Question

Three rods made of the same material and having same cross-section area but different length 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction is

• A. 900/11 °C
• B. 100 °C
• C. 0 °C
• D. 50 °C

Answer 1

Answer: (A)

900/11 °C

Answer 2

Assuming the rods of lengths 10 cm and 20 cm are at 100°C at their free ends, and the rod of length 30 cm is at 0°C at its free end, the heat flow rate into the junction from the first two rods must equal the heat flow rate out of the junction to the third rod. Let $T_J$ be the junction temperature. The heat flow rate is proportional to $\frac{kA \Delta T}{L}$. Since $k$ and $A$ are constant, we consider $\frac{\Delta T}{L}$. $\frac{100 - T_J}{10} + \frac{100 - T_J}{20} = \frac{T_J - 0}{30}$ Multiplying by 60: $6(100 - T_J) + 3(100 - T_J) = 2T_J$ $600 - 6T_J + 300 - 3T_J = 2T_J$ $900 = 11T_J$ $T_J = \frac{900}{11} ^\circ \text{C}$