If the work done in blowing a soap bubble of volume V is W , then the work done in blowing a soap bubble of volume 2 V under the same conditions will be

Step-by-step solution

The work done will be against surface tension and we know that surface tension is related to work as W = T × ∆ A Since, the surface area of sphere is 4 πR 2 and there are two free surfaces, we have W = T × 8 πR 2 ... ( i ) and volume of sphere = 4 3 πR 3 i.e. V = 4 3 πR 3 ⇒ R = 3 V 4 π 1 / 3 ... ( ii ) From Eqs. ( i ) and ( ii ) , we get W = T × 8 π × 3 V 4 π 2 / 3 ⇒ W ∝ V 2 / 3 ∴ W 1 ∝ V 1 2 / 3 and, W 2 ∝ V 2 2 / 3 W 2 W 1 = 2 V 1 V 1 2 / 3 ⇒ W 2 = 2 2 / 3 W 1 = 4 1 / 3 W