A glass tube, sealed at one end, while in a horizontal position, contains 240 mm ^ 3 of air separated from

A glass tube, sealed at one end, while in a horizontal position, contains 240 mm ^ 3 of air separated from the outside air by a column of mercury 15 cm long. What will be the volume of air in the tube if it is installed with the open end down? atmospheric pressure 0. MPa. Isothermal process

Given: We translate into the SI system;
Po = 0.1 MPa = 0.1 * 106 Pa;
V1 = 240 mm3;
T = const;
L = 15 cm = 0.15 m;
p = 13 546 kg / m3 – mercury;
R = 8.31 J / (mol * K);
g = 10 m / s2;
Find: V2 -?
Solution:

P1 = Po;
Let’s write the Mendeleev – Clapeyron equation: P1 * V1 = v * R * T;
P2 = Po + PPT;
PPT = p * g * L;

P2 * V2 = v * R * T;
Now let’s equate:
P1 * V1 = P2 * V2;
V2 = (V1 * P1) / P2 = (V1 * Po) / (Po + p * g * L) = V1 / (1 + (p * g * L) / Po);
V2 = 240 mm3 / (1 + (13546 * 10 * 0.15) / (0.1 * 106) = 199.5 mm3;
Answer: V2 = 199.5 mm3.