Question

A vertical hollow cylinder of height $1.52m$ is fitted with a movable piston of negligible mass and thickness. The lower half of the cylinder contains an ideal gas and the upper half is filled with mercury. The cylinder initially at $300K$. When the temperature is raised half of the mercury comes out of the cylinder. Find the temperature assuming the thermal expansion of mercury to be negligible.

Answer 1

At initial stage:
Pressure of gas $=$ Pressure of $Hg+$ Pressure of atmospheric air
$=76+76=152cm$
$T=300K$
$V=V_1/2$ where, $V_1$ is volume of cylinder.
At final state after heating:
Pressure of gas $=$ Pressure of $Hg+$ Pressure of atmospheric air
$=38+76=114cm$
$V=\frac{3V_1}{4}$
Applying gas equation, we have
$\frac{152\times V_1}{2\times 300}=\frac{144\times \left(3V_1/4\right)}{T}$
$T=\frac{114\times 3\times 2\times 300}{4\times 152}$
$=337.5K$