Surface Tension

Given: 27 drops of mercury coalesce to form a bigger drop.
Let the radius of each small drop be . The volume of one drop is:
The total volume of 27 small drops is:
Now, let the radius of the bigger drop formed by coalescing all 27 smaller drops be . The volume of the bigger drop is:
Since the total volume is conserved, we have:
Simplifying:
Next, we calculate the surface energy of the small drops and the big drop. The surface area of one small drop is:
The total surface area of 27 small drops is:
The surface area of the bigger drop is:
The surface energy is proportional to the surface area. The relative increase in surface energy is:
Final Answer: The relative increase in surface energy is -2/3.