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A bubble of air has a volume of 16 cm3 when at a depth of 6.5 m. As the bubble rises, it expands. What is the bubble’s volume just below the surface of the water? (Note: Assume the temperature of the air in the bubble doesn’t change, in which case pressure times volume is constant.)

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Answer:

[tex]26.0689859363\ cm^3[/tex]

Explanation:

Absolute pressure is given by

[tex]P_1=P_0+\rho gh\\\Rightarrow P_1=101325+1000\times 9.81\times 6.5\\\Rightarrow P_1=165090\ Pa[/tex]

[tex]P_2=101325\ Pa[/tex]

We have the relation

[tex]P_1V_1=P_2V_2\\\Rightarrow V_2=\dfrac{P_1V_1}{P_2}\\\Rightarrow V_2=\dfrac{165090\times 16\times 10^{-6}}{101325}\\\Rightarrow V_2=0.0000260689859363\ m^3\\\Rightarrow V_2=26.0689859363\ cm^3[/tex]

The bubble's volume just below the surface is [tex]26.0689859363\ cm^3[/tex]

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