A vertical cylinder of height 1.52m is fitted with a movable piston of negligible mass and thickness. The lower half of the cylinder contains ideal gas and upper half is filled with Hg. The cylinder is initially at 300K. When the temperature is raised, half of the mercury comes out of cylinder. The temperature is: (Assume no thermal expansion for Hg)

Options

A. 337.5
B. 364.5
C. 546
D. 600

Answer

A

Explanation

At initial stage:
Pressure of gas = Pressure of `Hg +` Pressure of atmospheric air
`= 76 + 76 = 152 cm`
`T = 300 K`
`V = V_(1)//2` where, `V_(1)` is volume of cylinder.
At final stage after heating:
Pressure of gas = Pressure of `Hg +` Pressure of atmospheric air
`= 38 + 76 = 114 cm`
`V = (3V_(1))/(4) , T = ?`
Applying gas equation, we have
`(152 xx V_(1))/(2 xx 300) = (114 xx (3V_(1) //4))/(T)`
`T = (114 xx 3 xx 2 xx 300)/(4 xx 152)`
`= 337.5 K`