Two soap bubbles of radii R₁ and R₂ kept in atmosphere are combined isothermally to form a big bubble of radius R. The expression for surface tension will be

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$\frac{P_{0} (R^{3} + R_{1}^{3} + R_{2}^{3})}{4 (R^{2} + R_{1}^{2} + R_{2}^{2})}$

$\frac{P_{0} (R_{1}^{3} + R_{2}^{3} - R^{3})}{4 (R^{2} - R_{1}^{2} - R_{2}^{2})}$

$P_{0} (R_{1}^{3} + R_{2}^{3} - R^{3})$

$4 P_{0} (R_{1}^{3} + R_{2}^{3} - R^{3})$

answer is B.

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Detailed Solution

According to isothermal process, $PV = P_{1} V_{1} + P_{2} V_{2}$
$\begin{array}{l} (P_{O} + \frac{4 T}{R}) \frac{4}{3} {πR}^{3} = (P_{o} + \frac{4 T}{R_{1}}) \frac{4}{3} {πR}_{1}^{3} + (P_{O} + \frac{4 T}{R_{2}}) \frac{4}{3} {πR}_{2}^{3} \\ P_{0} (R^{3} - R_{1}^{3} - R_{2}^{3}) = 4 T (R_{1}^{2} + R_{2}^{2} - R^{2}) \end{array}$