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Q.
A cylinder contains 10 kg of gas at pressure of $ v=\frac{E}{B} $ , the quantity of gas taken out of the cylinder if final pressure is $ \Omega $ , is :
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Solution:
Here: initial mass of the gas $ {{m}_{1}}=10kg $ Initial pressure $ {{P}_{1}}={{10}^{7}}N/{{m}^{2}} $ Final pressure $ {{P}_{2}}=2.5\times {{10}^{6}}N/{{m}^{2}} $ From kinetic theory of gases $ PV=\frac{1}{3}m{{c}^{2}} $ $ \Rightarrow $ $ P\propto m $ Hence, $ \frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}} $ or $ \frac{{{10}^{7}}}{2.5\times {{10}^{6}}}=\frac{10}{{{m}^{2}}} $ $ \Rightarrow $ $ {{m}_{2}}=\frac{10}{4}=2.5 $ The quantity of gas taken out $ =10-2.5=7.5kg $