First slide

Conduction

Question

The ends of two rods of different materials having thermal conductivities, radii of cross-section and Iengths in the ratio 1 : 2, arc maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 cal/s, then in shorter rod in cal/s will be

Moderate

A

1
B

2
C

8
D

16

Solution

We know that
$(ΔQ / Δt) = KA (ΔT / d) = {Kπr}^{2} (ΔT / d)$
$\begin{matrix} ∴ \frac{(ΔQ / Δt)_{1}}{(ΔQ / Δt)_{2}} = (\frac{K_{1} r_{1}^{2}}{d_{1}}) \times (\frac{d_{2}}{K_{2} r_{2}^{2}}) \\ = \frac{1}{2} \times \frac{2}{1} \times {(\frac{1}{2})}^{2} = \frac{1}{4} or (ΔQ / Δt)_{1} / 4 = 1 / 4 or (ΔQ / Δt)_{1} = 1 \end{matrix}$

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