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A cylinder contains 10 kg of gas at pressure of $10^7 \mathrm{~N} / \mathrm{m}^2$. The quantity of gas taken out of the cylinder, if final pressure is $2.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$ will be (temperature of gas is constant)
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The correct answer is:
7.5 kg
Intital mass of the gas $m_1=10 \mathrm{~kg}$
Initial pressure $P_1=10 \mathrm{~N} / \mathrm{m}^2$
Final pressure $P_2=2.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
According to kinetic theory of gases
$P V=\frac{1}{3} m c^{-2}$
or $\quad P \propto m$
Hence, $\quad \frac{P_1}{P_2}=\frac{m_1}{m_2}$
or $\quad \frac{10^7}{2.5 \times 10^6}=\frac{10}{m_2}$
or $\quad m_2=2.5 \mathrm{~kg}$
Hence, quantity of gas taken out from the cylinder is $10-2.5=7.5 \mathrm{~kg}$
Initial pressure $P_1=10 \mathrm{~N} / \mathrm{m}^2$
Final pressure $P_2=2.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
According to kinetic theory of gases
$P V=\frac{1}{3} m c^{-2}$
or $\quad P \propto m$
Hence, $\quad \frac{P_1}{P_2}=\frac{m_1}{m_2}$
or $\quad \frac{10^7}{2.5 \times 10^6}=\frac{10}{m_2}$
or $\quad m_2=2.5 \mathrm{~kg}$
Hence, quantity of gas taken out from the cylinder is $10-2.5=7.5 \mathrm{~kg}$
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