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

In each stroke, the gas expands from V = 10 L to V + v = 11 L, and then 1 L of gas is expelled. This means the fraction of gas remaining after each stroke is V/(V+v) = 10/11. Thus, after n strokes, the remaining pressure is P_n = P0 × (10/11)^n. After 1 stroke: P1 = 24.2 × 10/11 = 22 atm. After 2 strokes: P2 = 24.2 × (10/11)^2 = 20 atm. To reduce pressure η times, P0/P_n = η → (11/10)^n = η → n × ln(1.1) = ln η → n = ln η / ln 1.1.