A vessel of volume 10 l is evacuated by means of a piston air pump. One piston stroke captures the v — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

After each stroke, the gas expands from volume $V$ to $V + v$. By Boyle's Law, the new pressure is $P_{new} = P_{old} \times \frac{V}{V+v}$. Here, $V = 10 \text{ L}$ and $v = 1 \text{ L}$, so the ratio is $10/11$. After $n$ strokes, $P_n = P_0 \left(\frac{10}{11}\right)^n = 24.2 \left(\frac{10}{11}\right)^n$. For 1 stroke, $P_1 = 24.2 \times \frac{10}{11} = 22 \text{ atm}$. For 2 strokes, $P_2 = 22 \times \frac{10}{11} = 20 \text{ atm}$. To reduce pressure by $\eta$ times, $P_0 / P_n = \eta = \left(\frac{11}{10}\right)^n = (1.1)^n$. Taking natural log, $\ln \eta = n \ln 1.1 \implies n = \frac{\ln \eta}{\ln 1.1}$. Therefore, correct answer is A,B,C,D.