Question

The radius of a soap bubble is r. The surface tension of soap solution is S. Keeping temperature constant, the radius of the soap bubble is doubled, the energy necessary for this will be :

• A. $24\pi r^{2}S$
• B. $8\pi r^{2}S$
• C. $12\pi r^{2}S$
• D. $16\pi r^{2}S$

Answer 1

The correct option is A $24\pi r^{2}S$

The energy required to change increase the size of the bubble,

E = $Fdr$

E = $PAdr$

E = $\frac{4T}{r}\times 4\pi (4r^2-r^2)\times dr$

E = $48\times T\pi rdr$

E = $24T\pi r^2$