Energy conservation (Surface Energy of a liquid drop) Suppose, there are n identical liquid drops of radius r, which combines together to form a bigger drop of radius R.
If we try to calculate their surface energy then the surface energy of bigger drop would be less than that of the total surface energy of all drops.
But my professor, while solving a question also mentioned a fact that total energy is conserved(Initial Surface energy + Initial Gravitational Potential would be equal to that of the  final).
Now, he also mentioned that this process will be favorable since surface energy is decreasing in the process. But if the energy is conserved why is it favorable?
Even though surface energy decreases but potential energy has increased.
 A: Energy is always conserved, but it's possible for mechanical energy to be converted to heat, and that's what happens in this process.
Imagine you had two drops of an imaginary liquid with a zero viscosity and the two drops are just touching. The surface tension will pull the drops together, which means the liquid in the drops accelerates so it has a kinetic energy. The PE stored in the original surface of the two touching drops gets converted into KE of the liquid.
The problem is that by the time the two drops have merged to form a roughly spherical combined drop the liquid has acquired a velocity and with no viscosity it just keeps flowing and the combined drop deforms back into something like the original two drops. The shape of the drop will keep oscillating as the PE of the surface turns into KE of the liquid then back into PE of the surface.
However in a real liquid viscosity converts the KE of the flowing liquid into heat, and the drop quickly settles into a sphere with the liquid inside it stationary. The end result is the PE change as the drops coalesce has been converted to heat. Total energy is still conserved, but only if you count the increase in heat as well as the changes in PE and KE.
