What is the ratio of the volume of the bubble as it reaches the surface (Vs) to its volume at the bottom (Vb)?

Question

A diver named Jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is 4.0 degrees celcius, and the temperature at the surface is 23.0 degrees celcius .

Answer 1

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

Answer 2

3.74