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If T is the surface tension, the amount of work done in blowing a soap bubble from a diameter D to 2D . Ans is 6piD square T?
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If T is the surface tension, the amount of work done in blowing a soap...
Calculation of Work Done in Blowing a Soap Bubble


The work done in blowing a soap bubble depends on the surface tension of the soap solution, the diameter of the bubble, and the change in diameter of the bubble. To calculate the work done in blowing a soap bubble from a diameter D to 2D, we can use the following steps:


Step 1: Calculate the Surface Area of the Bubble


The surface area of a sphere is given by the formula:


S = 4πr2


Since the diameter of the bubble changes from D to 2D, the radius of the bubble changes from D/2 to D. Therefore, the surface area of the bubble changes from:


S1 = 4π(D/2)2 = πD2


to


S2 = 4πD2


Step 2: Calculate the Change in Surface Area


The change in surface area of the bubble is given by the difference between S2 and S1:


ΔS = S2 - S1 = 4πD2 - πD2 = 3πD2


Step 3: Calculate the Work Done


The work done in blowing the bubble is equal to the change in surface area multiplied by the surface tension of the soap solution:


W = ΔS × T = 3πD2 × T


Therefore, the amount of work done in blowing a soap bubble from a diameter D to 2D is:


W = 3πD2 × T = 3π(D/2)2 × 4T = 6πD2 T
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