A bubble of air released by a diver at the bottom of a pool of water become large as it approaches the surface of the water . Assume the temperature is constant and select the true statement. The pressure inside the bubble is

Options

A. greater near the bottom of the water
B. greater near the top of the water
C. same at all depths
D. cannot be determined from the given data

Answer

To solve the question regarding the behavior of a bubble of air released by a diver at the bottom of a pool of water, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Pressure at Different Depths**:
- At the bottom of the pool, the bubble experiences high pressure due to the weight of the water above it. This pressure is the sum of atmospheric pressure and the pressure exerted by the water column above the bubble.

2. **Pressure Inside the Bubble**:
- The pressure inside the bubble (let's call it P1) is initially greater than the pressure outside the bubble (P2) when it is at the bottom. This is because the external pressure includes both the atmospheric pressure and the hydrostatic pressure from the water.

3. **As the Bubble Rises**:
- As the bubble rises towards the surface of the water, the external pressure (P2) decreases. This is because the water column above the bubble becomes shorter, resulting in less hydrostatic pressure acting on the bubble.

4. **Volume Expansion of the Bubble**:
- According to Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure and volume are inversely related (P1V1 = P2V2), as the external pressure decreases, the volume of the bubble increases. This is why the bubble becomes larger as it approaches the surface.

5. **Comparison of Pressures**:
- At the bottom of the pool, the pressure inside the bubble (P1) is greater than the pressure outside (P2). As the bubble rises, P2 decreases, and the volume of the bubble increases until the pressures equalize.

6. **Conclusion**:
- Therefore, the true statement is that the pressure inside the bubble is greater near the bottom of the water compared to when it is near the surface.

### Final Answer:
The pressure inside the bubble is greater near the bottom of the water.

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