When an air bubble rise from the bottom of a deep lake to a point just below the water surface, the pressure of air inside the bubble

Options

A. is greater than the pressure outside it
B. is less than the pressure outside it
C. increase as the bubble moves up
D. decreases as the bubble moves up

Answer

To solve the problem of the pressure of air inside an air bubble as it rises from the bottom of a deep lake to a point just below the water surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Pressure Inside the Bubble**:
The pressure inside an air bubble is influenced by the external pressure and the surface tension of the bubble. The formula for the excess pressure inside a bubble is given by:
\[ P_{inside} = P_{outside} + \frac{4T}{R} \]
where \(T\) is the surface tension of the liquid and \(R\) is the radius of the bubble.

2. **Determine the External Pressure**:
When the bubble is at the bottom of the lake, the external pressure \(P_{outside}\) can be expressed as:
\[ P_{outside} = P_0 + \rho g h \]
where \(P_0\) is the atmospheric pressure, \(\rho\) is the density of the water, \(g\) is the acceleration due to gravity, and \(h\) is the depth of the bubble below the water surface.

3. **Calculate the Pressure at the Bottom of the Lake**:
At the bottom of the lake, the pressure inside the bubble can be calculated as:
\[ P_{inside, bottom} = P_0 + \rho g h + \frac{4T}{R} \]

4. **Consider the Pressure Just Below the Surface**:
As the bubble rises to a point just below the water surface, the depth \(h\) becomes 0. Thus, the external pressure at this point is simply:
\[ P_{outside, surface} = P_0 \]
Therefore, the pressure inside the bubble just below the surface becomes:
\[ P_{inside, surface} = P_0 + \frac{4T}{R} \]

5. **Compare the Pressures**:
From the above calculations, we can see that as the bubble rises from the bottom to just below the surface, the external pressure decreases (since \(h\) decreases), but the excess pressure due to surface tension remains constant. Thus, the pressure inside the bubble decreases as it rises.

6. **Conclusion**:
The pressure of air inside the bubble decreases as it rises from the bottom of the lake to just below the surface. Therefore, the final answer is that the pressure inside the bubble is greater than the atmospheric pressure but decreases as it rises.