A water drop of radius 10^-2 m is brokenn into 1000 equal droplets. Calculate the gain in surface energy. Surface tension of water ils 0.075Nm^-1
Answers
Answer:
Surface energy is defined as the amount of work done in increasing the area of the surface film through unity. So it's proportional to the surface area of the film.
Now it's given that the surface energy of a liquid drop is u and it's subdivided into 1000 equal droplets. In this process, the volume of the liquid will remain constant or unchanged but the newly formed 1000 drops will have different surface area than the original drop. Hence there will be a change in surface area, hence the surface energy will also be changed proportionally.
⇒ Volume of original drop = 1000× Volume of one drop
Let the radius of the original drop be R and of the newly formed droplet is r.
⇒
3
4
πR
3
=1000×
3
4
πr
3
⇒r=
10
R
The surface area of the original liquid drop is 4πR
2
and of the newly formed 1000 liquid drops is (1000×4πr
2
)
We know that r=
10
R
, so area of 1000 liquid drops =1000×4π(
10
R
)
2
=10×4πR
2
As we know that surface energy of a liquid drop is directly proportional to it's surface area, and the surface area becomes 10 times the original surface area, hence the surface energy will also become 10 times the original surface energy or 10u
Hence the surface energy becomes 10u So the Correct answer is B.