Change of bubble size?

Question

A bubble rises from the bottom of a lake of depth 80 m, where the temperature is 2°C. The water temperature at the surface is 17°C. If the bubble's initial diameter is 1.00 mm, what is its diameter when it reaches the surface? (Ignore the surface tension of water. Assume the bubble warms as it rises to the same temperature as the water and retains a spherical shape. Assume Patm = 1.0 atm.)

Answer 1

The temperature is going to have a much smaller effect than the change in pressure - the change is from 275K to 290K while the change in pressure is from about 8 atm to 1 atm (8.7 in salt water) 10 m = 32.8 ft, 1 atm supports 33 ft water, 80m about 8 atm.
Since volume is proportional to pressure (and temperature) the volume 4/3 pi r^3
(4 / 3) * pi * (.5^3) = 0.523598776 mm^3
8 times that is 4.189 mm^3
r = cube root of (4.189 / (4/3 pi) )
(4.18900 / (4 / (3 * pi)))^.33333 = 2.14504884 mm
2.14 is approximate radius (temp would increase it slightly)