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)

The temperature at the bottom of a 40 m deap lake is 12^(@)C and that

1.	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)
Answer» Solution :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)`