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A thin bubble of radius $R$ is formed using a soap solution of surface tension $T$ and atmospheric air at pressure $P_{0}$ . The final pressure inside the bubble is $P$ and the final volume of air inside is $V$ . The work done is increasing the surface energy of the bubble is $w_{1}$ and the work done in isothermal compression of air inside is $w_{2}$ . Then

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$w_{1} = 4 π R^{2} T$

$w_{2} = p v l n \frac{p}{p_{0}}$

$w_{1} = 8 π R^{2} T$

$ω_{2} = 0$

answer is B, C.

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Detailed Solution

$w_{1} = 8 π R^{2} T p_{0} v_{0} = p v ∴ w_{2} = n R θ \ln \frac{v_{0}}{v} = p v l n \frac{p}{p_{0}}$

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