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

Final state of gas is shown in figure-2.14 after half of mercury over flows. Let this temperature be T. Then from gas law for initial and final state of gas we have
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
Here initial pressure, volume and temperature of gas are
`P_(1)=76+(h)/(2)=76+76=152" cm of Hg"`
`V_(1)=(h)/(2)A=76A`
`T_(1)=300" K"`
Similarly after heating pressure, volume and temperature of gas are
`P_(2)=76+(h)/(4)=76+38=114" cm of Hg"`
`V_(2)=(3h)/(4)A=144" A"`
Thus from gas law, we have
`(152xx76" A")/(300)=(114xx114" A")/(T_(2))`
or `" "T_(2)=337.5" K"`