calculate the energy evolved when 8 droplets of water of radius 1/2mm each combine into one. where s=0.072N/m.
To calculate the energy evolved when the water droplets combine, we can use the formula for the surface energy of a droplet. The surface energy is given by the equation:
E = 4πr^2s
where:
E is the surface energy,
r is the radius of the droplet, and
s is the surface tension of water.
In this case, we have 8 droplets with a radius of 1/2 mm each combining into one droplet. So, the initial total surface area of the 8 droplets is:
A_initial = 8 × 4π(1/2 mm)^2
Next, we need to calculate the radius and surface area of the combined droplet. Since the droplets combine into one, the resulting droplet will have a radius twice that of the individual droplets:
r_combined = 2 × (1/2 mm) = 1 mm
The surface area of the combined droplet is:
A_combined = 4π(1 mm)^2
The change in surface area, ΔA, is obtained by subtracting the initial surface area from the final surface area:
ΔA = A_combined - A_initial
Finally, we can calculate the energy evolved using the surface energy formula mentioned earlier:
E = ΔA × s
Substituting the values we calculated, we can find the energy evolved.