Question

An air bubble at the bottom of a lake 35.0 m deep has a volume of 1.88 cm^3. If the temperature at the bottom is 5.4 C and at the top 19.5 C, what is the volume of the bubble just before it reaches the surface?

Answer 1

You have a temp change, and a pressure change. Figure the pressure at surface as one atm(10.3m water), and the pressure at 35 m is then 45.3m water total.

P1Vi/T1=P2V2/T2

V2=P1V2T2/T1P2 where condition 1 is at the depth, and condition 2 is at the surface. Be certain to change temps to Kelvins

Answer 2

PV/T = constant (remember T in Kelvin)
pressure = 1 atmosphere at surface, about 10^5 pascals
add to that rho g h for pressure at the bottom where rho is density of water (10^3 kg/m^3) and g is 9.8 m/s^2 and h is 35 m