Pressure inside a soap bubble just under surface

In summary, the pressure inside a small air bubble of 0.1 radius, situated just below the surface, is the sum of the surrounding pressure and the excess pressure (4s/r). However, there is a difference between the forces acting on the bubble above and below the surface, with the latter experiencing an additional hydrostatic pressure. This additional pressure may be negligible, but it should be taken into account when calculating the external pressure on the bubble. The 4s/r formula is derived differently for a bubble above and below the surface due to this difference in forces.
  • #1
takando12
123
5

Homework Statement


What should be the pressure inside a small air bubble of 0.1,, radius,situated just below the surface? st of water=7.2 *10-2 and atmospheric pressure=1.013*105.

Homework Equations

The Attempt at a Solution


I am of the understanding that the pressure inside the bubble is the sum of the surrounding pressure and the excess pressure( 4s/r). But what I don't understand is the surrounding pressure. Should I take the atmospheric pressure? But since it's just below the surface,the top of the bubble would be exposed to atmospheric pressure and the rest of the bubble to whatever pressure the water exerts( I don't think I'm right, I need help). So which pressure is it that I take for external?
 
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  • #2
takando12 said:

The Attempt at a Solution


I am of the understanding that the pressure inside the bubble is the sum of the surrounding pressure and the excess pressure( 4s/r). But what I don't understand is the surrounding pressure. Should I take the atmospheric pressure? But since it's just below the surface,the top of the bubble would be exposed to atmospheric pressure and the rest of the bubble to whatever pressure the water exerts( I don't think I'm right, I need help). So which pressure is it that I take for external?
Have you calculated how much difference that makes?
There is another difference between a bubble above the surface and one under the surface which might have rather more significance.
 
  • #3
haruspex said:
Have you calculated how much difference that makes?
There is another difference between a bubble above the surface and one under the surface which might have rather more significance.
if a bubble was under the surface, the pressure inside the bubble would be 4s/r + the hydrostatic pressure at that height( Pa+hρg).
I am unable to understand what exactly you mean by difference. Since the bubble is just below the surface,will the second term reduce to just Pa?
 
  • #4
I asked if you had calculated how much difference it makes taking into account that little extra hydrostatic pressure. I mean the numbers, not the algebraic expression. I suspect it is negligible.
takando12 said:
I am unable to understand what exactly you mean by difference.
There is rather an important difference in the forces. Do you know how the ##4\sigma/r## formula is derived? If you follow that through you should see why it is different.
 

Related to Pressure inside a soap bubble just under surface

1. What causes the pressure inside a soap bubble just under the surface?

The pressure inside a soap bubble just under the surface is caused by the surface tension of the soap film. This surface tension is created by the attraction between the water molecules and the soap molecules in the film.

2. How does the pressure inside a soap bubble change as it rises or falls?

The pressure inside a soap bubble decreases as it rises due to the decrease in the thickness of the soap film. As the bubble falls, the pressure increases due to the increase in the thickness of the film.

3. Does the temperature affect the pressure inside a soap bubble?

Yes, the temperature can affect the pressure inside a soap bubble. As the temperature increases, the air inside the bubble expands, causing an increase in pressure. Conversely, as the temperature decreases, the air inside the bubble contracts, resulting in a decrease in pressure.

4. How does the size of a soap bubble affect the pressure inside?

The size of a soap bubble does not directly affect the pressure inside. However, as the bubble grows larger, the surface tension decreases, leading to a decrease in pressure. Additionally, a larger bubble may have a thinner film, which can result in a lower pressure.

5. Can the pressure inside a soap bubble be measured?

Yes, the pressure inside a soap bubble can be measured using a pressure gauge. This can be done by inserting the gauge into the bubble without popping it, or by measuring the pressure of the air outside the bubble and subtracting it from the pressure of the air inside the bubble.

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