Question

The radius of a soap bubble is $r$ and the surface tension of soap solution is $T$. Keeping the temperature constant, the extra energy needed to double the radius of the soap bubble by blowing, is

• A. $16\pi r^{2}T$
• B. $32\pi r^{2}T$
• C. $8\pi r^{2}T$
• D. $24\pi r^{2}T$

Answer 1

Answer: (D)

Given: Initial radius of soap bubble $=r$; Surface tension of soap solution $=T$ and final radius of soap bubble $=2r$.
We know that energy to blow the soap bubble of radius $r,\left(E_1\right)=2\times 4\pi r^2\times T=8\pi r^{2}T$ and energy to blow a soap bubble of radius $2r,\left(E_2\right)=$ $2\times 4\pi (2r{)}^{2}T=32\pi r^{2}T.$
Therefore extra energy needed $=E_2-E_1=32\pi r^{2}T-8\pi r^{2}T=24\pi r^{2}T$