Volume Expansion Calculation: 0.81632 cm^3

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SUMMARY

The volume expansion of an air bubble exhaled by a diver at a depth of 19 meters is calculated to be 0.81632 cm³ when it reaches the surface temperature of 13°C. The initial volume of the bubble is 0.8 cm³, and the calculation utilizes the volume expansion formula ΔV = βVinitialΔT, where β is the coefficient of volume expansion (3400 x 10^-6). The problem incorporates atmospheric pressure at 1.02 × 10^5 Pa and the density of seawater at 542 kg/m³, demonstrating the relationship between temperature and volume in gas behavior.

PREREQUISITES
  • Understanding of gas laws, specifically the relationship between pressure, volume, and temperature.
  • Familiarity with the concept of volume expansion and the coefficient of volume expansion.
  • Basic knowledge of physics principles related to buoyancy and pressure in fluids.
  • Ability to perform calculations involving units of volume and temperature conversion.
NEXT STEPS
  • Study the Ideal Gas Law and its applications in real-world scenarios.
  • Learn about the properties of gases under varying pressure and temperature conditions.
  • Research the effects of depth on gas volume in underwater environments.
  • Explore advanced topics in thermodynamics related to gas expansion and contraction.
USEFUL FOR

This discussion is beneficial for physics students, divers, and professionals in marine science or engineering who are interested in the behavior of gases under pressure and temperature changes.

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Homework Statement



At 19 m below the surface of the sea (den-
sity of 542 kg/m^3), where the temperature is
7 degree C, a diver exhales an air bubble having a
volume of 0.8 cm^3.
If the surface temperature of the sea is 13 degree C,
what is the volume of the bubble immediately
before it breaks the surface? The acceleration
of gravity is 9.8 m/s^3 and the atmospheric
pressure is 1.02 × 105 Pa. Answer in units of
cm^3.

Homework Equations



\DeltaV = \betaVinitial\DeltaT

The Attempt at a Solution


Vfinal - Vinitial = \betaVinitial(Tfinal - Tinitial)
Vfinal = \betaVinital(Tfinal - Tinitial) + Vinitial
= (3400x10^-6)(0.8)(13-7) + 0.8
= 0.81632 cm^3
 
Physics news on Phys.org
Rather than attempt to use a volume expansion formula (which might only apply under certain conditions, such as constant pressure), consider the basic properties of a gas. How are pressure, volume, and temperature of a gas related?
 

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