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An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The lower end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be the length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)

1. 16 cm
2. 22 cm
3. 38 cm
4. 6 cm

Correct answer: 16 cm

Solution

Initially the trapped air column is 8 cm at P0 = 76 cm Hg. After sealing and raising 46 cm, the meniscus sits (54 - L) cm above the mercury surface, so the gas pressure is P = 76 - (54 - L) = 22 + L. Boyle's law: 76 x 8 = (22 + L) x L gives L^2 + 22L - 608 = 0, so L = 16 cm.

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