A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8 \mathrm{~cm}^3$. If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre. $\left(\right.$ Take $\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)$

Question

Aicharya · Accepted Answer

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

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8…

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