The excess pressure within a soap bubble is twice the excess pressure within a second soap bubble. If the volume of the first bubble is n times the volume of the second bubble, the value of n is

Step-by-step solution

The excess pressure inside a soap bubble of radius R and surface tension T is given by P = 4T R . Given that P₁ = 2P₂ , we can write: 4T R₁ = 2 ( 4T R₂ ) R₂ = 2R₁ R₁ R₂ = 1 2 The volume of a soap bubble is V = 4 3 R^3 . Given that V₁ = nV₂ , we have: n = V₁ V₂ = ( R₁ R₂ )^3 Substituting the ratio of radii: n = ( 1 2 )^3 = 1 8 = 0.125