The work done in blowing a bubble of radius R is W. What is the work done in making a bubble of radius 2R? Given both the bubble are to be made with the same solution.

Explanation

To solve the problem of finding the work done in making a bubble of radius 2R, given that the work done for a bubble of radius R is W, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for work done**:
The work done (W) in blowing a bubble is given by the formula:
\[ W = 2 \times \text{Area} \times \text{Surface Tension} \]
where the area of a bubble is the surface area of a sphere.

2. **Calculate the surface area of the bubble with radius R**:
The surface area (A) of a sphere is given by:
\[ A = 4\pi r^2 \]
For a bubble of radius R, the surface area is:
\[ A = 4\pi R^2 \]

3. **Substitute the surface area into the work done formula**:
Now substituting the area into the work done formula:
\[ W = 2 \times (4\pi R^2) \times \sigma = 8\pi R^2 \sigma \]

4. **Calculate the work done for a bubble of radius 2R**:
Now, we need to find the work done (W') for a bubble of radius 2R. The surface area for this bubble is:
\[ A' = 4\pi (2R)^2 = 4\pi \times 4R^2 = 16\pi R^2 \]
Now substituting this into the work done formula:
\[ W' = 2 \times (16\pi R^2) \times \sigma = 32\pi R^2 \sigma \]

5. **Relate W' to W**:
We know from our previous calculation that:
\[ W = 8\pi R^2 \sigma \]
Therefore, we can express W' in terms of W:
\[ W' = 4 \times W \]

6. **Conclusion**:
The work done in making a bubble of radius 2R is:
\[ W' = 4W \]

### Final Answer:
The work done in making a bubble of radius 2R is \( 4W \).