An air bubble of volume `1.0cm^(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`?

Explanation

Volume of the air bubble `V_(1)=1.0cm^(3)`
`-10^(-6)m^(3)`
Temperature, `T_(1)=12^(@)CimpliesT_(1)=273K+12^(@)C`
`=285K`
Temperature, `T_(2)=35^(@)CimpliesT_(2)=273K+35^(@)C`
`=308K`
Pressure on bubble `P_(1)` = Water pressure + Atmospheric pressure.
`=4.93xx10^(5)pa`
`therefore (P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
`V_(2)=((4.93xx10^(5))xx(1xx10^(-6))xx308)/(258xx(1.01xx10^(5)))`
`=(4.93xx308xx10^(-6)xx10^(-5)xx10^(-5))/(285xx1.01)`
`=(4.93xx308xx10^(-6))/(285xx1.01)=(1.518.44xx10^(-6))/(287.85)`
`=5.275xx10^(-6)m^(3)`
`therefore V_(2)=5.3xx10^(-6)m^(3)`