A vertical hollow cyclinder of height `1.52 m` is fitted with a movable piston of negligible mass and thickness. The lower half portion of the cyclinder contains an ideal gas and the upper half is filled with mercury. The cyclinder is initially at `300 K`. When the temperature is raised half of the mercury comes out of the cyclinder. Find the this temperature assuming the thermal expansion of the mercury to be negligible.

Explanation

(a) `P_(0)` : atmospheric pressure `= 0.76" m of Hg"`
`P_(0) + (m g)/(A) = P_(1) rArr 0.76 + 0.76 = P_(1)`
`P_(1) = 1.52" m of Hg"`
(b) `P_(0) + (m g)/(2 A) = P_(2) rArr 0.76 + 0.38 = P_(2)`
`P_(2) = 1.14" m of Hg"`
`(P_(1)V_(1))/(T_(1)) = (P_(2)T_(2))/(T_(2))`
`(1.52 xx A xx 0.76)/(300) =( 1.14 xx A xx 1.14)/(T_(2))`
`T_(2) = 337.5 K`