The surface tension of soap solution at a temperature `20^(@)`C is `2.5xx10^(-2) N m^(-1)`.The excess pressure inside a bubble of soap solution of radius 6mm is

Options

A. 12.5 pa
B. 14.2 pa
C. 15.5 pa
D. 16.7 pa

Explanation

To find the excess pressure inside a soap bubble, we can use the formula:

\[ \Delta P = \frac{4 \gamma}{R} \]

where:
- \(\Delta P\) is the excess pressure,
- \(\gamma\) is the surface tension of the liquid,
- \(R\) is the radius of the bubble.

### Step 1: Identify the given values
- Surface tension, \(\gamma = 2.5 \times 10^{-2} \, \text{N/m}\)
- Radius of the bubble, \(R = 6 \, \text{mm} = 6 \times 10^{-3} \, \text{m}\)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the formula for excess pressure:

\[ \Delta P = \frac{4 \times (2.5 \times 10^{-2})}{6 \times 10^{-3}} \]

### Step 3: Calculate the numerator
Calculate the numerator:

\[ 4 \times (2.5 \times 10^{-2}) = 10 \times 10^{-2} = 1 \times 10^{-1} \, \text{N/m} \]

### Step 4: Calculate the excess pressure
Now substitute the numerator back into the equation:

\[ \Delta P = \frac{1 \times 10^{-1}}{6 \times 10^{-3}} = \frac{0.1}{0.006} \]

### Step 5: Perform the division
Now, perform the division:

\[ \Delta P = \frac{0.1}{0.006} \approx 16.67 \, \text{Pa} \]

### Step 6: Round the answer
Rounding to two decimal places, we get:

\[ \Delta P \approx 16.7 \, \text{Pa} \]

### Final Answer
The excess pressure inside the bubble of soap solution is approximately \(16.7 \, \text{Pa}\).

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