Heat transfer

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Question

Two different rods A and B are kept as shown in figure.
The variation of temperature of different cross sections is plotted in a graph shown in figure.
The ratio of thermal conductivities of B to A is __________.

Moderate

Solution

$\begin{array}{l} ∵ {(\frac{ΔQ}{Δt})}_{A} = {(\frac{ΔQ}{Δt})}_{B} ∴ \frac{K_{A} A (100 - 70)}{30} = \frac{K_{B} A (70 - 35)}{70} \\ \Rightarrow K_{A} = \frac{K_{B}}{2} \Rightarrow \frac{K_{B}}{K_{A}} = 2 \end{array}$

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