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: Formula:
$W=8\pi r^2T$.

Step 2: Ratio:
$\dfrac{W_2}{W_1}=\dfrac{(2R)^2T_2}{R^2T_1}=4\dfrac{T_2}{T_1}$.

Step 3: Temperature effect:
$T$ decreases with temperature, so $T_2<T_1$. The ratio is slightly below 4. Option (A).

Final Answer:
The ratio is 4 times T2/T1, and T2 is less than T1. \[ \boxed{A} \]