Volume of Bubble: Solve for V2 at Depth of 30 m

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SUMMARY

The discussion focuses on calculating the volume of a bubble as it rises from a depth of 30 meters in a lake, transitioning from a temperature of 20°C to 35°C. The initial volume of the bubble is 1.00 cm³, and the pressure at the bottom is calculated to be 3.943 atm. The correct application of the ideal gas law, specifically the equation P1V1/T1 = P2V2/T2, reveals that the final volume of the bubble just before it breaks the surface is approximately 4.1448 cm³ when using absolute temperatures.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Knowledge of pressure calculations in fluid mechanics
  • Familiarity with temperature conversions to Kelvin
  • Basic algebra for solving equations
NEXT STEPS
  • Study the Ideal Gas Law and its applications in various scenarios
  • Learn about pressure variations in fluids and their effects on gas volumes
  • Explore temperature conversion methods, particularly Celsius to Kelvin
  • Investigate real-world applications of buoyancy and gas behavior in aquatic environments
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in thermodynamics and fluid mechanics, particularly in understanding gas behavior under varying pressure and temperature conditions.

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Homework Statement



A bubble with a volume of 1.00 cm3 forms at the bottom of a lake that is 30 m deep. The temperature at the bottom of the lake is 20°C. The bubble rises to the surface where the water temperature is 35°C. Assume that the bubble is small enough that its temperature always matches that of its surroundings. What is the volume of the bubble just before it breaks the surface of the water? Ignore surface tension.

Homework Equations



PV=nRT

P1V1/T1 = P2V2/T2

The Attempt at a Solution



P2 = 1atm
P1 = 1 atm + 1000 * 9.81 * 30 => 3.943atm

3.943atm*1cm3/20C = 1atm*V2/35C
V2=6.9cm3

This value for V2 is way too big, where did I screw up? Thanks
 
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You've used celsius instead of absolute temperature.
 
ahh

so,

3.943/293 = V2/308
V2=4.1448cm3?
 

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