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+2 votes
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in Physics by (54.6k points)

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? 

1 Answer

+3 votes
by (89.9k points)
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Best answer

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

by (10 points)
V. Good

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