Question

Two similar rods are joined as shown in figure. Then temperature of junction is (assume no heat loss through lateral surface of rod and temperatures at the ends are shown in steady state)

• A. ${50}^{\circ }C$
• B. ${75}^{\circ }C$
• C. ${66.6}^{\circ }C$
• D. ${33.3}^{\circ }C$

Answer 1

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

Let $\theta$ be the temperature of junction.

$H_1,H_2,H_{3}and{H}_4$ be the heat currents. Then
$H_1=H_2+H_3+H_4$
or $\frac{100-\theta }{R}=\frac{\theta -50}{R}+\frac{\theta -50}{R}+\frac{\theta -0}{R}$
(R = Thermal resistance of each part of two rods)
Solving these two equations, we get $\theta ={50}^{\circ }C$