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The gas inside a spherical bubble expands uniformly and slowly so that its radius increases from R to 2R. Let the atmospheric pressure be p₀ and surface tension be S. The work done by the gas in the process is

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$\frac{28 {πp}_{0} R^{3}}{3} + 24 {πSR}^{2}$

$\frac{25 {πp}_{0} R^{3}}{3} + 24 {πSR}^{2}$

$\frac{25 {πp}_{0} R^{3}}{3} + \frac{23 π {SR}^{2}}{2}$

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answer is A.

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Detailed Solution

$W = \int_{R}^{2 R} (p_{0} + \frac{4 S}{r}) 4 {πr}^{2} dr = 4 {πp}_{0} \times \frac{7 R^{3}}{3} + (4 π) (4 S) \times \frac{3 R^{2}}{2}$

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