Question

Work $W$ is required to form a bubble ofvolume $V$ from a given solution. What amountof work is required to be done to form a bubbleof volume 2$V$ ?

• A. $W$
• B. 2$W$
• C. $2^{1/3}W$
• D. $4^{1/3}W$

Answer 1

The correct option is D $4^{1/3}W$

$\begin{array}{c}Weknow,\\ W=T\times A\\ W=T\times 4\pi r^2\\ W\propto r^2\propto V^{\frac{2}{3}}\\ vol,V=\frac{4}{3}\pi r^3\\ \therefore r=V^{\frac{1}{3}}\end{array}$

hence, Option $D$ is correct.