A vertical hollow cylinder of height 1.52 m is fitted with a movable piston of negligible ,nass 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.

A vertical hollow cylinder of height 1.52 m is fitted with a movable p

1.	A vertical hollow cylinder of height 1.52 m is fitted with a movable piston of negligible ,nass 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.
Answer» Solution :Initially, PRESSURE = 76 + 76 = 152 cm of Hg From PV = NRT `(152 xx 76 xx A)/(300) = nR ` .... (1) final pressure = 76 + 38 = 114 cm of Hg `therefore (114 xx (76 + 38) A)/(T )= nR `.... (2) From (1) and (2) `(152 xx 76)/(300) = (114 xx 114)/(T)` `T = (300 xx 114 xx 114)/(152 xx 76) = (300 xx 3)/(4) xx (3)/(2) = 337.5 ` K