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 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.

Answer 1

Hint: To get the solution of the above mentioned question we have to know about the ideal gas equation. And one has to know that total pressure calculation in case of cylinders is the summation of pressure of Hg and pressure of atmospheric air.

Complete step by step answer:
At initial stage,
Pressure of gas = pressure of Hg + pressure of atmospheric air
$76 + 76$ = $152$ cm
From question, we have $T = 300K$
And $V = {V_1}/2$ , where ${V_1}$ is the volume of the cylinder.
At final stage after heating,
Pressure of gas = pressure of Hg + pressure of atmospheric air
$ = 38 + 76$
$ = 114$cm
Then,$V = 3{V_1}/4$
Applying gas equation,
=${P_1}{V_1}/{T_1} = {P_2}{V_2}/{T_2}$
=$152*{V_1}/2*300 = 144*\left( {3{V_1}/4} \right)/T$
$ \Rightarrow 337.5K$
Hence, the required answer is $337.5K$ .

Note: It is a theoretical gas composed of many randomly moving point particles that are not subject to interparticles. The ideal gas concept is useful because it obeys the gas law, a simplified equation of state, and is amenable to analysis under statistical mechanisms.
Real gas and ideal gas.
As the particle size of an ideal gas is extremely small and the mass is almost zero and no volume, ideal gas is also considered as a point mass.An ideal gas is defined as a gas that obey gas laws at all conditions of pressure and temperature.
Real gas is defined as a gas that does not obey gas laws at all standard pressure and temperature conditions. When the gas becomes massive and voluminous it deviates from its ideal behavior. Real gases have velocity, volume and mass.