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Two rectangular blocks, having identical dimensions, can be arranged either in configuration-I or in configuration-II as shown in Fig. One of the blocks has thermal conductivity K and the other has 2K. The temperature difference between the ends along x-axis is the same in both the configurations.
It takes 9s to transport a certain amount of heat from the hot end to the cold end in the configuration-I. The time to transport the same amount of heat in the configuration-II is ____sec.

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answer is 2.

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Detailed Solution

$R_{1} = \frac{L}{K A} + \frac{L}{2 K A} = \frac{3 L}{2 K A}$

$\frac{1}{R_{2}} = \frac{1}{(\frac{L}{K A})} + \frac{1}{(\frac{L}{2 K A})} \Rightarrow R_{2} = \frac{L}{3 K A}$

$Δ Q_{1} = Δ Q_{2}$

$\frac{Δ T}{R_{1}} t_{1} = \frac{Δ T}{R_{2}} t_{2} \Rightarrow t_{2} = \frac{R_{2}}{R_{1}} t_{1}$

$\Rightarrow t_{2} = (\frac{\frac{L}{3 K A}}{\frac{3 L}{2 K A}}) \times 9 \Rightarrow t_{2} = 2 \sec$

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