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  4. An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is 100 kpa, the absolute pressure at the bottom of lake in kpa is ... (assume no temperature variation):

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Q. An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is $100 \,kpa$, the absolute pressure at the bottom of lake in $kpa$ is ... (assume no temperature variation):

Jharkhand CECEJharkhand CECE 2005

Solution:

In an isothermal change temperature remains constant.
For isothermal change $P V=R T=$ constant
where, $P=h \rho g=$ height $\times$ density $\times$ gravity
$\therefore P_{1} V_{1}=P_{2} V_{2}$
Given,$ V_{2}=3 V_{1}, P_{2}=100\, k P a=100 \times 10^{3} Pa$
$\therefore P_{1}=\frac{P_{2} V_{2}}{V_{1}}$
$=\frac{100 \times 10^{3} \times 3 V_{1}}{V_{1}}=300\, kPa$