Under isothermal conditions, two soap bubbles of radii ' r₁ ' and '… | MHT CET 2021 (21 Sep, Shift 2)

Q51MHT CET 2021 · 21 SEP · SHIFT 2Difficult

Excess Pressure: Drops & Bubbles

Under isothermal conditions, two soap bubbles of radii ' $r_1$ ' and ' $r_2$ ' combine to form a single soap bubble of radius ' $R$ '. The surface tension of soap is ( $P =$ outside pressure)

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Answer: (c)

Isothermal: $P_{in}V$ total is conserved, with $P_{in} = P + \frac{4T}{r}$ .
$\left(P + \frac{4T}{R}\right)R^3 = \left(P + \frac{4T}{r_1}\right)r_1^3 + \left(P + \frac{4T}{r_2}\right)r_2^3$
$P(R^3 - r_1^3 - r_2^3) = 4T(r_1^2 + r_2^2 - R^2)$
$T = \frac{P(R^3 - r_1^3 - r_2^3)}{4(r_1^2 + r_2^2 - R^2)}$
So the answer is (c).

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Excess Pressure: Drops & Bubbles question from MHT CET 2021 (21 Sep, Shift 2)

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