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

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

1.	A vertical cylinder of height 100 cm contains air at a constant temperature and its top is closed by a frictionless pistion at atmospheric pressure (76 cm of Hg) as shown figure ( a). If mercury is slowly poured on the pistion, due to its weight air is compressed. Find the maximum height of the mercury column which can be put on the pistion.
Answer» Solution :When mercury is poured on the top of the piston, due to increase in pressure, the volume of air wiU 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 at1nospheric pressure is equivalent to the pressure due to a mercury column of height 76cm. If A be the area of cross secion of cylinder then we have according to Boyle.s law `P_(1) V_(1) = P_(2) V_(2) ` or `(76) (100 A) = (76 + x) (100 - x) A ` or `7600 = 7600 + 24 x - x^(2) " or " x = 24 ` cm .