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

Explanation

The equation of state for a given mass of gas, `(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`
Given conditions Final conditions
`P_(1) = 1 + 1 =2 "atm " P_(2) = 1 + (1)/(2) = (3)/(2)` atm
`V_(1) = 76 xx "(area) "V_(2) = 114 xx` (area)
`T_(1) = 300K " "T_(2) =?`
The temerature to which the cylinder is heated
`T_(2) = (P_(2)V_(2)T_(1))/(P_(1)V_(1)) = (3)/(2) xx (114 xx 300)/(76 xx 2) = 342K = `59^(@)C`