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Kinetic Theory

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Question : 5
Total: 14
An air bubble of volume 1.0cm3 rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35°C?
Solution:  
When the air bubble is at depth of 40 m
Volume of air bubble V1=1.0cm3=1.0×10−6m3
Pressure of air bubble P1 = 1 atm + 40 m depth of water = 1 atm + h1ρg
=1.013×105+40×103×9.8=4.93×105Pa
Temperature of air bubble T1=12+273=285K
When the air bubbles reaches at the surface of lake, pressure of air bubbles
P2=1 atm =1.013×105Pa
Temperature of air bubble T2=35°C=35+273=308K
Volume of air bubbles = ?
Now,
P1V1
T1
=
P2V2
T2

V2=
P1V1T2
T1P2
 =
4.93×105×1.0×10−6×308
285×1.01×105
 =5.275×10−6m3
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