What is the pressure of air in the air columns, when the tube was horizontal? — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

When horizontal, both columns have the same pressure P0. When vertical with 'A' up, the mercury column of length 20 cm moves down by 10 cm. The upper air column AB expands from 20 cm to 30 cm, and the lower column CD is compressed from 60 cm to 50 cm. By Boyle's Law: P_A = P0 × 20/30 = 2/3 P0, and P_D = P0 × 60/50 = 6/5 P0. The vertical force balance gives: P_D = P_A + 20 cm Hg → 6/5 P0 = 2/3 P0 + 20 → (18 - 10)/15 P0 = 20 → 8/15 P0 = 20 → P0 = 37.5 cm Hg. Thus, P_AB = P_CD = 37.5 cm Hg.