Question

A cylinder contains $ 10\,\,kg $ of gas at pressure of $ 10^7N/{{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)

Initial mass of the gas $m_1 = 10\,kg$
Initial pressure $P_{1}=10 N / m ^{2}$
Final pressure $P_{2}=2.5 \times 10^{6} N / m ^{2}$
According to kinetic theory of gases
$P V=\frac{1}{3} m \overline{c^{2}}$
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 $m_{2}=2.5\, kg$
Hence, quantity of gas taken out from the cylinder is $10-2.5=7.5 \,kg$