Question

A cylinder contains $10kg$ 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

Answer 1

Answer: (D)

Intital mass of the gas $m_1=10kg$
Initial pressure $P_1=10N/m^2$
Final pressure $P_2=2.5\times 10^{6}N/m^2$
According to kinetic theory of gases
$PV=\frac{1}{3}m{c}^{-2}$
or $P\propto m$
Hence, $\frac{P_1}{P_2}=\frac{m_1}{m_2}$
or $\frac{10^7}{2.5\times 1^6}=\frac{10}{m_2}$
or $m_2=2.5kg$
Hence, quantity of gas taken out from the cylinder is
$10-2.5=7.5kg$