A vertical hollow cylinder of height 1.52 m is fitted with a movable piston of neglible 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.

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 neglible 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.
Answer» SOLUTION :INITIALLY, Pressure = 76 + 76 = 152 CM of Hg From `PV=nRT rArr (152 times 76 timesA)/(300)=nR"…….(1)"` Final pressure = 76 + 38 = 114 cm of Hg `therefore (114 times (76+38)A)/T=nR"……(2)"` From (1) and (2) `rArr (152 times 76)/(300)=(114 times 114)/T, T=(300 times 114 times 114)/(152 times 76)=(300 times3)/4 times 3/2=3375K=337.5^(@)C`