Calculate Pressure Underwater for a 1cm3 Air Bubble at 291m

In summary, the question is asking for the new volume of a 1-cm3 air bubble at a depth of 291 meters and a temperature of 4 oC when it rises to the surface of a lake with a temperature of 10.4 oC. The depth of the water does make a difference and the pressure at any depth is equal to the weight of a column of water divided by its cross-sectional area. The weight of the column of water can be calculated by multiplying the density of water (1gm/cc) by the volume of water (area of base times height). The total pressure at depth is the sum of the pressure from the water and atmospheric pressure. Using the previous calculations, the pressure at a depth of
  • #1
vworange
9
0
A 1-cm3 air bubble at a depth of 291 meters and at a temperature of 4 oC rises to the surface of the lake where the temperature is 10.4 oC, to the nearest tenth of a cm3, what is its new volume?

I guess my real question is: does the depth of the water make any difference or do i assume it's constant pressure? If i can't make that assumption, how do i calculate the pressure the water has on this?

The obvious answer is that if it's to the nearest tenth of a cm3, it's still coming out to 1.0 cm3 which is wrong.
 
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  • #2
The depth of the water makes a huge difference. The pressure at depth is equal to the weight of a column of water of cross-sectional area A divided by that area A. The A divides out, leaving the pressure at any depth the same. You need to figure out how much a column of water 291 meters high with a given cross-sectional area would weigh, and divide by the area you used. That will give you the pressure.
 
  • #3
I don't have cross-sectional area. How else can I go about getting the pressure... between surface and the depth given? I assume the initial pressure goes something along the lines of 9.81x291 (g*h).
 
  • #4
Boyles law --> P.V/T = constant (pressure * volume / Temperature)
1 meter water = 0.0967841105 atmospheres

Just remember T is in Kelvin i.e 4 degrees = 277 degrees K

Surface pressure is 1, hence at 291 meters = 1+291*0.0967...

You have all the data, I have not got a calculator.
 
  • #5
The area can be anything you want it to be. It divides out of the calculation. The weight of the column of water is the density of water (1gm/cc) times the volume of the water. The volume of a column of water is the area of the base times the height. The pressure is the weight divided by the area, so the area divides out. The pressure from the water is just the density times the height.

The toatal pressure at depth is the pressure from the water plus atmospheric pressure. The previous reply quotes the pressure due to a depth of one meter of water in terms of atmospheres and then states that the pressure at depth is the sum of one atmosphere plus the pressure due to the depth of water. That approach is good now that you know the pressure from one meter of water. The calculation I suggested would give you that number also. If you can use that number to satisfy anyone who might be grading your work, use it. If you have to justify the number, I have told you how to find it.
 

FAQ: Calculate Pressure Underwater for a 1cm3 Air Bubble at 291m

1. How do you calculate the pressure of a 1cm3 air bubble at 291m underwater?

To calculate the pressure of a 1cm3 air bubble at 291m underwater, we can use the formula P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth. In this case, we would substitute the values for ρ (1000 kg/m3), g (9.8 m/s2), and h (291m) to calculate the pressure.

2. What is the density of water at a depth of 291m?

The density of water at a depth of 291m is approximately 1000 kg/m3. This value can vary slightly depending on factors such as temperature and salinity.

3. How does the pressure of a 1cm3 air bubble change as it descends to a depth of 291m?

The pressure of a 1cm3 air bubble will increase as it descends to a depth of 291m. This is due to the increased weight of the water above the bubble, which causes an increase in pressure according to the formula P = ρgh.

4. What would be the pressure of a 1cm3 air bubble at 291m if it was filled with a gas other than air?

The pressure of a 1cm3 air bubble at 291m would depend on the type of gas it is filled with. The formula P = ρgh can still be used, but the value for ρ would need to be adjusted based on the density of the gas. For example, a bubble filled with helium (ρ = 0.1785 kg/m3) would have a lower pressure at 291m compared to a bubble filled with air.

5. Is it possible to calculate the pressure of a larger air bubble at a depth of 291m using the same formula?

Yes, the formula P = ρgh can be used to calculate the pressure of any size air bubble at a depth of 291m. However, the pressure calculated would be for the entire volume of the bubble, not just a single 1cm3 section.

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