Blow a bubble
Two soap bubbles of same radius coalesce isothermally to form a bigger bubble of radius .
The range of for this to happen is .
Find the value of .
The answer is 2.674.
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1 solution
Since the Surface Tension and the atmospheric pressure have not been given we just take the ( P / 4 T ) Ratio to be positive.
As the no. of moles is constant we must have ( P o + 4 T / r ) ( 4 / 3 π r 3 ) ∗ 2 = ( P o + 4 T / R ) ( 4 / 3 π R 3 ) .
Solving for the ratio P / 4 T = ( 2 r 2 − R 2 ) / ( R 3 − 2 r 3 ) > 0 .
So This yields a valid interval as ( √ 2 , 2 ( 1 / 3 ) .
So the ans is 2 . 6 7 4 ....
Note:Here T denotes the surface Tension of soap solution and we make use of the fact that the Pressure inside is greater than the pressure outside by 4 T / R