A soap bubble of radius R is blown. After heating the solution, a second bubble of radius 2R is blown. The work required to blow the second bubble in comparison to that required for the first bubble is

Step-by-step solution

The work done in blowing a soap bubble of radius R is given by W = 2 4 R^2 T = 8 R^2 T , where T is the surface tension of the soap solution. For the first bubble of radius R , the work done is W₁ = 8 R^2 T₁ . For the second bubble of radius 2R , the work done is W₂ = 8 (2R)^2 T₂ = 32 R^2 T₂ . The ratio of the work done is W₂ W₁ = 32 R^2 T₂ 8 R^2 T₁ = 4 T₂ T₁ . When the solution is heated, its temperature increases. The surface tension of a liquid decreases with an increase in temperature, so T₂ Therefore, W₂ W₁ An