Several soap bubbles made from the same soap solution combine to form one bubble. Which assumptions are used in obtaining the relation R(final)² = R₁² + R₂² + ... for the final radius?
Select all that apply

Question

Several soap bubbles made from the same soap solution combine to form one bubble. Which assumptions are used in obtaining the relation R(final)² = R₁² + R₂² + ... for the final radius?

G1 Physics · Accepted Answer

For each soap bubble in vacuum, P = 4S/R. For an ideal gas, nRT = PV. If temperature T and surface tension S are common to all bubbles, n ∝ PV ∝ (1/R)R³ ∝ R². Conservation of total gas amount then gives R(final)² = R₁²+R₂²+.... Thus the derivation uses vacuum, common temperature, no gas loss and common surface tension. Therefore all four statements are correct.