What is the volume of a diver's air bubble at the surface of the sea?

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In summary, the problem involves a diver exhaling an air bubble at a depth of 25.1 meters below the surface of the sea, with a temperature of 3.00 C and a volume of 1.00 cm^3. The question is to determine the volume of the bubble just before it breaks the surface, given that the surface temperature of the sea is 15.00 C. Through calculations using the ideal gas law, it was found that the volume of the bubble just before it breaks the surface is 1.74 x 10^-5 cubic meters, taking into account the absolute pressure of the gas underwater and the temperature difference. It was also noted that the temperature scale must be converted to an absolute scale in
  • #1
dave2945
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Hello everyone. Here is my problem:

At 25.1 meters below the surface of the sea (density is 1025 (kg)/m^3),
where the temp is 3.00 C, a diver exhales an air bubble that has a volume of 1.00 cm^3. If the surface temp of the sea is 15.00 C, what is the volume of the bubble just before it breaks the surface.

Here is what I got: (d=density)

pv=nrt under water P+dgh=p
PV=nrT surface so, (P+dgh)v=nrt and PV=nrT

The nr's cancel, so (PV/((P+dgh)(v)))=T/t
Simplifying, I get that V=((P+dgh)vT)/(Pt)

Only thing is, I don't have pressure at surface. I tried using 1.013X10^5 N/m^2 (1 atm) and got .174 m^3. And, I did remember to change to .01 meters from 1.00 cm^3. Answer seems reasonable but wrong. Any help would be appreciated.
 
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  • #2
dave2945 said:
And, I did remember to change to .01 meters from 1.00 cm^3. Answer seems reasonable but wrong. Any help would be appreciated.

Just a quick check, you know that 1.00 cm3 [itex]\neq[/itex] 0.01 m3 right?
 
  • #3
Oh yeah. It is 1.00X10^-6 m^3, right??
 
  • #4
dave2945 said:
Oh yeah. It is 1.00X10^-6 m^3, right??
Yup, that's right.
 
  • #5
OK, I tried that, subbing 10^-6 m^3, got 1.74X10^-5 cubic meters and still not right. Hmmmm..
 
  • #6
Anyone have any ideas?
 
  • #7
I have a question about the equation you use for the pressure of the gas underwater. Shouldn't the pressure of the gas underwater be equal to the pressure of the water since they are both in equilibrium at that height; which is just "dgh," not "P + dgh."
 
  • #8
JMuse said:
I have a question about the equation you use for the pressure of the gas underwater. Shouldn't the pressure of the gas underwater be equal to the pressure of the water since they are both in equilibrium at that height; which is just "dgh," not "P + dgh."
One must look at the 'absolute' pressure. At the surface of the water, the local or ambient pressure is 1 atm (~14.7 psia). As one descends in the water, the mass of water above contributes to pressure, and the local pressure in the water is given by Pa + [itex]\rho[/itex]gh, where h is the depth of water, and [itex]\rho[/itex] is density.

When the air bubble is released, it is at same pressure as the water. Now there is also a difference in temperature which must also be considered for this problem. As the temperature of the bubble increases, it would also expand due to temperature, but the bubble is always at the same pressure as the water around it.
 
  • #9
dave2945 said:
Anyone have any ideas?
Please show the work. Remember that the temperature scale in °C (Celsius) is a 'relative' scale, and one must convert to an absolute scale K, if one uses ratios.

T (K) = T (°C) + 273.15
 
  • #10
Oh, ok. I just screwed up by not converting to K's. Thank u much for the help Astronuc.
 

Related to What is the volume of a diver's air bubble at the surface of the sea?

1. What is the importance of varying depths of water?

The varying depths of water are important for several reasons. Firstly, they affect the circulation and mixing of nutrients and oxygen in aquatic ecosystems, which is crucial for the survival of marine organisms. Additionally, varying depths of water can impact the temperature and salinity of the water, which can have a significant impact on the distribution and abundance of marine life.

2. How do varying depths of water impact ocean currents?

Varying depths of water play a critical role in the formation and movement of ocean currents. As water moves from shallow to deeper areas, it creates a pressure gradient that drives the flow of ocean currents. This is known as thermohaline circulation and is essential for the distribution of heat and nutrients throughout the world's oceans.

3. What are the different layers of varying depths in the ocean?

The ocean can be divided into three main layers based on varying depths: the surface layer, the pycnocline, and the deep ocean. The surface layer is the top layer of water that receives the most sunlight and is affected by wind and waves. The pycnocline is the middle layer where the density of water increases rapidly with depth, creating a barrier to mixing. The deep ocean is the bottom layer, where water is typically colder and denser, and there is little to no sunlight.

4. How do varying depths of water affect marine life?

Varying depths of water have a significant impact on marine life. The different layers of water have varying levels of light, temperature, and nutrients, which can affect the distribution and behavior of marine organisms. For example, some species may prefer to live in shallow waters with more sunlight, while others may thrive in deeper, colder waters with fewer predators.

5. What are the potential consequences of changing varying depths of water?

Changing varying depths of water, such as through sea level rise or ocean acidification, can have serious consequences for marine ecosystems. It can disrupt the delicate balance of temperature, salinity, and nutrients, leading to changes in the distribution and abundance of marine life. It can also impact the formation and movement of ocean currents, which can have global effects on climate patterns.

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