Question

Two rods of same dimension, but made of different materials are joined end to end with their free ends being maintained at ${100}^{o}C$ and $0^{o}C$ respectively. The temperature of the junction is ${70}^{o}C$. Then the temperature of the junction if the rods are interchanged will be equal to $T{}^{o}C$ Find $T:$

Answer 1

${\theta }_1={\theta }_2$

$\frac{k_1.A\left(100-70\right)}{l}=\frac{k_2.A\left(70-0\right)}{l}$

$k_1\times 30=k_2\times 70$ $k_1=\frac{7}{2}{k}_2$

$\frac{k_2.A\left(100-T‘\right)}{l}=\frac{k_1.A\left(T-0\right)}{l}$

$k_2\left(100-T\right)=\frac{7}{3}{k}_2\left(T\right)$

$3\left(100-T\right)=7T$

$300-3T=7T$

$10T=300$

Hence, $T={30}^0$