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.