If a liquid of radius .R. is sprayed in to .n. small drops of equal radius .r. what is the work done in the process.

Explanation

The surface tension of liquid = T(say)
Surface energy of large drop = `4piR^(2)T`
Surface energy of all small drops together = `n4pir^(2)T`
The total surface area of all small drops put together is more than the surface area of large drop. Hence the system required external work to be done on it.
`therefore` External work = total final energy - initial energy
`W=n4pir^(2)T-4piR^(2)T" "...(1)`
The total volume of liquid is constant before and after spraying
`therefore(4/3pir^(3))n=4/3piR^(3)rArrr=R/n^(1//3)rArrr^(2)=R^(2)/n^(2//3)" "...(2)`
`thereforeW=4piR^(2)Tn/n^(2//3)-4piR^(2)T`
`rArrW=4piR^(2)T[n^(1//3)-1]`