Question

Three rods made of same material and having the same cross-section have been joined as shown in figure. Each rod is of the same length. The ends are kept at $0^{\circ }C$, ${90}^{\circ }C$ and ${60}^{\circ }C$. The temperature of the junction of the rods will be

• A. ${45}^{\circ }C$
• B. ${50}^{\circ }C$
• C. ${55}^{\circ }C$
• D. ${60}^{\circ }C$

Answer 1

The correct option is B ${50}^{\circ }C$


Let
$H_1$ be the heat flowing from $C$ to $B$
$H_2$ be the heat flowing from $D$ to $B$
$H$ be the heat flowing from $B$ to $A$

As there is no heat loss

$H_1+H_2=H$

From thermal analogus of ohms law($R$ be thermal resistance of each rod)
$H_1=\frac{{90}^{\circ }-T}{R}$
$H_2=\frac{{60}^{\circ }-T}{R}$
$H=\frac{T-0^{\circ }}{R}$

$\frac{{90}^{\circ }-T}{R}+\frac{60-T}{R}=\frac{T-0^{\circ }}{R}$
$T=\frac{150}{3}={50}^{\circ }C$