Question

The pressure of a medium Is changed from $1.01\times {10}^{5}Pa$ to $1.165\times {10}^{5}Pa$ and the change in volume is $10\%$ keeping the temperature constant. The bulk modulus of the medium Is______.

Answer 1

Step 1: Given parameters

initial pressure$\left(P_1\right)$=$1.01\times {10}^{5}Pa$

final pressure $\left(P_2\right)$=$1.165\times {10}^{5}Pa$

Change in volume $(∆V)$=$10\%$

Step 2: Formula used

$K=\frac{∆P}{(∆V/V)}$

Step 3: Calculation of bulk modulus

$K=\frac{∆P}{\left(\frac{∆V}{V}\right)}$

$\mathit{K}\mathbf{=}\frac{{\mathbf{P}}_{\mathbf{2}}\mathbf{-}{\mathbf{P}}_{\mathbf{1}}}{\left(\frac{∆V}{V}\right)}$
$K=\frac{(1.165\times {10}^5-1.01\times {10}^5)}{\left({\displaystyle \frac{10}{100}}\right)}Pa$

$K=1.6\times {10}^{5}Pa$

Hence, the bulk modulus of the medium is $1.6\times {10}^{5}Pa$.