SUMMARY
The gauge pressure of a spherical balloon with a diameter of 60.0 cm, initially at atmospheric pressure (101.3 kPa) and a temperature of 20.0 °C, is calculated when submerged 25.0 m under seawater at a temperature of 11.0 °C. At this depth, the total pressure exerted on the balloon includes both the atmospheric pressure and the hydrostatic pressure due to the water column. The hydrostatic pressure can be calculated using the formula P = ρgh, where ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth. The gauge pressure is then determined by subtracting the atmospheric pressure from the total pressure at that depth.
PREREQUISITES
- Understanding of gauge pressure and absolute pressure concepts
- Familiarity with the hydrostatic pressure formula (P = ρgh)
- Knowledge of gas laws, particularly relating to temperature and pressure
- Basic skills in algebra for solving equations
NEXT STEPS
- Research the properties of seawater, including density at various temperatures
- Learn about the Ideal Gas Law and its application in pressure calculations
- Study the effects of temperature on gas volume and pressure
- Explore real-world applications of gauge pressure in underwater environments
USEFUL FOR
Students studying physics, particularly those focusing on fluid mechanics and thermodynamics, as well as professionals in fields related to underwater exploration and engineering.