Question

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio between the volume of the first and the second bubble?

Answer 1

Answer:

Explanation:

Let the excess pressure inside the soap bubble = P

Excess pressure inside the first soap bubble = 3P

Let the radius of first bubble = x

Let the radius of second bubble = R

Thus, excess pressure in first bubble = 3P = 4S/x

excess pressure in second bubble = P = 4S/r (1)

Thus,

3(4S/r) = 4S/x

= x = R/3

Volume of first soap bubble (V1) = 4/3πx³

Volume of first soap bubble (V2)= 4/3πR³

Ratio of volumes

V1/ V2 = 4/3πx³/4/3πR³

= x³ = nR³

= (R/3)³ = nR³

n = 1/27 = 0.037

Thus, the volume of the first bubble is n times the volume of the second where n is 0.037