Under isothermal conditions, a soap bubble of radius 3 cm merges with a soap bubble of radius 4 cm. Both bubbles are in vacuum. Find the radius (in cm) of the single bubble that results.

Correct answer: 5

Solution

For soap bubbles in vacuum the relevant conserved quantity leads to R² = R1² + R2². (In vacuum the pressure inside each bubble is 4T/R and applying isothermal P*V conservation with no external pressure yields the squares adding.) Thus R = sqrt(3² + 4²) = sqrt(9 + 16) = sqrt(25) = 5 cm.

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