In a narrow glass tube, placed horizontally, there is a column of air 80 mm long, locked with a column

In a narrow glass tube, placed horizontally, there is a column of air 80 mm long, locked with a column of mercury 40 mm long. What is the length of the air column if the tube is positioned vertically with the open end up? Atmospheric pressure 760 mm Hg

Given:
L1 = 80mm,
d = 40mm.
P1 = 760mm. rt. Art.
To find:
L2 -?
Since the temperature and the amount of air in the tube do not change, you can use the Boyle-Mariotte law:
P1 * V1 = P2 * V2;
The volume is determined by the product of the cross-sectional area of the tube and the length of the air column:
V1 = L1 * S,
V2 = L2 * S;
P1 * L1 = P2 * L2;
L2 = L1 * (P1 / P2);
When the tube is positioned vertically, atmospheric pressure plus the pressure of the mercury column, which is determined by the height of the column, acts on the air column:
P2 = P1 + d;
L2 = 80mm * (760/800) = 76mm.