Question

A cylinder contains 10 kg of gas at pressure $ {{10}^{7}}N/{{m}^{2}}. $ The quantity of gas taken out of cylinder if final pressure is $ 2.5\times {{10}^{7}}N/{{m}^{2}} $ is: (assume the temperature of gas is constant)

• A. zero
• B. 7.5 kg
• C. 2.5 kg
• D. 6 kg

Answer 1

Answer: (D)

According to Boyles law PV = constant (at constant temperature) $ \Rightarrow $ $ P\propto \frac{1}{V}\Rightarrow P\propto \frac{1}{m/d}\Rightarrow P\propto \frac{1}{m} $ Hence , $ \frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}} $ $ \left( \begin{align} & \text{Given: }{{\text{P}}_{1}}={{10}^{7}}N/{{m}^{2}} \\ & {{P}_{2}}=25\times {{10}^{7}}N/{{m}^{2}} \\ & {{m}_{1}}=10\,kg \\ \end{align} \right) $ $ \frac{{{10}^{7}}}{2.5\times {{10}^{7}}}=\frac{{{m}^{2}}}{10} $ So, $ {{m}_{2}}=\frac{10}{2.5}=4\,kg $ Quantity of gas taken out is $ =10-4=6\,kg $