A vertical cylinder of height `100cm` contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to `75cm` of mercury. Mercury is slowly poured over the piston.Find the maximum height of the mercury column that can be put on the piston.

Explanation

When mercury is poured on the top of the piston, due to increase in pressure, the volume of air will decrease according to Boyle's law. If final mercury column of height `x` is poured on the pistion then gas pressure in equilibrium can be given as
`P_(f) = (76 + x)cm` of `Hg`
As atmospheric pressure is equilivalent to the pressure due to a mercury column of height `76cm`. If `A` be the area of cross section of cylinder then according to Boyle's law `P_(1)V_(1) = P_(2)V_(2)` or
`(76)(100A) = (76 + x)(100 - x)A` or
`7600 = 7600 + 24x - x^(2)` or `x = 24 cm`.