If an air bubble of radius $5.00 ext{ mm}$ is formed at a depth of $40.0 ext{ cm}$ inside a contai

Question

If an air bubble of radius $5.00	ext{ mm}$ is formed at a depth of $40.0	ext{ cm}$ inside a container containing soap solution (relative density $1.20$, $S = 2.50 	imes 10^{-2}	ext{ N/m}$), what is the total pressure inside the bubble? ($P_{atm} = 1.01 	imes 10^5	ext{ Pa}$)

Professor PC Thomas Classes · Answer

An air bubble inside a liquid has ONE interface, so $\Delta P = \frac{2S}{r} = \frac{2 	imes 0.025}{0.005} = 10	ext{ Pa}$. Hydrostatic pressure $P_h = ho gh = 1200 	imes 9.8 	imes 0.40 = 4704	ext{ Pa}$. Total pressure $P = P_{atm} + P_h + \Delta P = 101000 + 4704 + 10 = 105714	ext{ Pa} \approx 1.06 	imes 10^5	ext{ Pa}$.