A vertical cylinder of height 100 cm contains air at a constant temperature and its top is closed by a frictionless piston at atmospheric pressure (76 cm of Hg) asshown in figure-2.12. If mercury is slowly poured on the piston, due to its weight airis compressed. Find the maximum height of the mercury column which 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 piston than gas pressure in equilibrium can be given as
`P_(f)=(76+x)" cm of Hg"`
As atmospheric pressure is equivalent to the pressure due to a mercury column of height 76 cm. If A be the area of cross section of cylinder then we have according to Boyle's Law
`P_(1)V_(1)=P_(2)V_(2)`
or `" "(76" cm")(100" A")=(76+x)(100-x)A`
or `" "7600=7600+24x-x^(2)`
or ` " "x=24" cm"`