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Question
A vertical cylinder of height 100 cm contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to 75 cm of mercury. Mercury is slowly poured over the piston. Find the maximum height of the mercury column that can be put on the piston.
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Solution
Here,
h = 1 m
P1 = 0.75 mHg = 0.75 ρg Pa
ρ = 13500 kg/m3
Let h be the height of the mercury above the piston.
P2 = P1 + hρg
Let the CSA be A.
V1 = Ah = A
V2 = (1 - h)A
Applying Boyle's law, we get
P1 V1 = P2 V2
⇒ 0.75 ρgA = P2 (1 - h)A
⇒ 0.75 ρg = (0.75 ρg + hρg)(1 - h)
⇒ 0.75 = (0.75 + h)(1 - h)
⇒ h = 0.25 m
h = 25 cm
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