If the radius of a soap bubble is r and surface tension of the soap solution is T. Keeping the temperature constant,
If the radius of a soap bubble is r and surface tension of the soap solution is T. Keeping the temperature constant, what is the extra energy needed to double the radius of soap bubble?
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Initial radius = r
Surface Tension = T
Surface Area = 4πr2
Energy required to blow a soap babble of radius r (E1) = Surface Tension × 2 × Surface Area
(∵2 because bubble has two surfaces)
E1 = T × 2 × (4 π r2)
E1 = 8 π r2 T →1)
Final Radius = 2r
Surface Tension = T
Surface Area = 4 π (2r)2
= 16 π r2
Energy required to blow a soap bubble of Radius 2 r (E2)
= surface Tension × 2 × Surface Area
E2=T × 2 × (416 π r2)
= 32 π r2 T → 2)
Extra energy required : → E2 – E1
= 32 π r2 T – 8 π r2 T
= 24 π r2 T
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