Question

A number of droplets, each of radius $r$, combine to form a drop of radius $R$. If $T$ is the surface tension, the rise in temperature will be

• A. $\frac{2T}{r}$
• B. $\frac{3T}{R}$
• C. $2T[\frac{1}{r}-\frac{1}{R}]$
• D. $3T[\frac{1}{r}-\frac{1}{R}]$

Answer 1

The correct option is D $3T[\frac{1}{r}-\frac{1}{R}]$

$\frac{4}{3}\pi R^3=n\times \frac{4}{3}\pi r^3$ or $R^3=n{r}^3$
Energy evolved $=(n\times 4\pi r^2-4\pi r^2)T$
Now, $\theta =\frac{Q}{V\rho S}=\frac{Q}{V}=$ (In C.G.S. system, $\rho =1$ and $S=1$)
$\therefore \theta =\frac{[n\times 4\pi r^2-4\pi R^2]T}{\frac{4}{3}\pi R^3}$
$=\frac{3T[n{r}^2-R^2]}{R^3}$
$=3T[\frac{n{r}^2}{n{r}^3}-\frac{R^2}{R^3}]=3T[\frac{1}{r}-\frac{1}{R}]$.