An air bubble of radius R is formed at a depth h in a liquid of density and surface tension T . The absolute pressure inside this air bubble is found to be equal to the absolute pressure inside a soap bubble of radius 2R situated in the open atmosphere. If the atmospheric pressure is P₀ , what is the surface tension T' of the soap solution?

Step-by-step solution

The absolute pressure inside an air bubble of radius R at a depth h in a liquid is the sum of atmospheric pressure, hydrostatic pressure, and the excess pressure (which has only one free surface): P_ air bubble = P₀ + g h + 2T R The absolute pressure inside a soap bubble of radius 2R in the atmosphere (which has two free surfaces) is: P_ soap bubble = P₀ + 4T' (2R) = P₀ + 2T' R According to the problem, these two absolute pressures are equal: P₀ + g h + 2T R = P₀ + 2T' R Cancelling P₀ from both sides: g h + 2T R =