A certain number of spherical drops of a liquid of radius r...

∆ U = \left(ST\right)\left(∆ A\right)$<br />$A\left(initial\right) = \left(4\pi{r}^{2}\right)n$<br />$A\left(final\right) = 4\pi{R}^{2}$<br />$∆ A = \left(4\pi{r}^{2}\right)n - 4\pi{R}^{2}$<br />\left(\dfrac{4}{3}\pi{r}^{3}\right)n = \dfrac{4}{3}\pi{R}^{3}$
$n = \dfrac{{R}^{3}}{{r}^{3}}$
$∆ A = 4\pi\left[\dfrac{{R}^{3}}{{r}^{3}} . {r}^{2} - {R}^{2}\right] = 4\pi\left[\dfrac{{R}^{3}}{r} - \dfrac{{R}^{3}}{R}\right] =$\left(\dfrac{4\pi{R}^{3}}{3}\right)3\left[\dfrac{1}{r} - \dfrac{1}{R}\right]$<br />$∆ A = 3V\left[\dfrac{1}{r} - \dfrac{1}{R}\right]$<br />$∆ U = 3VT\left[\dfrac{1}{r} - \dfrac{1}{R}\right]