A scuba diver 18 m below the surface of a lake breathes out, releasing bubbles i

Question

A scuba diver 18 m below the surface of a lake breathes out, releasing bubbles into the water. How much do the bubbles expand on their way up? Specifically, for a given bubble, what is the ratio of its volume as it reaches the surface to its volume down where it was created?

Explanation / Answer

Assume the bubble to contain an ideal gas PV = N*kB*T -> P = N*kB*T/V Where N is the no of molecules, kB is Boltzman's constant and P, V and T have the usual meanings. Use the information you were given concerning the bottom to work out the number of molecules present. Also, at the bottom of the lake, the bubble is subjected to pressure due to the water above it. P = ro*g*h, where ro is the water density. Putting it all together N*kB*Ts/Vs = N*kB*Tb/Vb + ro*g*h

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