Question

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 :

• A. 7.5 kg
• B. 15.2 kg
• C. 10.5 kg
• D. none of these

Answer 1

Answer: (A)

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 $=10-2.5=7.5kg$