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  4. Four rods, of different radii r and length l , are used to connect two reservoirs of heat at different temperatures. The rod that will conduct the heat fastest will be

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Q. Four rods, of different radii $r$ and length $l$ , are used to connect two reservoirs of heat at different temperatures. The rod that will conduct the heat fastest will be

NTA AbhyasNTA Abhyas 2020Thermal Properties of Matter

Solution:

$\frac{\Delta T}{\Delta t}=KA\left(\frac{\Delta T}{\Delta x}\right)= \, K\left(\pi r^{2}\right)\frac{\Delta T}{\left(l\right)}$
$\therefore \, \left(\frac{\Delta Q}{\Delta t}\right) \, \propto \frac{r^{2}}{l} \, $ , which is maximum in this case.