Mechanical Properties Of Solids

Question

What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of 2.0 x 10⁵ Nm^-2 from the following data? Density of kerosene = 800 kg m^-³ and speed of sound in kerosene= 1330 ms^-1.

0.97 cm^-3

0.66 cm^-3

0.15 cm^-3

0.59 cm^-3

Solution

0.15 cm^-3

As, we know that

v = $\sqrt{\frac{R}{ρ}}$

where, k = bulk modulus of elasticity

⇒ k = v² ρ

= (1330)² × 800 N/m²

Also k = $\frac{\frac{F}{A}}{\frac{∆ V}{V}}$

ΔV = $\frac{pressure}{k}$

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

ΔV = 0.15 cm³