How do i solve this??

Question

A spherical air bubble originating for a suba diver at a depth of 18.0 m has a diameter of 1.0 cm. what will the bubble's diameter be when it reaches the surface? (assume constant temperature.)

Answer 1.4 cm

Answer 1

yeah

Answer 2

You use Boyle's Law, which states that pressure and volume have a constant product for isothermal (constant temperature) processes. At the surface of the water, the pressure is standard atmospheric pressure of 101325 Pa. 18 m below the surface, you need to add the fluid pressure of rho*g*h, where rho is the density of water, 1000 kg/m^3, g is gravitational acceleration, 9.8 m/s^2, and h is the depth underwater, 18 m. So the underwater pressure is P1 and the surface pressure is P2.

Now, the bubble has an initial underwater diameter, D1, of 1 cm = 0.01 m. The volume of a sphere is (4/3)pi*r^3, and r^3 = (1/8)d^3, but we can ignore all of the constants because they will factor out. So to find our unknown diameter of the bubble at the surface, D2, we can just say that P1*V1 = P2*V2 ==> P1*D1^3 = P2*D2^3 ==> D2^3 = (P1/P2)*D1^3 ==> D2 = [(P1/P2)*D1^3]^(1/3), where you calculated P1 and P2 previously, and D1 was given.