A vertical cylinder of height 100 cm contains air at a constant temperature.
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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P1 = Atmospheric pressure = 75 × ƒg
V1 = 100 × A
P2 = Atmospheric pressure + Mercury pessue = 75ƒg + hgƒg (if h = height of mercury)
V2 = (100 – h) A
P1V1 = P2V2
=>75ƒg(100A) = (75 + h)ƒg(100 – h)A
=> 75 × 100 = (74 + h) (100 – h) => 7500 = 7500 – 75 h + 100 h – h2
=> h2 – 25 h => 0 => h2 = 25 h => h = 25 cm
Height of mercury that can be poured = 25 cm
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