Question

An air bubble has a volume of 1.0 cm³ when it is released by a submarine 140 m below the surface of a freshwater lake. What is the volume of the bubble when it reaches the surface? Assume that the temperature and the number of air molecules in the bubble remain constant during the ascent.

Answer 1

Given,

V1 = 1 cm^3 ; d = 140 m

We know that density of water = rho = 1000 kg/m^3

At the depth, 1 m^2 will occupy

V = 140 x 1 m^2 = = 140 m^3

m = V x rho = 140 x 1000 = 140,000 kg

W = mg = 140,000 x 9.8 = 1372000 N

Pressure per m^2 will be:

P = 1.372 x 10^6 Pa

P(atm) = 1.01 x 10^5 Pa

The pressure at the given depth will be:

P1 = 1.372 x 10^6/(1.01 x 10^5) + 1 = 14.58 atm

We know that

P1V1 = P2V2

V2 = (P1V1/P2) = V1 (P1/P2)

V2 = 1 cm^3 x 14.58 = 14.58 cm^3

Hence, V2 = 14.58 cm^3