Question 270: Properties of Matter

Question

The surface tension of soap solution is $$3.5 	imes 10^{-2} \mathrm{~Nm}^{-1}$$. The amount of work done required to increase the radius of soap bubble from $$10 \mathrm{~cm}$$ to $$20 \mathrm{~cm}$$ is _________ $$	imes ~10^{-4} \mathrm{~J}$$.
$$(\operatorname{take} \pi=22 / 7)$$

Accepted Answer

To calculate the work done to increase the radius of a soap bubble, we can use the formula:
$$
W = T \Delta A
$$
where W is the work done, T is the surface tension, and ÃÂA is the change in surface area.
For a soap bubble, we need to consider both the inner and outer surfaces, so the surface area is doubled. The surface area of a sphere is:
$$
A = 4\pi r^2
$$
The initial surface area of the soap bubble is:
$$
A_1 = 2 \cdot 4\pi (0.1\,\mathrm{m})^2 = 8\pi (0.1\,\mathrm{m})^2
$$
The final surface area of the soap bubble is:
$$
A_2 = 2 \cdot 4\pi (0.2\,\mathrm{m})^2 = 8\pi (0.2\,\mathrm{m})^2
$$
The change in surface area is:
$$
\Delta A = A_2 - A_1 = 8\pi(0.2\,\mathrm{m})^2 - 8\pi(0.1\,\mathrm{m})^2
$$
Now, we can calculate the work done:
$$
W = T \Delta A = (3.5 	imes 10^{-2}\,\mathrm{Nm}^{-1})[8\pi(0.2\,\mathrm{m})^2 - 8\pi(0.1\,\mathrm{m})^2]
$$
Using the given value of ÃÂ:
$$
W = (3.5 	imes 10^{-2}\,\mathrm{Nm}^{-1})[8(22/7)(0.2\,\mathrm{m})^2 - 8(22/7)(0.1\,\mathrm{m})^2]
$$
$$
W = (3.5 	imes 10^{-2}\,\mathrm{Nm}^{-1})[8(22/7)(0.04\,\mathrm{m^2}) - 8(22/7)(0.01\,\mathrm{m^2})]
$$
$$
W = (3.5 	imes 10^{-2}\,\mathrm{Nm}^{-1})[8(22/7)(0.03\,\mathrm{m^2})]
$$
$$
\begin{aligned}
& W=2 	imes 1.32 	imes 10^{-2} \\
&W =2 	imes 132 	imes 10^{-4} \mathrm{~J} \\
& W=264 	imes 10^{-4} \mathrm{~J}
\end{aligned}
$$
The work done to increase the radius of the soap bubble is 264 ÃÂ 10Ã¢ÂÂ»Ã¢ÂÂ´ J.

Properties of Matter

The surface tension of soap solution is $3.5 \times 10^{-2} \mathrm{~Nm}^{-1}. The amount of work done required to increase the radius of soap bubble from 10 \mathrm{~cm} to 20 \mathrm{~cm} is _________ \times ~10^{-4} \mathrm{~J}. (\operatorname{take} \pi=22 / 7)

Integer / Numeric Answer Type