Chapter 5: Problem 35
A bubble of air released at the bottom of a pool of water becomes larger as it approaches the water surface. This is due to (1) decreasing pressure on the bubble as it rises (2) high temperature of water near the water surface (3) changing surface tension of the water (4) decreasing stability of the bubble with the height from the bottom
Short Answer
Expert verified
Option 1: decreasing pressure on the bubble as it rises.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Pressure Changes
When discussing why a bubble of air released at the bottom of a pool increases in size as it rises, understanding pressure changes is key. As the bubble ascends, the pressure exerted by the water on the bubble decreases. This can be explained by Boyle's Law, a fundamental principle in physics.
Boyle's Law states: \[ P_1V_1 = P_2V_2 \] where \(P_1\) and \(P_2\) are the initial and final pressures, and \(V_1\) and \(V_2\) are the initial and final volumes, respectively.
This relationship tells us that at constant temperature, the volume of a gas increases as the pressure decreases.
Therefore, as the bubble ascends and the pressure drops, its volume expands. This decrease in pressure is the primary reason the bubble grows in size.
Boyle's Law states: \[ P_1V_1 = P_2V_2 \] where \(P_1\) and \(P_2\) are the initial and final pressures, and \(V_1\) and \(V_2\) are the initial and final volumes, respectively.
This relationship tells us that at constant temperature, the volume of a gas increases as the pressure decreases.
Therefore, as the bubble ascends and the pressure drops, its volume expands. This decrease in pressure is the primary reason the bubble grows in size.
Gas Volume
The volume of gas in the bubble changes due to the variations in pressure as it moves upward through the water. According to Boyle's Law, if the temperature remains constant, the volume of the air in the bubble will increase as the pressure decreases.
This happens because the gas molecules are less compressed as the external pressure decreases, allowing the bubble to expand.
In simpler terms:
This happens because the gas molecules are less compressed as the external pressure decreases, allowing the bubble to expand.
In simpler terms:
- The deeper the bubble is, the higher the pressure around it.
- As the bubble rises, the pressure decreases.
- With the drop in pressure, the gas molecules in the bubble spread out, making the bubble larger.
Water Surface Tension
Surface tension affects the shape and stability of the bubble: it is the elastic tendency of water's surface, which makes it contract and resist external force. While surface tension can impact the bubble's shape, its role in changing the bubble's volume as it rises is minimal compared to pressure changes.
However, it's crucial to understand that:
However, it's crucial to understand that:
- Surface tension tries to minimize the surface area of the bubble.
- As the bubble increases in size, the effects of surface tension become less significant compared to the large volume changes due to pressure.
- The interaction between surface tension and pressure helps the bubble maintain its spherical shape as it rises.
Bubble Dynamics
Bubble dynamics encompasses the behavior and movement of bubbles underwater. Several factors affect bubble dynamics, but pressure change is the most significant in the context of a bubbling rising in water. Other important factors include:
- Temperature: Higher temperatures can cause slight expansion, but pool water temperature changes are usually too small to matter greatly.
- Stability: As bubbles rise, they may become less stable due to deformation caused by water currents and turbulence. This doesn't significantly affect bubble volume.
- Shape: Initially small and perfectly spherical, bubbles can become more spherical or slightly deformed as they rise due to changing surface tension and pressure dynamics.
