First slide

Conduction

Question

Two rods 1 and 2 have cross sectional areas A and 2A. Ratio of their length is 1 : 2, ratio of their coefficient of thermal conductivities is 4 : x. When the ends of the rods are maintained at temperatures ${θ_{1}}^{o} C$ and ${θ_{2}}^{o} C (θ_{1} > θ_{2})$ , they conduct heat at the same rate. Then the value of x is

Moderate

A

8
B

4
C

2
D

1

Solution

In steady state $\frac{K_{1} A (θ_{1} - θ_{2})}{l_{1}} = \frac{K_{2} 2 A (θ_{1} - θ_{2})}{l_{2}}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{l_{1}}{l_{2}} .2 \Rightarrow \frac{4}{x} = \frac{1}{2} .2 \Rightarrow x = 4$

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