Ideal Gas Law Question: Solving for Volume at Surface

In summary, the question is asking for the final volume of an air bubble released by a scuba diver at a depth of 32m in a lake with a temperature of 5°C, as it rises to the surface where the temperature is 25°C. The pressure and temperature both change, so the ideal gas law equation must be used to solve for the final volume. The correct answer can be found by rearranging the final equation and plugging in the given numbers.
  • #1
Borat321
5
0
Here's an ideal gas law question:

A scuba diver is 32 m below the surface of a lake, where the temperature is 5°C. He releases an air bubble with a volume of 12 cm^3. The bubble rises to the surface, where the temperature is 25°C. What is the volume of the bubble right before it breaks the surface? (Hint: Remember that the pressure also changes.)

I thought it would be the following:

Initial:
Pressure @ 32m = 4.2atm, since 10m=1atm under water
12cm^3=.012 litres
5C= 278K

Final:
Pressure @ 0m = 1atm
V= unknown
25C= 298K

Then, use PV/T=PV/T... but apparently it's wrong - does anyone know why?
 
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  • #2
seems right, what's the correct answer?
 
  • #3
Should be fine, all you have to do is rearrange the final equation you wrote for the second volume and plug the numbers in.
 

1. What is the Ideal Gas Law and how is it used to solve for volume at the surface?

The Ideal Gas Law is a fundamental equation in thermodynamics that describes the behavior of gases under various conditions. It states that the product of pressure and volume of a gas is directly proportional to the number of moles of gas, the universal gas constant, and the temperature of the gas. This equation can be rearranged to solve for volume when given the other variables at the surface.

2. What are the variables needed to solve for volume at the surface using the Ideal Gas Law?

The variables needed are pressure, number of moles, universal gas constant, and temperature. These can be measured or calculated based on the conditions at the surface.

3. Can the Ideal Gas Law be used for any gas at any surface?

Yes, the Ideal Gas Law is applicable to any gas, as long as the gas behaves ideally and the conditions at the surface are within the range of validity for the equation. This means that the gas molecules are not interacting with each other and that the temperature is not too low or too high.

4. How can I make sure that my calculations using the Ideal Gas Law for volume at the surface are accurate?

To ensure accuracy, it is important to use consistent units for all the variables and to make sure that the conditions at the surface are within the range of validity for the Ideal Gas Law. It is also helpful to double-check your calculations and use multiple data points to confirm the results.

5. Can the Ideal Gas Law be used to predict the behavior of gases at different surfaces?

Yes, the Ideal Gas Law can be used to predict the behavior of gases at different surfaces as long as the conditions at those surfaces fall within the range of validity for the equation. This allows scientists to make predictions and model the behavior of gases in different environments.

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