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    Question

    A soap bubble expands isothermally and its radius

    doubles. The work done by surface tension during this expansion is: 
    A 4πR²T Correct Answer Incorrect Answer
    B 24πR²T Correct Answer Incorrect Answer
    C 16πR²T Correct Answer Incorrect Answer
    D 8πR²T Correct Answer Incorrect Answer

    Solution

    When a soap bubble expands, work is done against surface tension to increase the surface area. A soap bubble has two surfaces (inner and outer), so total surface area is twice that of a single sphere. Let:

    • Initial radius =
    • Final radius = 2R
    • Surface tension = T
    Initial surface area of one surface = 4πR2 Since there are two surfaces, total initial area: A1 = 2. 4πR2 = 8πR2 Final surface area with radius 2R: A2 = 2. 4π(2R)2 = 32πR2 Work done by surface tension Work done = T ⋅ ΔA = T ⋅ (A2 – A1) W = T.(32πR2 - 8πR2) W = 24πR2T

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