A bubble of air is underwater at temperature 15^o C and the pressure 1.5 bar. If the bubbles rises to the surface where the temperature is 25^o C and the pressure is 1.0 bar, what will happen to the volume of the bubble?

Volume will become greater by a factor of 1.6

Volume will become greater by a factor of 1.1

Volume will become smaller by a factor of 0.70

Volume will become greater by a factor of 2.9

Solution

Volume will become greater by a factor of 1.6

fraction numerator straight p subscript 1 straight V subscript 1 over denominator straight T subscript 1 end fraction space equals space fraction numerator straight p subscript 2 straight V subscript 2 over denominator straight T subscript 2 end fraction space space space space left parenthesis ideal space gas space equation right parenthesis or fraction numerator 1.5 space straight x space straight V subscript 1 over denominator 288 end fraction space equals space fraction numerator 1 space straight x space straight V subscript 2 over denominator 298 end fraction therefore space space straight V subscript 2 space equals space 1.55 space straight V subscript 1 space

i.e., volume of bubble will be almost 1.6 times to initial volume of bubble.

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