Ideal Gas Law: Solving Air Bubble Volume at Different Depths

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SUMMARY

The discussion centers on calculating the volume of an air bubble using the Ideal Gas Law as it ascends from a depth of 50 meters to the surface. The initial volume of the bubble is 1 cm³, with a temperature of 17°C and a pressure of 5 atm at that depth. Upon reaching the surface at 27°C, the correct volume of the bubble is determined to be 5.2 cm³, although the initial calculations were incorrect due to the omission of atmospheric pressure. The correct application of the Ideal Gas Law equation p₁V₁/T₁ = p₂V₂/T₂ is crucial for accurate results.

PREREQUISITES
  • Understanding of the Ideal Gas Law (pV=nRT)
  • Knowledge of pressure variations with depth in fluids
  • Basic algebra for solving equations
  • Familiarity with temperature conversion between Celsius and Kelvin
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  • Review the Ideal Gas Law applications in real-world scenarios
  • Learn about pressure changes in fluids and their effects on gas volume
  • Study temperature conversion methods and their importance in gas calculations
  • Explore common mistakes in gas law calculations and how to avoid them
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Students studying physics or chemistry, educators teaching gas laws, and anyone involved in practical applications of gas behavior under varying pressure and temperature conditions.

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Homework Statement



An air bubble of volume 1cm^3 is located at a depth of 50m beneath the surface where the temperature is 17C. When the bubble goes up to the surface where the temperature is 27C, how much will its volume be? Take the atmospheric pressure to be 1atm. Assume the pressure increases 1atm for every 10 meters.


Homework Equations



Ideal Gas Law:
pV=nRT

The Attempt at a Solution



p_{1}v_{1}/T_{1}=p_{2}v_{2}/T_{2}

I plugged in:

5\times10^{5}\times1\times10^{-6}/290=1\times10^{5}\times V_{2}/300

Solving for V2, I get 5.2cm^3, but according to the solutions, that's not the answer...
I'd like to know what I'm doing wrong.
Thanks for the help!
 
Last edited:
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At 50 m, the pressure due to the water is 5 atm. You still have to add in the atmospheric pressure.
 
Last edited:

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