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

Given :-

At the initial stage:-

Pressure of gas = pressure of Hg(mercury) + pressure of atmospheric air
Pressure of Gas = 76 cm of Hg + 76 cm of air.
Pressure of Gas P₁ = 152 cm.

Cylinder initial  (T₁) = 300 K
Now as per the given condition.
 V = V₁ /2 , here V₁ is the volume of the cylinder.
 V = 76/2 =38
After heating , 
Pressure of Gas = Pressure of Hg + Pressure of Atmospheric air
= 38 + 76
P₂= 114 cm.

Here as per the condition , V₂ = 3V₁ /4
Now applying the Gas equation .

$\frac{P_{1} V_{1} }{T _{1} }$ = $\frac{P _{2} V _{2} }{T_{2} }$

= (152 x V₁) / 2 x 300 = [144 x (3V₁/4) ] / T₂
= (300 × 2 × 3 × 114) / 152 × 4
T₂ = 337.5 K

Hence the temperature assuming the thermal expansion is 337.5 K 


Hope it Helps. :-)

Answer 2

Pressure of gas = pressure of Hg(mercury) + pressure of atmospheric air Pressure of Gas = 76 cm of Hg + 76 cm of air. Pressure of Gas P₁ = 152 cm.  Cylinder initial  (T₁) = 30  V = V₁ /2 , here V₁ is the volume of the cylinder.  V = 76/2 =38 After heating ,  Pressure of Gas = Pressure of Hg + Pressure of Atmospheric air = 38 + 76 P₂= 114 cm.   , V₂ = 3V₁ /4 Now applying the Gas equation .     = (152 x V₁) / 2 x 300 = [144 x (3V₁/4) ] / T₂ = (300 × 2 × 3 × 114) / 152 × 4 T₂ = 337.5