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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2006

  • question_answer
    The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble, the required surface energy in doing so is given by :

    A)  \[32\pi {{R}^{2}}T\]                                       

    B)         \[24\pi {{R}^{2}}T\]

    C)         \[8\pi {{R}^{2}}T\]                          

    D)         \[4\pi {{R}^{2}}T\]

    Correct Answer: B

    Solution :

    Initial surface energy:                 \[{{U}_{1}}=2\times 4\pi {{R}^{2}}T=8\pi {{R}^{2}}T\] Final surface energy \[{{U}_{2}}=2\times 4\pi {{(2R)}^{2}}T=32\pi {{R}^{2}}T\] Hence, required energy                 \[=32\pi {{R}^{2}}T-8\pi {{R}^{2}}T\]                 \[=24\pi {{R}^{2}}T\]


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