Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration I I as shown in the figure. One of the blocks has thermal conductivity K and the othe

Question

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

TestHub · Accepted Answer

In the first combination, the 2 blocks are having thermal conductivity $2 K$ and $2 K$ respectively are in series combination.

Therefore the Keq will be $\frac{1}{K} + \frac{1}{2 K}$

and the Keq in case of parallel combination is 3K

$Heat transferred = Rate \times time. $
$∴ {Rate}_{1} \times {time}_{1} = {Rate}_{2} \times {time}_{2} .$
$\frac{Δ T \times 9}{\frac{L}{KA} + \frac{L}{2 KA}} = \frac{Δ T \times t}{\frac{L}{3KA}}$
$\Rightarrow t = 2$

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