Question

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

• A. 0.14 cm${}^3$
• B. 2 cm${}^3$
• C. 14 cm${}^3$
• D. cannot be determined

Answer 1

The correct option is A

0.14 cm${}^3$

$v=\sqrt{\frac{B}{\rho }}\Rightarrow 1330=sqrt\frac{B}{800}\Rightarrow (1330{)}^2\times 800=B$

$B=1.41\times {10}^{9}N{m}^{-2}$

Now

$B=\frac{\Delta P}{\frac{(\Delta v}{v}}$ (By definition)

$\frac{1.41\times {10}^9\times Deltav}{{10}^{-3}{m}^3}=-(2\times {10}^5)$

$\Delta v=-\frac{2\times {10}^2}{1.41\times {10}^9}$

$Delta=-1.41\times {10}^{-7}{m}^3$

$\Delta =-0.14c{m}^3$