Question

If T is surface tension of soap solution , the amount of work done in blowing a soap bubble from a diameter D to a diameter 2D is

Answer 1

Answer:

In this case, work done = increase in surface energy, i.e.

$$W=T\Delta A\\ \Rightarrow W=T\times \left[ 2\left( 4\pi { D }^{ 2 } \right) -2\left( 4\pi { \left( \frac { D }{ 2 } \right) }^{ 2 } \right) \right] \\ \Rightarrow \boxed{ W=6\pi { D }^{ 2 }T}$$

Note: In calculation, area of sphere have been multiplied with 2, since there are two surfaces in soap bubble.

Answer 2

The amount of work done in blowing a soap bubble is $6\pi D^2 T$.

Explanation:

The  amount of work done in blowing a soap bubble is given by

$\Delta W=2T\Delta A$         (multiply by 2 because a bubble has two surfaces in contact with air)

Here, T is the surface tension and $\Delta A$ is the increase in area.

For blowing a soap bubble from a diameter D to a diameter 2D above equation can be written as,

$\Delta W=2T [4\pi(\frac{2D}{2})^2-4\pi(\frac{D}{2})^2]$

$\Delta W=2T[4 \pi(D^2-\frac{D^2}{4})]$

$\Delta W =6\pi D^2 T$

Thus, the amount of work done in blowing a soap bubble is $6\pi D^2 T$.

#Learn More: Work done in soap bubble.

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