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 the mercury to be negligible.

Explanation

Initial pressureof gas `P_(1)=P_(0)+H/2dg, P_(0)`is atmospheric pressure
Initial volume of gas `V_(1)=V/2`
Initial temperature `T_(1)=300K`
When half of the mercury comes out of the cylinder the final pressure of gas
`P_(2)=P_(0)+H/4 dg` and final volume of the gas.
`V_(2)=V/2+V/4=(3V)/4`
we have `(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
`impliesT_(2)=(P_(2)V_(2))/(P_(1)V_(1)) T_(1)=((P_(0)+H/4dg).((3V)/4)xx300)/((P_(0)+H/2dg). V/2)`
Putting the value `P_(0)=0.76dg` (atmosphere pressure) we get
`T_(2)=337.5K`.