A total of n identical soap bubbles, each of radius r, exist in vacuum. They are made from the same soap solution and combine isothermally without loss of gas into a single bubble. What is the final radius?
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Question

A total of n identical soap bubbles, each of radius r, exist in vacuum. They are made from the same soap solution and combine isothermally without loss of gas into a single bubble. What is the final radius?

Options

G1 Physics · Accepted Answer

For a soap bubble in vacuum, P = 4S/R. At constant temperature, amount of gas ∝ PV ∝ (1/R)R³ ∝ R². For n identical initial bubbles, R(final)² = n r². Therefore, R(final) = r√n. Correct option: C.