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 condition)

• 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 $50{}^{\circ }C$


At junction, incoming heat will be same as outgoing heat.
Let, $T$ be the temperature at junction and R be the thermal resistance.
So,
$H=H_1+H_2+H_3$
$\frac{100-T}{R}=\frac{50-0}{R}+\frac{T-50}{R}+\frac{T-50}{R}$
$\Rightarrow 100-T=2T-50$
$\Rightarrow 3T=150\therefore T=50{}^{\circ }C$