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Two identical conducting rods are first, connected independently to two vessels, one containing water at 100^oC and the other containing ice at 0^oC. In the second case, rods are joined end to end and are connected to the same vessels. If $q_{1} and q_{2}$ (in g/s) are the rates of melting of ice in two cases, then the ratio of $q_{1} / q_{2}$ is ______.

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answer is 4.

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Detailed Solution

$\begin{array}{l} \frac{Temperature difference}{Thermal resistance} = L (\frac{dm}{dt}) \\ \frac{dm}{dt} \propto \frac{1}{Thermal resistance} \\ q \propto \frac{1}{R} \end{array}$

The rods are in parallel in the first case and they are in series in the second case.

$\frac{q_{1}}{q_{2}} = \frac{2 R}{(R / 2)} = 4$

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