Effects of pressure on an air bubble

[studentmom]

Homework Statement

an air bubble originating from a scuba diver at a depth of 18.0m has a diameter of 1.0cm. What will be the bubble's diameter when it reaches the surface?
assume constant temperature

Homework Equations

I'm not sure what equation to use for this...

The Attempt at a Solution

I know that an increase in pressure should have an effect on the size of the air bubble. But I don't know where to start.

 

[interested_learner]

What is the pressure inside the bubbles? What is pressure outside the bubbles? Are they the same? Different? How does the pressure inside the bubbles relate to bubble size? Given a set number of molecules in the bubble, will a higher pressure bubble have a smaller volume or a larger volume?

Answer those questions and you will have your answer.

 

[m2003]

Can you please provide more information or guidance?

I would approach this problem by considering the gas laws, specifically Boyle's Law. This law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. In this case, the air bubble is at a depth of 18.0m, which means it is experiencing a higher pressure than at the surface. As the bubble rises to the surface, the pressure decreases, causing the volume of the bubble to increase.

To solve this problem, we can use the equation V1P1 = V2P2, where V1 and P1 are the initial volume and pressure of the air bubble, and V2 and P2 are the final volume and pressure at the surface.

We know that the initial volume, V1, is 1.0cm^3 and the initial pressure, P1, is the pressure at a depth of 18.0m. We can use the equation P1 = ρgh, where ρ is the density of water (1000 kg/m^3), g is the acceleration due to gravity (9.8 m/s^2), and h is the depth (18.0m). This gives us a pressure of 17640 Pa.

At the surface, the pressure, P2, is equal to atmospheric pressure, which is 101325 Pa. We can now solve for V2:

V2 = (V1P1)/P2 = (1.0cm^3 * 17640 Pa)/101325 Pa = 0.0175 cm^3

Therefore, the diameter of the bubble at the surface will be approximately 2.7 cm, assuming the bubble maintains a spherical shape. This is a significant increase from the initial diameter of 1.0 cm, highlighting the impact of pressure on the size of the air bubble.

 

[kyle8921]

I can provide a response to the given content by using the ideal gas law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature. In this case, the air bubble is experiencing an increase in pressure as it rises to the surface, which will result in a decrease in its volume. This can be calculated using the equation P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Since the temperature is assumed to be constant, we can use the equation to find the final volume of the air bubble:

P1V1 = P2V2
(18.0m * 1.0cm) = (1.0atm * V2)
V2 = (18.0m * 1.0cm) / (1.0atm)
V2 = 18.0cm

Therefore, the diameter of the air bubble when it reaches the surface will be 18.0cm. This is a significant increase from its initial diameter of 1.0cm due to the decrease in pressure as it rises. It is important to note that this calculation assumes ideal gas behavior and does not take into account any external factors that may affect the size of the air bubble.