Fluid MechanicsHard
Question
A soap bubble of radius R and surface tension T is formed in vacuum. It is slowly charged so that it slowly expands. It is stopped charging when the radius becomes 2R. Find the amount of charge given to the bubble.
Options
A.Q = 
B.Q = 
C.Q = 
D.None of these
Solution
we have initially Pin = 
......(1)
Now when extra charge is given, for equilibrium we have
P′in +
......(1)
Now we have P′in =
[isothermal change]
where vi- initial volume of bubble
vf- final volume of bubble
so, P′in =
so, (1) equation will give
so, σ2 =
so, σ = 
now charge Q = σ. 4π(2R2) = 4π.(4R2) = 
Q =
......(1)Now when extra charge is given, for equilibrium we have
P′in +
......(1)Now we have P′in =
[isothermal change]where vi- initial volume of bubble
vf- final volume of bubble
so, P′in =
so, (1) equation will give
so, σ2 =
so, σ = now charge Q = σ. 4π(2R2) = 4π.(4R2)
= Q =
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