First slide

Conduction

Question

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be

Moderate

A

45°C
B

60°C
C

30°C
D

20°C

Solution

$\begin{array}{l} \frac{Q_{1}}{t} + \frac{Q_{2}}{t} = \frac{Q}{t} \\ \frac{kA (90 - θ)}{L} + \frac{kA (90 - θ)}{L} \\ = \frac{kA (θ - 0)}{L} \\ = 180 - 2 θ = θ \\ \Rightarrow θ = 60^{\circ} \end{array}$

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