Bulk modulus of a liquid is 2 x 10^9 Pa initially and final pressure are 1 atm and 5 atm respectively.

Question

Bulk modulus of a liquid is \(2\times 10^9\) Pa initially and final pressure are 1 atm and 5 atm respectively. Find initial volume of the liquid if change in volume is \(0.8\ cm^3\).

(1) \(2\times 10^3\ cm^3\)

(2) \(4\times 10^3\ cm^3\)

(3) \(2\times 10^{-4}\ cm^3\)

(4) \(4\times 10^{-3}\ cm^3\)

Answer 1

Correct option is : (2) \(4\times 10^3\ cm^3\)

\(\beta = \frac{\Delta P}{\frac{\Delta V}{V}}\Rightarrow \ V = \frac{\Delta V\beta}{\Delta P}\)

\( = \frac{0.8\times 10^{-6} \times 2 \times 10^9}{4\times 10^5} = 4\times 10^{-3}\ m^3 = 4\times 10^3\ cm^3\)