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An air bubble of volume 1.0 cm^(3) rises...

An air bubble of volume `1.0 cm^(3)` 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`. ? Given `1 atm = 1.01 xx 10^(5) Pa`.

Text Solution

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`V_(1)=10^(-6)m^(3)`
Pressure on hubble `P_(1)=` Water pressure `+` Atmospheric pressure
`=pgh+Patm`
`=4.93xx10^(5)Pa`
`T_(1)=285k`, `T_(2)=308k`
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
`V_(2)=(4.93xx10^(5)xx1xx10^(-6)xx308)/(285xx1.01xx10^(5))=5.3xx10^(-6)m^(3)`.
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