What is the bubble's diameter as it reaches the surface of the lake, where the water temp is 20.0°C?
A diver 52.0 m deep in 10.0°C fresh water exhales a 0.5950 cm bubble. Assuming the bubble is always in thermal equilibrium with the surrounding water.
I used ideal gas-law with initial and final. Found final volume made is equal to the volume of a sphere but somehow mastering physics says my answer is wrong. Please Help!
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Did you convert T to ºK?
(pV/T)a = (pV/T)b
pa = po + ρgh = 101325Pa + 1000kg/m³ * 9.8m/s² * 52m = 610925 Pa
pb = po = 101325 Pa
Va = 4π(0.00595m/2)³/3 = 1.1e-7 m³
Ta = 283ºK
Tb = 293ºK
610925 * 1.1e-7 / 283 = 101325 * V / 293
V = 6.9e-7 m³ = 4πr³/3 → r = 0.0055 m
so diameter d = 0.011 m = 1.1 cm
(almost double!)