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Question

A bulb of unknown volume V contains a gas at 1 atm pressure. This bulb was connected to another evacuated bulb of volume 0.5L through a stop cock. When the stop cock was opened, the pressure at each bulb becomes 7.58×104 Pa mm while the temperature remained constant. Calculate V in litres.

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Solution

From ideal gas equation,
PV=nRT
At constant temperature,
PV=constant
P1V1=P2V2.....(1)
Given:-
Pressure of first bulb (P1)=1atm=1.013×105Pa
Volume of first bulb (V1)=V
After opening the stop cock,
Total pressure (P2)=7.58×104Pa
Total volume (V2)=(V+0.5)L
Now from eqn(1), we have
1.01×105×V=7.58×104×(V+0.5)
10V=7.5V+3.75
2.5V=3.75
V=1.5L
Hence the volume of the bulb is 1.5L.

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