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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.)

User Filofel
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2 Answers

3 votes

Final answer:

The volume of the bubble just below the surface of the water is 16 cm3.

Step-by-step explanation:

To solve this problem, we can use Boyle's law, which states that the pressure times the volume of a gas is constant if the temperature remains constant. In this case, the volume of the air bubble at the bottom of the water is 16 cm3 and the depth is 6.5 m. As the bubble rises, the pressure decreases, causing the volume to increase. We can set up a proportion to solve for the volume just below the surface of the water.

Using the formula P1V1 = P2V2, where P1 is the pressure at the bottom of the water, V1 is the initial volume, P2 is the pressure just below the surface, and V2 is the volume just below the surface, we can plug in the values and solve for V2.

Since the temperature of the air in the bubble doesn't change, we can assume that the pressure times the volume is constant. Therefore, we have:

P1V1 = P2V2

Using the given values, we have:

(1 atm)(16 cm3) = (?, just below the surface) V2

To find V2, we can rearrange the equation:

V2 = (P1V1) / P2

Since the pressure just below the surface is atmospheric (1 atm), we can substitute that value in:

V2 = (1 atm)(16 cm3) / (1 atm)

V2 = 16 cm3

Therefore, the volume of the bubble just below the surface of the water is 16 cm3.

User Jason Sparc
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4.6k points
7 votes

Answer:


26.0689859363\ cm^3

Step-by-step explanation:

Absolute pressure is given by


P_1=P_0+\rho gh\\\Rightarrow P_1=101325+1000* 9.81* 6.5\\\Rightarrow P_1=165090\ Pa


P_2=101325\ Pa

We have the relation


P_1V_1=P_2V_2\\\Rightarrow V_2=(P_1V_1)/(P_2)\\\Rightarrow V_2=(165090* 16* 10^(-6))/(101325)\\\Rightarrow V_2=0.0000260689859363\ m^3\\\Rightarrow V_2=26.0689859363\ cm^3

The bubble's volume just below the surface is
26.0689859363\ cm^3

User Brasileric
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5.4k points