An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg (figure). The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
Given
Cross sectional area A =10cm2=10
10-4m2
mass of piston = 1kg
Pressure inside chamber = 100kPa=105Pa
Pressure due to the weight of the piston =Pp
Pressure of vessel P1=pressure of chamber+ pressure due to piston
P1=105+9.8
103
Volume of gas inside the vessel V1=length of gas column
area.
Given length of gas column=20cm=0.2m
V1=length 
A
V1=0.2
10
10-4=2
10-4m3
After evacuation, pressure of chamber will be zero. So, pressure inside vessel after evacuation P2 will just be pressure due to piston.
P2=0+9.8
103
Let L be the final length of the gas column
Final volume V2=AL=10
10-4
L
Since, it is given in question that temperature remains constant, we can apply boyle’s law which states that ‘PV=constant when temperature is constant’.
Applying boyle’s law before and after evacuation,
P1V1=P2V2
(105+9.8
103)
2
10-4=9.8
103
10
10-4
L
The length of the gas column after evacuation =2.2m
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