In a cylinder-piston arrangement air is under a pressure P₁ and constant temperature t. A soap bubble lies inside the cylinder, surface tension is T. The soap bubble is to be reduced to half its size, the required pressure P₂ to which air should be compressed by slowly pulling the piston into the cylinder is

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$8 P_{1} + \frac{12 T}{r}$

$8 P_{1} + \frac{24 T}{r}$

$8 P_{1} + \frac{3 T}{r}$

$8 P_{1} + \frac{2 T}{r}$

answer is A.

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Detailed Solution

$[p_{1} + \frac{4 T}{r}] \frac{4}{3} {πr}^{3} = [p_{2} + \frac{4 T}{r / 2}] \frac{4}{3} π {(\frac{r}{2})}^{3}$
$as pv = constant ∴ p_{2} = 8 p_{1} + \frac{24 T}{r}$

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