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Conduction

Two identical...

Question

Two identical rods are connected between two containers one of them is at $100^{0} C$ and another is at $0^{0} C$ . If rods are connected in parallel then the rate of melting of ice $q_{1} g m / s e c$ . If they are connected in series then rate is $q_{2}$ . Then the ratio $q_{2} / q_{1}$ is

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Solution

The correct option is D $1 / 4$
Let the length of the rods be $l$ , and cross sectional area of each rod be $A$ .
The rate of heat transferred across a rod $\propto \frac{A}{l}$
When connected in parallel, the net cross sectional area becomes $2 A$ and length remains $l$ .
Thus $q_{1} \propto \frac{2 A}{l}$
When connected in series, the net length of the rods becomes $2 l$ , and cross sectional area remains $A$
Hence, $q_{2} \propto \frac{A}{2 l}$
Thus, $\frac{q_{2}}{q_{1}} = \frac{1}{4}$

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