Q43 / 60 · JEE Advanced 2013 (Paper 1) · Physics

Two rectangular blocks, having identical dimensions, can be arranged either in configuration  I or in configuration II 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
Figure

  • Correct answer
    A
    2.0 s
  • B
    3.0 s
  • C
    4.5 s
  • D
    6.0 s

Solution

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

Therefore the Keq will be 1K  +12K

and the Keq in case of parallel combination is 3K

Heat transferred = Rate × time. ​
∴    Rate 1 × time 1 = Rate 2 × time 2 .
Δ T × 9 L KA + L 2 KA = Δ T × t L 3KA
⇒   t = 2

Hence, the correct answer is option: 'A'.

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