Question

Radius of a soap bubble is 'r', surface tension of soap solution is T. Then without increasing the temperature, how much energy will be needed to double its radius

• A. $4 \pi r ^ { 2 } T$
• B. $2 \pi r ^ { 2 } T$
• C. $12 \pi r ^ { 2 } T$
• D. $24 \pi r ^ { 2 } T$

Answer 1

Answer: (D)

$24 \pi r ^ { 2 } T$

Answer 2

$W = 8 \pi T \left( R _ { 2 } ^ { 2 } - R _ { 1 } ^ { 2 } \right) = 8 \pi T \left[ ( 2 r ) ^ { 2 } - ( r ) ^ { 2 } \right] = 24 \pi r ^ { 2 } T$