Question

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)

• A. 437 K
• B. 337.5 K
• C. 275 K
• D. 137.K

Answer 1

The correct option is B 337.5 K

Initially at $300K$,

Pressure on the gas,$P_1=P_0$ + 76 = 76+76 = 152cm of Hg

Volume of the gas,$V_1=76A$

At the later temperature,

Pressure of the gas, $P_2=P_0$ + 38 = 76+38 = 114cm of Hg

Volume of the gas, $V_2=114A$

For the gas, ideal gas law holds,

$⟹\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$⟹T_2=337.5K$