Two soap bubbles are combined isothermally to form a single bubble. In this process, the change in volume and surface area are respectively V and A. If p is the atmospheric pressure, and S is the surface tension of the soap solution, the correct relation, among the following, is
Text Solution
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Let the radii of the two-soap bubble be a and b, respectively, and radius of a single larger
bubble be c.
As excess pressure for a soap bubble is 
and external pressure is p,
So, 
and 
...(i)
and 
and 
...(ii)
Now, as mass is conserved,
i.e., 
(as 
)
As the temperature is constant,
i. e. , T a = T b = T c
So p a V a +p b V b = p c V c
This, in the light of eqns. (i) and (ii) becomes,
i.e., 
...(iii)
Now, V = 
(a 3 + b 3 - c 3 )
And A = 
(a 2 + b 2 -c 2 )
or 4SA + 3pV = 0
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