Copper and iron rods of identical dimensions | vedclass

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(B) The rate of heat flow through a rod is given by $H = \frac{KA \Delta T}{l}$.For the wax to melt at the same rate,the heat flow $H$ must be the sam

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$\sqrt{10}:3$

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(B) The rate of heat flow through a rod is given by $H = \frac{KA \Delta T}{l}$.For the wax to melt at the same rate,the heat flow $H$ must be the same for both rods,and the temperature gradient must be maintained such that the time taken to reach a certain distance is proportional to the thermal diffusivity.However,for rods of identical cross-section where the wax melts along the length,the condition for equal melting rate is $K \propto l^2$.Thus,$\frac{l_1}{l_2} = \sqrt{\frac{K_1}{K_2}}$.Given $\frac{K_1}{K_2} = \frac{10}{9}$.Therefore,$\frac{l_1}{l_2} = \sqrt{\frac{10}{9}} = \frac{\sqrt{10}}{3}$.

Copper and iron rods of identical dimensions are coated with wax. The ratio of thermal conductivity of copper to iron is $10:9$. If one end of each rod is placed in hot water,the wax melts. Find the ratio of the lengths of the rods for which the wax melts at the same rate.

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