Calculate the pressue inside air bubble of diameter 0.2 mm situated just below the surface of water. Surface tension of water is `72 xx 10^(-3) Nm^(-1)`.

Explanation

To calculate the pressure inside an air bubble of diameter 0.2 mm situated just below the surface of water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Diameter of the bubble, \( d = 0.2 \, \text{mm} = 0.2 \times 10^{-3} \, \text{m} \)
- Surface tension of water, \( T = 72 \times 10^{-3} \, \text{N/m} \)
- Atmospheric pressure, \( P_0 = 1.013 \times 10^5 \, \text{Pa} \) (standard atmospheric pressure)

2. **Calculate the Radius of the Bubble:**
- The radius \( R \) is half of the diameter:
\[ R = \frac{d}{2} = \frac{0.2 \times 10^{-3}}{2} = 0.1 \times 10^{-3} \, \text{m} \]

3. **Use the Formula for Excess Pressure:**
- The excess pressure \( P_{\text{excess}} \) inside the bubble can be calculated using the formula:
\[ P_{\text{excess}} = \frac{2T}{R} \]

4. **Substitute the Values into the Formula:**
- Substitute \( T \) and \( R \) into the equation:
\[ P_{\text{excess}} = \frac{2 \times 72 \times 10^{-3}}{0.1 \times 10^{-3}} = \frac{144 \times 10^{-3}}{0.1 \times 10^{-3}} = 1440 \, \text{Pa} \]

5. **Calculate the Total Pressure Inside the Bubble:**
- The total pressure \( P_{\text{total}} \) inside the bubble is given by:
\[ P_{\text{total}} = P_0 + P_{\text{excess}} \]
- Substitute the values:
\[ P_{\text{total}} = 1.013 \times 10^5 + 1440 \]
- Convert \( 1.013 \times 10^5 \) to Pa:
\[ P_{\text{total}} = 101300 + 1440 = 102740 \, \text{Pa} \]

6. **Final Result:**
- The pressure inside the air bubble is:
\[ P_{\text{total}} \approx 1.027 \times 10^5 \, \text{Pa} \]