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Homework Statement
A glass tube filled with air at room temperature is 1.54m long. The tube is closed on one end, and open on the other. When submerging the open end in water, the water in the tube rises by 0.14m.
How much of the tube is above the water's surface?
The correct answer is 0.40m.
Homework Equations
Boyle's law
Run-of-the-mill hydrostatics equations
The Attempt at a Solution
First comes Boyle's law: ##p_2=\frac{p_1V_1}{V_2}=\frac{p_1Ah_1}{Ah_2}=\frac{p_1h_1}{h_2}##, where ##p_1## is the air pressure in the tube outside of water; ##p_2## is the pressure of the air in the tube whilst submerged; and ##h## represents the height of the air.
We can fill this in: ##p_2=\frac{10^5 \ \mathrm{Pa}\cdot 1.54\ \mathrm{m}}{1.40\ \mathrm{m}}=1.1\cdot 10^5 \ \mathrm{Pa}##.
Since this is the air's pressure on the surface of the water in the tube, the pressure in the water at the highest point is equal to ##p_2##.
How to continue from this point? I've tried thinking about a mercury barometer but I'm not sure. My idea was to look at the gauge pressure at the very top of the water (##10^4\ \mathrm{Pa}##), and use some hydrostatics equation. I don't know how I would go about that last part though.
Thanks in advance.