Question

Four rods of same material and having the same cross-section and length have been joined as shown. The temperature of the junction of four rods will be

• A. 20°C
• B. 30°C
• C. 45°C
• D. 60°C

Answer 1

Answer: (C)

45°C

Answer 2

In steady state, the net heat flow into the junction of four rods of equal thermal resistance is zero. If the temperatures at the free ends of the rods are $T_1, T_2, T_3, T_4$ and the junction temperature is $T$, then the net heat flow is $\frac{T_1-T}{R} + \frac{T_2-T}{R} + \frac{T_3-T}{R} + \frac{T_4-T}{R} = 0$. This simplifies to $T = \frac{T_1+T_2+T_3+T_4}{4}$. Substituting the given temperatures $0^\circ$C, $30^\circ$C, $60^\circ$C, and $90^\circ$C, we get $T = \frac{0+30+60+90}{4} = \frac{180}{4} = 45^\circ$C.