Two spherical soap bubbles of radii R₁ and R₂ exist in vacuum. They contain the same gas at the same temperature and are made from the same soap solution of surface tension S. They combine isothermally without loss of gas to form one spherical soap bubble of radius R. Which relation is correct?
Options

Question

Two spherical soap bubbles of radii R₁ and R₂ exist in vacuum. They contain the same gas at the same temperature and are made from the same soap solution of surface tension S. They combine isothermally without loss of gas to form one spherical soap bubble of radius R. Which relation is correct?

Options

G1 Physics · Accepted Answer

For a soap bubble in vacuum, the outside pressure is zero. Therefore the gas pressure inside a bubble of radius R is P = 4S/R. For an ideal gas at fixed temperature, amount of gas ∝ PV. The bubble volume is V = 4πR³/3. Hence, PV ∝ (1/R)R³ ∝ R². Therefore the amount of gas in each bubble is proportional to the square of its radius. When two bubbles combine without loss of gas, R² = R₁²+R₂². Thus, R = √(R₁²+R₂²). Correct option: B.