Question

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

• A. slightly less than \(4\) times
• B. exactly double
• C. slightly less than double
• D. slightly more than \(4\) times

Hint:

Work is 8 pi r^2 T. Heating reduces T.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The work done in blowing a bubble equals the increase in its surface energy. A soap bubble has two surfaces, so \(W=T\times2\times4\pi r^2=8\pi r^2T\).

Step 2: Compare the radii:
If \(T\) were the same, \(W\propto r^2\). The second bubble has radius \(2R\), so the work would be \(4\) times.

Step 3: Effect of heating:
Heating the solution lowers the surface tension \(T\). The second bubble is blown at a lower \(T\), so the work is slightly less than exactly 4 times.

Step 4: Choose:
Option (A). Option (D) would need \(T\) to increase, and (B) and (C) ignore the square of the radius.

Final Answer:
Radius doubles, so the work is about 4 times, slightly less due to lower T. \[ \boxed{\text{Slightly less than 4 times}} \]