Question 3: Properties of Matter

Question

In an isothermal process 2 water drops of radius $$1 \mathrm{~mm}$$ are combined to form a bigger drop. Find the energy change in this process if $$T=0.1 \mathrm{~N} / \mathrm{m}$$.

Accepted Answer

Given, surface tension of water, $$T=0.1 \mathrm{~N} / \mathrm{m}$$
Radius of small drops, $$r=1 \mathrm{~mm}=10^{-3} \mathrm{~m}$$
If $$R$$ be the radius of bigger drops, then volume remains conserved.
$$\begin{aligned}
	ext{i.e.,} \quad V_1 & =V_2 \
\frac{4}{3} \pi R^3 & =2 	imes \frac{4}{3} \pi r^3 \
R^3 & =2 r^3=2 \cdot\left(10^{-3}ight)^3 \
	herefore \quad R & =2^{1 / 3} 	imes 10^{-3} \mathrm{~m}
\end{aligned}$$
$$	herefore$$ Change in energy during isothermal combination,
$$\begin{aligned}
\Delta E & =T \cdot \Delta A \
& =T\left[A_2-A_1ight] \
& =0.1\left[2 	imes 4 \pi r^2-4 \pi R^2ight] \
& \begin{aligned}
& =0.1 	imes 4 \pi\left[2 r^2-R^2ight] \
& =0.4 \pi\left[2 	imes 10^{-6}-2^{2 / 3} 	imes 10^{-6}ight] \
& =0.4 \pi 	imes 10^{-6} 	imes 0.41 \
& =0.52 	imes 10^{-6} \mathrm{~J}=0.52 \mu \mathrm{J} \simeq 0.5 \mu \mathrm{J}
\end{aligned}
\end{aligned}$$

Answer

$$1 \mu \mathrm{J}$$

Answer

$$0.5 \mu \mathrm{J}$$

Answer

$$0.25 \mu \mathrm{J}$$

Answer

$$0.75 \mu \mathrm{J}$$

Properties of Matter

In an isothermal process 2 water drops of radius $1 \mathrm{~mm} are combined to form a bigger drop. Find the energy change in this process if T=0.1 \mathrm{~N} / \mathrm{m}$.

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