JEE Advanced 2013 · Paper 1 · Physics Q5

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PhysicsSingle correct+2Question 5 of 60

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 $\kappa$ and the other $2\kappa$ . 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 the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

Configuration I: the two blocks (κ and 2κ) placed end to end along the x-axis, so heat flows through them in series. Configuration II: the 2κ block stacked on top of the κ block, so heat flows along x through both side by side (in parallel).

2.0 s

3.0 s

4.5 s

6.0 s

Answer and worked solution

Official answer: A

Thermal resistances (each block has length $L$ and area $A$ ):

I (series): $\dfrac L{\kappa A}+\dfrac L{2\kappa A}=\dfrac{3L}{2\kappa A}$ .
II (parallel): $\dfrac1R=\dfrac{\kappa A}L+\dfrac{2\kappa A}L$ , so $R=\dfrac L{3\kappa A}$ .

Time ∝ resistance: $t_{II}=9\times\dfrac{1/3}{3/2}=2$ s.

(A)

Topics:Conduction

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JEE Advanced 2013 · Paper 1, Physics question 5