Question

A fractional change in volume of oil is $1$ percent when a pressure of $2\times 107N{m}^{-2}$ is applied calculate the bulk modulus and its compressibility :

• A. $3\times {10}^{8}N{m}^{-2},0.33\times {10}^{-9}{m}^2{N}^{-1}$
• B. $5\times {10}^{8}N{m}^{-2},2\times {10}^{-10}{m}^2{N}^{-1}$
• C. $2\times {10}^{9}N{m}^{-2},5\times {10}^{-10}{m}^2{N}^{-1}$
• D. $5\times {10}^{9}N{m}^{-2},2\times {10}^{-9}{m}^2{N}^{-1}$

Answer 1

The correct option is C $2\times {10}^{9}N{m}^{-2},5\times {10}^{-10}{m}^2{N}^{-1}$

$\frac{△V}{V}=0.01$

$P=2\times {10}^7$

$B=\frac{P}{△V/V}$

$=\frac{2\times {10}^7}{{10}^{-2}}$

$B=2\times {10}^{9}N{m}^{-2}$

$C=\frac{1}{B}=\frac{1}{2\times {10}^{-9}}=5\times {10}^{-10}{m}^2{N}^{-1}$