At room temperature, the surface tension of water is 72.0 mJ·m^–2. What is the energy required to change a spherical drop of water with a diameter of 1.80 mm to three smaller spherical drops of equal size? The surface area of a sphere of radius r is 4πr^2 and the volume is 4πr^3/3.

To calculate the energy required to change a spherical drop of water into three smaller drops, we need to consider the change in surface area and the change in volume.

1. Determine the initial and final radii of the droplets:
Given that the diameter of the original drop is 1.80 mm, the initial radius (r_initial) can be calculated as half of that value, r_initial = 0.90 mm.
Since we need to divide the original droplet into three equal-sized droplets, the final radius (r_final) of each smaller droplet will be one-third of the initial radius, r_final = r_initial / 3.

2. Calculate the initial and final surface areas:
The initial surface area (A_initial) of the original droplet can be calculated using the formula for the surface area of a sphere: A_initial = 4πr_initial^2.
Similarly, the final surface area (A_final) of each smaller droplet can be determined using the same formula and the final radius: A_final = 4πr_final^2.

3. Calculate the change in surface area:
The change in surface area (ΔA) can be calculated as the difference between the initial and final surface areas: ΔA = A_initial - 3 * A_final. Note that we subtract 3 times the final surface area because we are dividing the original droplet into three smaller droplets.

4. Calculate the energy required:
Finally, to find the energy required, we can use the formula: Energy = Surface Tension * Change in Surface Area.
Given that the surface tension of water is 72.0 mJ·m^–2, and considering that surface tension is measured in energy per unit area, we can express it as 72.0 × 10^–3 J·m^–2.
Therefore, the energy required is: Energy = (72.0 × 10^–3 J·m^–2) * ΔA.

By following these steps, you can calculate the energy required to change the spherical drop of water into three smaller drops of equal size.