If a number of small droplets off water each of radius r coalesce to form a single drop of radius R, show that the rise in temperature is given by `T = ( 3 sigma )/( rho c ) [ ( 1)/( r ) - ( 1)/( R )]` where `sigma ` is the surface tension of water, `rho` its density and c is its specific heat capacity.

Explanation

To derive the formula for the rise in temperature \( T \) when small droplets of water coalesce into a larger drop, we can follow these steps:

### Step 1: Equate the Volumes
When \( n \) small droplets of radius \( r \) combine to form a single larger droplet of radius \( R \), the total volume before and after coalescing must remain the same.

The volume of one small droplet is:
\[
V_{\text{small}} = \frac{4}{3} \pi r^3
...