Question

A specimen of oil having an initial volume of 600cm^3 is subjected to a pressure increase of 3.6×10^6Pa, and the volume is found to decrease by 0.45cm^3. What is the bulk modulus of the material? The compressibility?

Answer 1

Answer: $48\times 10^6\ Pa,\ 2.083\times 10^{-8}\ Pa^{-1}$

Explanation:

Given

Initial volume is $V_1=600\ cm^3$

Pressure increase $P=3.6\times 10^6\ Pa$

Volume decrease $\Delta V=-0.45\ cm^3$

Bulk modulus is given by

$\Rightarrow k=-V\dfrac{dP}{dV}$

Insert the values

$\Rightarrow k=-600\times \dfrac{3.6\times 10^6}{-0.45}\\\\\Rightarrow k=48\times 10^6\ Pa$

Compressibility is the inverse of bulk modulus

$\therefore \text{Compressibility= }\dfrac{1}{k}\\\\\Rightarrow \dfrac{1}{48\times 10^6}=2.083\times 10^{-8}\ Pa^{-1}$