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An ideal gas filled in a cylinder occupies volume $\mathrm{V}$. The gas is compressed isothermally to the volume $\mathrm{V} / 3 .$ Now the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules escape to bring the pressure in the cylinder back to its original value.
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The correct answer is:
$66 \%$
$\frac{P_{1} V_{1}}{n_{1}}=\frac{P_{2} V_{2}}{n_{2}}$
$\frac{P_{1} V}{n_{1}}=\frac{P_{1} \cdot \frac{V}{3}}{n_{2}}$
$\Rightarrow n_{2}=\frac{n_{1}}{3}$
Now, $\frac{2}{3}$ of Gas will come out to make the presence $\mathrm{P}_{1}$
Hence $66.66\%$
$\frac{P_{1} V}{n_{1}}=\frac{P_{1} \cdot \frac{V}{3}}{n_{2}}$
$\Rightarrow n_{2}=\frac{n_{1}}{3}$
Now, $\frac{2}{3}$ of Gas will come out to make the presence $\mathrm{P}_{1}$
Hence $66.66\%$
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