How Does the Volume of a Diver's Exhaled Bubble Change from Deep Sea to Surface?

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In summary, the problem involves a diver exhaling a bubble at a depth of 25m below the surface of the sea. The temperature and density of the sea are given, and the ideal gas equation is used to calculate the pressure at that depth. The volume of the bubble just before it breaks the surface is then found using the ideal gas equation again, using the pressure calculated at the surface and the temperature and volume at the starting depth. The use of the equation P = Po + density(g)(h) is debated, but ultimately deemed acceptable.
  • #1
latitude
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Homework Statement


Well, I did get an answer to this, but I don't think I did it right. It kinda seems wrong to me, so I wanted a second opinion :)

At 25 m below the surface of the sea (Density = 1025 kg/m^3), where the temperature is 5 degrees Celsius, a diver exhales an air bubble having a volume of 1 cm^3. If the surface temp of the sea is 20 degrees Celsius, what is the volume of the bubble just before it breaks the surface?


Homework Equations


Ideal gas: PV = nRT
P = Po + (DENSITY)gh ??Not sure if I should use this??


The Attempt at a Solution



P = Po + Density(g)(h) = 1.013 x 10^5 Pa + (1025)(9.81)(25)
P = 3.5 x 10^5 Pa (This seems fairly logical to me... kinda? But I'm not very logical :P)

Under the sea
(3.5 x 10^5)(0.01 m^3) = n(3.814)(278 degrees K)
n = 3.3
At surface
(1.013 x 10^5)(V) = (3.3)(3.814)(293)
V = 0.036 m^3, or 3.6 cm^3... that's fairly reasonable, isn't it?? But I'm not sure if using the P = Po + density(g)(h) was all right when the height is below the sea like that ??
 
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  • #2
You can use pv=nRT remember that 'nR' isconstant.
Then you just need to find the pressure at 25m underwater, p = density * g * h
 
  • #3
Forgive me if I sound dense (I may very well be!) but isn't that kind of what I did? If it's been smart enough to note they were constant, I could have done it with less work
 
  • #4
latitude said:
But I'm not sure if using the P = Po + density(g)(h) was all right when the height is below the sea like that ??

Looks OK to me.
 

Related to How Does the Volume of a Diver's Exhaled Bubble Change from Deep Sea to Surface?

1. What is the ideal gas law and how is it used to solve temperature problems?

The ideal gas law is a mathematical equation that describes the behavior of an ideal gas at a constant pressure. It states that the product of the pressure (P) and volume (V) of a gas is directly proportional to its temperature (T) and the number of moles (n) of gas present, and is given by the equation PV = nRT, where R is the gas constant. This equation can be rearranged to solve for temperature when the other variables are known.

2. What is absolute temperature and how is it different from other temperature scales?

Absolute temperature, also known as thermodynamic temperature, is a temperature scale that is based on the absolute zero point, which is the lowest possible temperature at which all molecular motion ceases. It is different from other temperature scales, such as Celsius and Fahrenheit, because it does not use arbitrary reference points and is therefore a more accurate and universally applicable scale.

3. How does the kinetic theory of gases explain the relationship between temperature and pressure?

The kinetic theory of gases states that the temperature of a gas is directly proportional to the average kinetic energy of its molecules. As temperature increases, the molecules have more kinetic energy and therefore move faster, resulting in more collisions with the walls of the container and an increase in pressure. This is why temperature and pressure are directly related in the ideal gas law.

4. How does the ideal gas law account for deviations from ideal gas behavior?

The ideal gas law assumes that gas particles have no volume and do not interact with each other. However, in real gases, the particles do have volume and do interact, which can lead to deviations from ideal gas behavior. To account for these deviations, the ideal gas law can be modified by including a correction factor, called the compressibility factor, which adjusts for the differences between ideal and real gases.

5. How can the ideal gas law be used in practical applications?

The ideal gas law has many practical applications in fields such as chemistry, physics, and engineering. It can be used to calculate the volume of a gas at a given pressure and temperature, determine the amount of gas present in a container, and predict the behavior of gases in various systems. It is also used in the design of equipment such as pressure vessels, gas turbines, and refrigeration systems.

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