Calculating the Volume of a Bubble at Different Depths in the Sea

In summary, the problem involves a diver exhaling an air bubble at a depth of 24.0 m below the surface of the sea with a temperature of 5.00°C. The surface temperature of the sea is 20.0°C. Using the Ideal Gas Law and accounting for hydrostatic pressure, the volume of the bubble just before it breaks the surface can be calculated. However, the calculations provided by the student did not work and it was suggested to use absolute temperatures and consider the hydrostatic pressure. The pressure at 24 m down can be found using the formula P = (density of water) x (g) x (depth of water). Since the topic of hydrostatic pressure has not been covered, it is unclear
  • #1
zcabral
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Homework Statement



At 24.0 m below the surface of the sea (density = 1025 kg/m3), where the temperature is 5.00°C, a diver exhales an air bubble having a volume of 1.20 cm3. If the surface temperature of the sea is 20.0°C, what is the volume of the bubble just before it breaks the surface?
cm^3

Homework Equations



P1V1/T1=P2V2/T2 (thats what i tried)

The Attempt at a Solution


i got answers like 4.8, 1.68 by plugging into the equation...but as usual plug and chug never works...can u help please? i think I am missing how to find pressure from 24 m below surface. how do u do that?
 
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  • #2
It would be more helpful to a reader here if you showed the calculations you made, rather than simply giving the answers you found that didn't work. You do want to use the "Ideal Gas Law". Did you use absolute temperatures in your calculation (Kelvins, rather than degrees Celsius)? Did you remember that the pressure at 24 m. down is the hydrostatic pressure of 24 meters of water plus the one atmosphere of pressure from the air above the water's surface?

i think I am missing how to find pressure from 24 m below surface. how do u do that?

Have you had the topic on hydrostatic pressure? The pressure from the water will be

P = (density of water) x (g) x (depth of water).
 
Last edited:
  • #3
no we haven't covered that so wat pressure wud i used for when its just about to break the surface of the water since i don't know exactly how deep it is? wud that just be 1 atm?
 

1. How do you calculate the volume of a bubble at different depths in the sea?

To calculate the volume of a bubble at different depths in the sea, you will need to know the depth of the water, the temperature and pressure at that depth, and the size of the bubble. Once you have this information, you can use the ideal gas law (PV=nRT) to calculate the volume of the bubble.

2. What is the ideal gas law?

The ideal gas law is a mathematical equation that relates the pressure, volume, amount, and temperature of a gas. It can be used to calculate the volume of a bubble at different depths in the sea, as long as the gas inside the bubble behaves like an ideal gas.

3. How does the depth of the sea affect the volume of a bubble?

The depth of the sea affects the volume of a bubble because as depth increases, the pressure of the water also increases. This increased pressure pushes on the bubble, causing it to compress and decrease in volume.

4. Why is temperature important when calculating the volume of a bubble at different depths in the sea?

Temperature is important when calculating the volume of a bubble because it affects the pressure of the gas inside the bubble. As temperature increases, the pressure of the gas also increases, causing the bubble to expand and increase in volume. This is why it is important to take into account the temperature at different depths in the sea when calculating the volume of a bubble.

5. How does the size of the bubble impact its volume at different depths in the sea?

The size of the bubble does impact its volume at different depths in the sea. Smaller bubbles will be more easily compressed by the increased pressure at greater depths, resulting in a smaller volume. On the other hand, larger bubbles will be less affected by the increased pressure and may not change significantly in volume at different depths.

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