Q. A cylinder contains $10\ kg$ of gas at pressure of $10^{7}\ N/m^{2}.$ The quantity of gas taken out of the cylinder, if final pressure is $2.5 \times 10^{6}\ N/m^{2},$ will be (Temperature of gas is constant)
A) $15.2\ kg$
B) $3.7\ kg$
C) Zero
D) $7.5\ kg$
Explanation
(d) $PV = mrT \Rightarrow P \propto m\ \ \lbrack\because V,r,T \rightarrow$ constant]
$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{P_{1}}{P_{2}} \Rightarrow \frac{10}{m_{2}} = \frac{10^{7}}{2.5 \times 10^{6}} \Rightarrow m_{2} = 2.5\ kg.$
Hence mass of the gas taken out of the cylinder
$= 10 - 2.5 = 7.5kg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.