Question

A submarine deep underwater releases a bubble of air. The total pressure at this depth is P. The bubble has diameter, D, and absolute temperature, T. As the bubble rises, it expands. When it reaches a certain smaller depth, where the total pressure is 0.22P, it has absolute temperature 1.17. In terms of D, what is the diameter of the bubble at this depth? You may assume that no air leaves the bubble, and that the air behaves as an ideal gas.

Answer 1

Answer:

P V = n R T      ideal gas equation

P2 V2 / P1 V1 = T2 / T1    

V2 / V1 = T2 / T1 * P1 / P2 = T2 P1 / (T1 P2)

V2 / V1 = (1.17 T1) / T1 * (P1 / .22 P1)      assuming absolute temp as 1.17 P1

V2 / V1 = 1.17 / .22 = 5.32

V = 4/3 pi R^3 = 4/3 pi (D/2)^3 = 4/3 pi D^3 / 8 = pi D^3 / 6

V2 / V1 = D2^3 / D1^3

D2 = (V2 / V1 * D1^3)^1/3

D2 = 5.32^1/3 * D = 1.75 D      (D1 = D)