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

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Solution

At initial stage:
Pressure of gas = Pressure of Hg + Pressure of atmospheric air $= 76 + 76 = 152 c m$

$T = 300 k$
$V = V_{1} / 2$
where, $V_{1}$ is volume of cylinder.

At final state after heating:
Pressure of gas = Pressure of Hg + Pressure of atmospheric air $= 38 + 76 = 114 c m$

$V = \frac{3 V_{1}}{4}$
Applying gas equation, we have

$\frac{152 \times V_{1}}{2 \times 300} = \frac{144 \times (3 V_{1} / 4)}{T}$

$= 337.5 k$

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Q. A vertical hollow cylinder of height

1.52 m

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 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 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. Then the temperature is (the thermal expansion of mercury to be negligible)