Surface Tension

To determine the gain in surface energy when a big oil droplet is broken into smaller droplets, follow these steps:
Given:
Radius of the big droplet ( ):
Number of small droplets ( ):
Surface tension of oil ( ):
Step 1: Calculate the Volume of the Big Droplet
The volume of the big droplet is:

Step 2: Volume of Each Small Droplet
Since the big droplet breaks into equal droplets, the volume of each small droplet is:

Let the radius of each small droplet be . Then:


Step 3: Calculate the Surface Areas
Surface area of the big droplet ( ):

Total surface area of the small droplets ( ):

Step 4: Determine the Change in Surface Area

Step 5: Calculate the Gain in Surface Energy
The surface energy is given by:

Approximating :