Air is pushed into a soap bubble of radius r to double its radius.
Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution is S, the work done in the process is
(a) 8πr2S
(b) 12πr2S
(c) 16πr2S
(d) 24πr2S.
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The correct answer is (d) 24πr2S.
Explanation:
The surface tension S is equal to surface energy per unit area, S = U/A
→U = SA
The total area of the soap bubble =2*4πr² =8πr²
The total surface energy of the original bubble =8πr²S
The total surface area of the expanded bubble = 2*4π(2r)² =32πr²
The total surface energy of the expanded bubble =32πr²S
The work done in the process = increase in the surface energy of the bubble =32πr²S - 8πr²S =24πr²S
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