Question

A spherical drop of water of radius 1mm is sprayed million droplets all of same size. Find the energy expended in doing so

Answer 1

the energy expended in spraying million droplets all of same size is $8.95 X 10^{-5} J$

1. The energy expended in spraying million droplets all of same size is given by
2. E = (Sf-Si)T here Sf is the final surface area ,Si is the initial surface area and T is the surface tension of water 0.072 N/m
3. First to calculate the radius of the final drop by comparing both initial and final volume which remains constant
4. $\frac{4}{3} \pi (ri)^{3} =10^{6} \frac{4}{3} \pi (rf)^{3}$ so the final radius is
5. $rf =10^{-2} (10)^{-3}=10^{-5}$ m
6. now E = $(4\pi (10^{6}X(rf)^{2} - (ri)^{2})T=4x3.14(10^6 X10^{-10} -10^{-6})X(72X10^{-3} ) =8.95 X 10^{-5} J$