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(B) The rate of heat flow $(Q)$ through a rod is given by the formula: $Q = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivity,$A$ is the cr

Vedclass · Accepted Answer

$L = 100 \, cm; r = 2 \, cm$

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(B) The rate of heat flow $(Q)$ through a rod is given by the formula: $Q = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivity,$A$ is the cross-sectional area,$\Delta T$ is the temperature difference,and $L$ is the length.Since $K$ and $\Delta T$ are constant for all rods,$Q \propto \frac{A}{L}$.Given $A = \pi r^2$,we have $Q \propto \frac{r^2}{L}$.We calculate the ratio $\frac{r^2}{L}$ for each option:$A: \frac{1^2}{50} = \frac{1}{50} = 0.02$$B: \frac{2^2}{100} = \frac{4}{100} = 0.04$$C: \frac{0.5^2}{25} = \frac{0.25}{25} = 0.01$$D: \frac{1.5^2}{75} = \frac{2.25}{75} = 0.03$Comparing these values,the ratio is maximum for option $B$ $(0.04)$. Therefore,the rod in option $B$ conducts the most heat.

Two ends of rods of length $L$ and radius $r$ of the same material are kept at the same temperature difference. Which of the following rods conducts the most heat?

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