Question

surface energy of a liquid drop is U and it is paid into 1331 identical droplets surface energy of a liquid droplet will be ​

Answer 1

when the surface energy of a liquid drop is Uand it is spread into 1331 identical droplets then the surface energy of a liquid is 10U

Explanation:

let R is the Radius of initial drop

and r is the radius of droplets

if the droplet is sprayed into multiple droplets, the total volume is unchanged, thus we can write  

             $n(\frac{4}{3})\pi r^{3} =\frac{4}{3} \pi R^{3}$

    or      $r = R(\frac{1}{1331}) ^{\frac{1}{3} }$

the total surface area of the droplet is $n4\pi r^{2}$

$4\pi R^{2}$ is the surface area of the original drop, so the total area has increased by a factor of $n^{\frac{1}{3} }$

the surface energy is the work required to increase the surface area of a substance by unit area. then, the surface energy is proportional to surface area. hence the surface energy is increased by a factor of $n^{\frac{1}{3} }$ and is $n^{\frac{1}{3} } u$

the original surface energy was u, so the increase in surface energy is

$n^{\frac{1}{3} } u - u = [n^{\frac{1}{3} }-1]u$

if n = 1331 then $n^{\frac{1}{3} } =11$

and [11-1]u = 10u