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, $\frac{dQ}{dt}=L\left(\frac{dm}{dt}\right)$
$\frac{Temperature \, difference}{Thermal \, resistance}= \, L\left(\frac{dm}{dt}\right)$
$\left(\frac{dm}{dt}\right) \propto \, \frac{1}{Thermal \, resistance} \, $
$q \propto \frac{1}{R}$
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 $ $\frac{q_{1}}{q_{2}}= \, \frac{2 R}{R / 2}= \, \frac{4}{1}$