Which of the following circular rods, (given radius r and length l) each made of the same material and whose ends are maintained at the same temperature will conduct most heat?
a) r = 2r₀; l = 2l₀
b) r = 2r₀; l = l₀
c) r = r₀; l = 2l₀
d) r = r₀; l = l₀

Explanation:

Heat flow in a circular rod is given by

where Q= heat flow

k=thermal conductivity

A=area of cross-section

dT=Change in temperature

dx=change in length

Also A can be written as

thus Q is Proportional to

For option (a)

(b)

(c)

(d)

So Rod b will conduct the most Heat

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