A vertical cylinder of height 100cm contains air at a constant temperature and its top is closed by a frictionless piston at atmospheric pressure (76 cm of Hg) as shown figure - a. If mercury is slowly poured on the piston, due to its weight air is compressed. Find the maximum height of the mercury column which can be put on the piston.

A vertical cylinder of height 100cm contains air at a constant tempera

1.	A vertical cylinder of height 100cm contains air at a constant temperature and its top is closed by a frictionless piston at atmospheric pressure (76 cm of Hg) as shown figure - a. If mercury is slowly poured on the piston, due to its weight air is compressed. Find the maximum height of the mercury column which can be put on the piston.
Answer» SOLUTION :When MERCURY is poured on the top of the piston, due to increase in pressure, the volume of air will DECREASE. If final mercury column of height x is poured on the piston then 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)(100A)=(76+x)(100-x)A" (or) "7600=7600+24x-x^(2)" (or) "x=24cm`