1000 drops of a liquid each of diameter 4mm combine to form a single large drop if surface tention of liquid is 35dyne/cm calculate the energy evolved by the system in this process

The energy evolved in the process can be calculated using the formula for the change in surface energy, which is given by:

ΔE = E_final - E_initial

The surface energy (E) is given by the formula E = σA, where σ is the surface tension and A is the surface area.

First, we need to calculate the initial surface area of the 1000 small drops. The surface area (A) of a sphere is given by the formula A = 4πr², where r is the radius. The diameter of each small drop is given as 4mm, so the radius is 2mm or 0.2cm. Therefore, the surface area of each small drop is:

A_small = 4π(0.2cm)² = 0.16π cm²

Since there are 1000 such drops, the total initial surface area is:

A_initial = 1000 * 0.16π cm² = 160π cm²

Next, we need to calculate the final surface area when all the drops combine to form one large drop. The volume of the large drop is equal to the total volume of the small drops. The volume (V) of a sphere is given by the formula V = 4/3πr³. Therefore, the volume of each small drop is:

V_small = 4/3π(0.2cm)³ = 0.008π cm³

Since there are 1000 such drops, the total volume is:

V_total = 1000 * 0.008π cm³ = 8π cm³

This is also the volume of the large drop. We can use this to find the radius of the large drop, using the formula for the volume of a sphere:

8π cm³ = 4/3πr³

Solving for r, we get r = (6cm)^(1/3) ≈ 1.82cm

Therefore, the surface area of the large drop is:

A_final = 4π(1.82cm)² ≈ 41.78π cm²

Now we can calculate the change in surface energy. The surface tension (σ) is given as 35dyne/cm. Therefore, the initial surface energy is:

E_initial = σA_initial = 35dyne/cm * 160π cm² = 5600π dyne

And the final surface energy is:

E_final = σA_final = 35dyne/cm * 41.78π cm² ≈ 1462.3π dyne

Therefore, the change in surface energy (and hence the energy evolved by the system) is:

ΔE = E_final - E_initial = 1462.3π dyne - 5600π dyne = -4137.7π dyne

The negative sign indicates that energy is released by the system. Therefore, the energy evolved by the system in this process is approximately 4137.7π dyne.