/m^2$ is applied.

• A. The bulk modulus of the oil is $2\times {10}^{9}N{m}^{-2}$
• B. Compressibility of the oil is $5\times {10}^{-10}{m}^2{N}^{-1}$
• C. The bulk modulus of the oil is $2\times {10}^{7}N{m}^{-2}$
• D. Compressibility of the oil is $5\times {10}^{-9}N{m}^{-2}$

Answer 1

The correct option is B Compressibility of the oil is $5\times {10}^{-10}{m}^2{N}^{-1}$

$\begin{array}{c}\text{Given pressure}=2\times {10}^{7}N/m^2\\ \text{Fractional change on volume}=1\%\\ \begin{array}{cc}\text{Bulk modulus}& =\frac{\text{Pressure}}{\frac{\Delta v}{v}}\\ =& \frac{2\times {10}^7}{{10}^{-2}}=2\times {10}^{9}N/m^2\end{array}\end{array}$

$\begin{array}{cc}\text{Compressibility}& =\frac{1}{B}=\frac{1}{2\times {10}^9}\\ & =5\times {10}^{-10}{m}^2/N\end{array}$