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Question:

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

Volume will become smaller by a factor of 0.70

Volume will become greater by a factor of 1.6

Volume will become greater by a factor of 1.1

Volume will become greater by a factor of 2.5

Solution:

The pressure, temperature and volume under two different sets of conditions are related by the following expression.
P₁V₁/T₁ = P₂V₂/T₂. (1)
Let V be the initial volume. Substitute values in the above expression.
1.5 × V / 288 = 1 × V₂ / 298
V₂ = 1.5 × 298 / 288
V₂ = 1.55V
i.e. volume of a bubble will be almost 1.6 times the initial volume of a bubble.