A soap bubble of radius R has formed at normal temperature and pressure under isothermal conditions. Complete the work done. The surface tension of soap solution is `T`.

Explanation

To solve the problem of calculating the work done in forming a soap bubble of radius \( R \) under isothermal conditions, we can follow these steps:

### Step 1: Understand the Structure of the Soap Bubble
A soap bubble consists of two layers of soap film. Each layer has a surface area, and since the soap bubble is spherical, we can calculate the surface area of a single layer.

### Step 2: Calculate the Surface Area of the Soap Bubble
The surface area \( A \) of a single soap film layer of a sphere is given by the formula:
\[ A = 4\pi R^2 \]
Since the soap bubble has two layers, the total surface area \( A_{total} \) of the soap bubble is:
\[ A_{total} = 2 \times 4\pi R^2 = 8\pi R^2 \]

### Step 3: Determine the Work Done
The work done \( W \) in expanding the soap bubble can be calculated using the formula:
\[ W = \text{Surface Tension} \times \text{Change in Area} \]
Here, the surface tension of the soap solution is denoted by \( T \), and the change in area is the total surface area of the bubble, which we found to be \( 8\pi R^2 \).

### Step 4: Substitute the Values
Substituting the values into the work done formula gives:
\[ W = T \times (8\pi R^2) \]
Thus, the work done in forming the soap bubble is:
\[ W = 8\pi R^2 T \]

### Final Answer
The work done in forming the soap bubble is:
\[ W = 8\pi R^2 T \]

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