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A cylinder with movable piston contains air under pressure P₀ and a small soap bubble of radius r. The surface tension of soap solution is T and the temperature of the system is kept constant. The pressure to which the air should be compressed by slowly pushing the piston into the cylinder for the soap bubble to reduce its size by half is _____________

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$8 [P_{0} + \frac{3 T}{r}]$

$7 P_{0} + \frac{24 T}{r}$

$8 [P + \frac{T}{r}]$

$8 P_{0} + \frac{21 T}{r}$

answer is A.

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Detailed Solution

$(P_{0} + \frac{4 T}{r}) V = (P + \frac{4 T}{\frac{r}{2}}) \frac{V}{8} \Rightarrow P = 8 (P_{0} + \frac{3 T}{r})$

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