Two rods having thermal conductivity in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is 100 o C and free end of the second rod is 20 o C. Then temperature of the junction is
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Temperature of interface $\theta = \frac{K_1 \theta_1 + K_2 \theta_2}{K_1 + K_2}$ It is given that $\frac{K_1}{K_2} = \frac{5}{3} \Rightarrow K_1 = 5K \text{ and } K_2 = 3K$ $\theta = \frac{5K \times 100 + 3K \times 20}{5K + 3K} = \frac{560K}{8K} = 70^\circ C$
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