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. $15.2kg$
• B. $3.7kg$
• C. $zero$
• D. $7.5kg$

Answer 1

Answer: (D)

Initial 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
$PV=\frac{1}{3}m\overline{c^2}$
or $P\propto m$
Hence, $\frac{P_1}{P_2}=\frac{m_1}{m_2}$
or $\frac{10^7}{2.5\times 10^6}=\frac{10}{m_2}$
or $m_2=2.5kg$
Hence, quantity of gas taken out from the cylinder is $10-2.5=7.5kg$