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)

$24\, \pi r^{2} T$

Answer 2

Given: Initial radius of soap bubble $=r$; Surface tension of soap solution $=T$ and final radius of soap bubble $=2 r$. 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 $2 r,\left(E_{2}\right)=$ $2 \times 4 \pi(2 r)^{2} T=32 \pi r^{2} T .$ Therefore extra energy needed $=E_{2}-E_{1}=32 \pi r^{2} T-8 \pi r^{2} T=24 \pi r^{2} T$