CBSE Class 11-science Answered

If we consider the atmospheric pressure to be 'P_s' and the internal pressure to be 'P_i' then the net pressure would be written as

P_net = P_i - P_a

Now, as the radius of the drop has increased, work has been done by the net internal pressure.

So, this work done will be

W = force x displacement

or

W = (pressure x area) x displacement

and in this case

W = (pressure x area) x increase in drop radius

so, the work done will be

W = (P _net x 4?r ² ) x dr (1)

but, the increase potential energy will be twice

dU = 16?r.dr x S (2)

this is because in case of a bubble there are two free surfaces, the outside surface and the inside surface. The potential energy will thus change accordingly.

so, as (1) equals (2), we have

(P_net x 4?r²) x dr = 16?r.dr x S

or

the net pressure inside a bubble will be

P_net = 4S / r [twice than the that inside the drop]

which is the required expression