Givem: Tworods $A$ and $B$ of different matarials but Same Cross 8ectiom are joimed as in figure. The free end of $A$ is maintained at $100^{\circ} C$ and the end of $B$ is maintaimed at $0^{\circ} C$

To Find: If $l_2=2 l_1, k_1=2 k_2$ and rods are Thermally imsulated from side to prevent heat Cosses them the temperatwre $\theta$ of the jumction of dwo rods is

Solution: we knowe that, Heaf current(H) $H=\frac{K \times A}{l}(\Delta T)$ and $H=\frac{V}{R}=\frac{\Delta T}{R}$

$R=U / K A$

Heat current is some so $i=\frac{V}{R}$

$R_{\text {eqa. }}=R_1+R_2 \Rightarrow \frac{l_1}{K_1 A}+\frac{l_1}{K_2 A} \times 2=\frac{S l_1}{K_1 A}$

$R^{\prime}=l_1 / K_1 A$

$i_1=\frac{v}{R^{\prime}}=\frac{100-0}{S^{\prime} R^{\prime}}=\frac{20}{R^{\prime}}$

$i_{\Delta}=i_1=\frac{100-\theta}{R^{\prime}} \Rightarrow \frac{100-\theta}{R^{\prime}}=\frac{20}{R^{\prime}}$

$\Rightarrow \theta=100-20=80^{\circ}$