Question

Find the change in the volume of 1.0 litre kerosene when it is subjected to an extra pressure of $2.0\times {10}^{5}N{m}^{-2}$ from the following data. Density of kerosene $=800kg{m}^{-3}$ and speed of sound in kerosene = $1330m{s}^{-1}$.

Answer 1

We know that, $v=\sqrt{\left(\frac{K}{p}\right)}$

where K =bulk modulus of elasticity

$\Rightarrow k=v^2\rho =(1330{)}^2\times 800N/m^2$

We know, $K=\frac{\left(\frac{F}{A}\right)}{\left(\frac{\Delta V}{V}\right)}$

$\Rightarrow \Delta V=\frac{\text{Pressure}}{K}$

$=\frac{2\times {10}^5}{13330\times 1330\times 800}$

So $\Delta V=0.15c{m}^{-3}$