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Question

Air is pumped into the tubes of a cycle rickshaw at a pressure of 2atm. The volume of each tube at this pressure is 0.002m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300K and that the air behaves as an ideal gas.

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Solution

The pressure of the air is P1=2atm=2×105pa
The volume of the tube is V1=0.002m3
The constant temperature of the tube is T1=300K

Using the ideal gas relation:
P1V1=n1RT1

n=P1V1RT1

=2×105×0.0028.3×300=48.3×3=0.1606

Now, after the tube gets punctured,
P2=1atm=105pa
V2=0.005m3,
T2=300K

Using the ideal gas relation again:
P2V2=n2RT2

n2=P2V2RT2

=105×0.00058.3×300

=53×8.3×110=0.02

Δn= moles leaked out =0.160.02=0.14

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