An air bubble is released from the bottom of a swimming pool and ascends to the surface.

(a) In a clear, coherent, paragraph-length response, describe any changes in the bubble size and describe the motion of the bubble as it ascends to the surface. Explain the factors that affect the size of the bubble and the bubble’s motion. Include a description of any forces acting on the bubble from the time it is at the bottom of the pool until it reaches the surface.

(b) Draw a diagram of all the forces acting on the bubble. Make sure the forces are in correct proportion.

(c) The bubble does not collapse under the pressure of the water. Explain how the behavior of the gas atoms keep the bubble from collapsing.

(d) The bubble has an initial volume of VD, begins at a depth of D below the surface of the water, and reaches the surface where the pressure is PS. The density of the water is r.

i. Derive an expression for the initial pressure (PD) in the bubble in terms of the given quantities and known constants.

ii. Assume the air temperature in the bubble remains the same as it rises. Derive an expression for the volume (VS) of the bubble when it reaches the surface.

(e) Now assume that the bubble rises quickly to the surface, and that there is negligible thermal energy transfer between the bubble and the swimming pool. Base your answers on this assumption.

i. Sketch the process on the PV diagram. Indicate on the axis the initial and final pressures and volumes.

ii. How does the value PSVS compare to the value PDVD? __Greater than PDVD __Equal to PDVD __Less than PDVD Justify your answer.

(f) The bubble passes through higher temperature water as it nears the sun-warmed surface of the pool. Unexpectedly, this allows a sizable amount of thermal energy to transfer from the water to the bubble as it rises. How does this affect the final volume of the bubble? Justify your answer.