Question

A soap bubble of diameter $a$ is produced using the soap solution of surface tension $T$. Find the energy required to double the radius of the bubble without change of temperature.

• A. $2\pi a^{2}T$
• B. $6\pi a^{2}T$
• C. $3\pi a^{2}T$
• D. $12\pi a^{2}T$

Answer 1

Answer: (B)

$6\pi a^{2}T$

Initial surface area of the bubble=$2\times 4\pi (\frac{a}{2}{)}^2=2\pi a^2$

(Factor $2$ multiplied to account for both inner and outer surface)

Thus initial total energy=$T\times 2\pi a^2$

Final surface area =$2\times 4\pi (2\times \frac{a}{2}{)}^2=8\pi a^2$

Thus final total energy=$T\times 8\pi a^2$

Hence, the energy required to increase the radius of bubble is = $6\pi a^{2}T$