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A cylinder contains 10 kg of gas at pressure of $10^{7} N / m^{2} .$ The quantity of gas taken out of the cylinder, if final pressure is $2 .5 \times 10^{6} N / m^{2},$ will be (Temperature of gas is constant)

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15.2 kg

7.5 kg

Zero

3.7 kg

answer is D.

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Detailed Solution

$\begin{array}{l} PV = mrT \Rightarrow P \propto m [∵ V, r, T \to constant] \\ \Rightarrow \frac{m_{1}}{m_{2}} = \frac{P_{1}}{P_{2}} \Rightarrow \frac{10}{m_{2}} = \frac{10^{7}}{2 .5 \times 10^{6}} \Rightarrow m_{2} = 2 .5 kg \end{array}$

Hence mass of the gas taken out of the cylinder $= 10 - 2 .5 = 7 .5 kg .$

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