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 , $\frac{P_1}{P_2}=\frac{m_2}{m_1}$ $\left(\begin{array}{rl}& \text{Given: }{\text{P}}_1={10}^{7}N/m^2\\ & P_2=25\times {10}^{7}N/m^2\\ & m_1=10kg\end{array}\right)$ $\frac{{10}^7}{2.5\times {10}^7}=\frac{m^2}{10}$ So, $m_2=\frac{10}{2.5}=4kg$ Quantity of gas taken out is $=10-4=6kg$