A vertical cylinder of height 100cm contains air at a constant temperature. The top is closed by a friction less 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.

Explanation

Given, `P_1 = Atomospheric pressure`
` = 75 xx rho g, `
` V_1= 100 xx A`
` (P_2) = Atmospheric pressure`
+ Mercury pressure
`= 75 rho g + h rho g `
` (if h = height of mercury )`
` V_2 = (100 - h)`
` ((P_1)(V_1))= ((P_2)(V_2))`
` rArr 75 rho g (100 A)`
` = ((75 +h) rho g (100 - h) A)`
` rArr (75 xx 100) = ((75+h)(100-h))`
` rArr 7500= 7500 - 75h +100h - (h^2)`
` rArr (h^2) - 100 h + 75h = 0 `
` h^2 - 25 h = 0 `
` rArr (h^2) = 25 h `
` h = 25 cm `
Height of Mercury that can be poured
` = 25 cm ` .