The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperature $100^{o} C$ and $0^{o} C$ . The temperature of the junction is $700^{o} C$ . Find the temperature of the junction if the rods are interchanged.

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Solution

Now Q/t remains same in both cases
in case I : $\frac{K_{A} \times A (100 - 70)}{l} = \frac{K_{b} \times A \times (70 - 0)}{l}$
$⟹ 30 K_{A} = 70 k a$
In case II : $\frac{K_{B} \times A \times (100 - θ)}{l} = \frac{K_{A} \times A \times (θ - 0)}{l}$
$⟹ 100 K_{b} - K_{B} θ = K_{A} θ$
$⟹ 100 K_{B} - K_{B} θ = \frac{70}{30} K_{B} θ$
$⟹ 100 = \frac{7}{3} θ + θ$
$⟹= \frac{300}{10} = 30^{0} C$

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