Question 213: Properties of Matter

Question

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)

Accepted Answer

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

Properties of Matter

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)

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