Question

Two identical conducting rods are first connected independently but simultaneously between two vessels, one containing water at $100{}^{\circ }C$ and the other containing ice at $0{}^{\circ }C$ . In the second case, the rods are connected in series and then the combination is connected between the same vessels. Let $q_1$ and $q_2$ be the rate of melting of ice (in $g{s}^{-1}$ ) in the two cases respectively. The ratio $\frac{q_1}{q_2}$ is

• A. $\frac{1}{2}$
• B. $\frac{2}{1}$
• C. $\frac{4}{1}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

Heat current, $\frac{dQ}{dt}=L\left(\frac{dm}{dt}\right)$
$\frac{Temperaturedifference}{Thermalresistance}=L\left(\frac{dm}{dt}\right)$
$\left(\frac{dm}{dt}\right)\propto \frac{1}{Thermalresistance}$
$q\propto \frac{1}{R}$
In the first case rods are in parallel and thermal resistance is $\frac{R}{2}$ while in second case rods are in series and thermal resistance is $2R$ .
$\therefore$ $\frac{q_1}{q_2}=\frac{2R}{R/2}=\frac{4}{1}$