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79. Problem 17.55 (RHK) We have to show that the pressure difference between the
inside and the outside of a bubble of radius r is
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,
where
is the
surface tension of the liquid from which the bubble is blown.|
Solution: Click For PDF Version A soap bubble of radius r, comprises of two surfaces,
each of area
Let the radius of the bubble be increased virtually by an infinitesimal
amount
The source of additional surface energy
is the virtual work,
As the bubble is in equilibrium the pressure inside the bubble is
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; the
inner and the outer surface of the bubble. Let
be the surface tension of the solution. By definition
of the bubble is
.
, done by
the gauge pressure
inside
the bubble. That is
,
where
is the
atmospheric pressure outside the bubble. Bubble experiences an inward force
because of surface tension which is balanced by the gauge pressure inside the
bubble.