A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm³. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was _______ litre.

(Take 1 atm = 10⁵ Pa)

<p>Given, Initial pressure of liquid $\left(\mathrm{P}_{\mathrm{i}}\right)=1 \mathrm{~atm}$</p> <p>Final pressure of liquid $\left(\mathrm{P}_{\mathrm{f}}\right)=5 \mathrm{~atm}$</p> <p>Change in pressure $(\mathrm{dP})=\mathrm{P}_{\mathrm{f}}-\mathrm{P}_{\mathrm{i}}=4 \mathrm{~atm}$</p> <p>$=4 \times 10^5 \mathrm{~Pa}$</p> <p>Change in volume $(\mathrm{dV})=-0.8 \mathrm{~cm}^3$</p> <p>Bulk modulus $(B)=2 \times 10^9 \mathrm{~Pa}$</p> <p>Now, $B=\frac{-d P}{(d V / V)} \Rightarrow V=-B\left(\frac{d V}{d P}\right)$</p> <p>$$\begin{aligned} \Rightarrow \mathrm{V} & =-2 \times 10^9 \times \frac{\left(-0.8 \times 10^{-6}\right)}{4 \times 10^5} \\ & =4 \times 10^{-3} \mathrm{~m}^3=4 \text { litre } \end{aligned}$$</p>