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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 is 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.

$(a)\;432.5K\qquad(b)\;312.3K\qquad(c)\;337.5K\qquad(d)\;234.3K$

thanks for the solution

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A)
Initially at lower end
P = 76cm of Hg + 76cm of air = 152cm
T = 300K
$V = \large\frac{V_1}{2}$
Where $V_1$ is the volume of the cylinder
Finally at lower end
P = 76cm of air + 38cm of Hg = 114 cm
T = ?
$V = \large\frac{3V_1}{4}$
$\therefore \large\frac{P_1V_1}{T_1} = \large\frac{P_2V_2}{T_2}$
$\large\frac{152\times V_1}{2\times300} = \large\frac{114\times3V_1}{4\times T}$
$\therefore T = \large\frac{114\times3\times2\times300}{152\times4}$
= 337.5K
Hence answer is (c)
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