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 mercury to be negligible.

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337.5 K

237.5 K

137.5 K

437.5 K

answer is C.

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Detailed Solution

$\begin{array}{l} P_{1} = 76 + 76 = 152 cm of Hg \end{array}$ , $V_{1} = 76 A, T_{1} = 300 K$

$P_{2} = 76 + 38 = 114 cm of Hg$

$V_{2} = 114 A, T_{2} = T$

Using Ideal Gas Equation, $\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

$T = \frac{114 \times 114 \times 300}{152 \times 75} = 337 .5 K$

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