Question

A number of water droplets each of radius r coalesce together to form a bigger droplet of radius R. The rise in temperature dθ is

• A. (a) $rac{2T}{rJ}$
• A. (b) $\frac { 3 T } { J }$ $\left( \frac{1}{r} - \frac{1}{R} \right)$
• A. (c) −$rac{3T}{J}$
• A. (d) $\frac { 3 T } { J }$ $\left( \frac{1}{r} + \frac{1}{R} \right)$

Answer 1

(b)

Let n drops coalesce to form a big drop. Then

N $\frac{4}{3}\pi r^{3}$ = $\frac{4}{3}\pi r^{3}$⇒ n = $\frac{R^{3}}{r^{3}}$

Heat produced =$\frac{workdone}{J}$

= S.T $\frac{decreaseinarea}{J}$ = mcdθ

⇒ dθ = $\frac{3T}{J}\left( \frac{1}{r} - \frac{1}{R} \right)$