The temperature at the bottom of a 40 m deap lake is `12^(@)C` and that at the surface is `35^(@)C`. An air bubble of volume `1.0cm^(3)` rises from the bottom to the surface. Find its volume. (atmospheric pressure = 10 m of water)

Explanation

Let `P_(1),V_(1) and T_(1)` be the pressure, bubble volume and absolute temperature at the bottom of the lake and let `P_(2), V_(2) and T_(2)` be the corresponding quantities at the surface. Then
`(P_(2)V_(2))/(T_(1)) rArr V_(2)=(P_(1)T_(2))/(P_(2)T_(1))V_(1)`
`V_(2)=((10+40)/(10))((273+35)/(273+12))xx1=(5xx308)/(285)`
`V_(2)=5.4cm^(3)`