Question

An air bubble of radius 3cm rises from a depth of 7.0cm in a swimming pool. What will the radius of the bubble just before it reaches the water surface. Assuming that the water temperature is uniform, take approximate height of water barometer at 10.34m

Answer 1

The air bubble's radius just before reaching the water surface depends on the depth and the hydrostatic pressure equation. To calculate accurately, water temperature and atmospheric pressure details are needed. when the bubble reaches the surface of the water, it has a radius of 10.5 mm.

The situation described involves an air bubble rising from a depth within a swimming pool to the water surface. The relevant principles for this scenario include the ideal gas law and the hydrostatic pressure equation.

1. Ideal Gas Law:
`\(PV = nRT\)`, where
`\(P\)` is the pressure,
`\(V\)` is the volume,
`\(n\)` is the number of moles,
`\(R\)` is the ideal gas constant, and
`\(T\)` is the temperature.

2. Hydrostatic Pressure Equation:
`\(P = P_0 + \rho gh\)`, where
`\(P\)` is the pressure at depth,
`\(P_0\)` is the atmospheric pressure at the water surface,
`\(\rho\)` is the density of water,
`\(g\)` is the acceleration due to gravity, and
`\(h\)` is the depth.

Given that the bubble rises from a depth of 7.0 cm to the water surface, we can consider the change in pressure and use the ideal gas law to find the change in volume, assuming the number of moles and temperature remain constant.

The radius of the bubble just before reaching the water surface can be obtained by considering the change in volume as it rises, taking into account the initial and final pressures.

This problem involves physics and thermodynamics concepts and calculations. If you need a detailed numerical solution, you may need to provide additional information such as the temperature of the water and the atmospheric pressure at the water surface.