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(B) The rate of heat conduction $H$ through a cylindrical rod is given by the formula $H = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivit

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Length $1 \ m$,radius $2 \ cm$

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(B) The rate of heat conduction $H$ through a cylindrical rod is given by the formula $H = \frac{KA \Delta T}{L}$,where $K$ is the thermal conductivity,$A$ is the cross-sectional area,$\Delta T$ is the temperature difference,and $L$ is the length of the rod.Since $A = \pi r^2$,the rate of heat conduction is proportional to $\frac{r^2}{L}$.For option $(a)$: $\frac{r^2}{L} = \frac{1^2}{1} = 1$.For option $(b)$: $\frac{r^2}{L} = \frac{2^2}{1} = 4$.For option $(c)$: $\frac{r^2}{L} = \frac{1^2}{2} = 0.5$.For option $(d)$: $\frac{r^2}{L} = \frac{2^2}{2} = 2$.Comparing these values,the ratio $\frac{r^2}{L}$ is maximum for option $(b)$,therefore it will conduct the most heat.

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperatures?

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