Question

If a number of little droplets of liquid of density $\rho$ surface tension $T$ and specific heat $C$, each of radius $r$ coalesce to form a single drop of radius $R$ then the rise in temperature will be:

• A. $\frac{3T}{\rho C}(\frac{1}{r}+\frac{1}{R})$
• B. $\frac{3T}{\rho C}(\frac{1}{r}-\frac{1}{R})$
• C. $\frac{3T}{2\rho C}(\frac{1}{r}+\frac{1}{R})$
• D. $\frac{3T}{2\rho C}(\frac{1}{r}-\frac{1}{R})$

Answer 1

The correct option is B $\frac{3T}{\rho C}(\frac{1}{r}-\frac{1}{R})$

Work done $W=4\pi T{R}^2(n^{1/3}-1)$

We know $n^{1/3}=\frac{R}{r}$ ,using $n{V}_2=V_1$

$W=4\pi T{R}^2(\frac{R}{r}-1)$

Now $mc\Delta T=W$

$\frac{4\pi R^3\rho c\Delta t}{3}=W=4\pi T{R}^2(\frac{R}{r}-1)$

$\Delta t=\frac{3T}{\rho C}(\frac{1}{r}-\frac{1}{R})$